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| author | FOSSEE Git User | 2017-07-13 19:33:27 +0530 |
|---|---|---|
| committer | FOSSEE Git User | 2017-07-13 19:33:27 +0530 |
| commit | 16d89ed8065e3385dfda78f9516fa8934431fdd6 (patch) | |
| tree | 0f57da126a244c6daabbbdaf93f43ac6a7d8f2be /Engineering_Mechanics | |
| parent | 957caeb5d812f7005222e7cd1de66abfcc0ccc63 (diff) | |
| parent | 920fbc095386afd4dfcd95d85ef7ef9072b3d5d7 (diff) | |
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Merge branch 'master' of https://github.com/FOSSEE/Python-Textbook-Companions
Diffstat (limited to 'Engineering_Mechanics')
| -rw-r--r-- | Engineering_Mechanics/chapter_1.ipynb | 866 | ||||
| -rw-r--r-- | Engineering_Mechanics/chapter_11.ipynb | 1353 | ||||
| -rw-r--r-- | Engineering_Mechanics/chapter_12.ipynb | 1392 | ||||
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| -rw-r--r-- | Engineering_Mechanics/chapter_14.ipynb | 1114 | ||||
| -rw-r--r-- | Engineering_Mechanics/chapter_15.ipynb | 2687 | ||||
| -rw-r--r-- | Engineering_Mechanics/chapter_16.ipynb | 1312 | ||||
| -rw-r--r-- | Engineering_Mechanics/chapter_17.ipynb | 879 | ||||
| -rw-r--r-- | Engineering_Mechanics/chapter_18.ipynb | 1586 | ||||
| -rw-r--r-- | Engineering_Mechanics/chapter_2.ipynb | 648 | ||||
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| -rw-r--r-- | Engineering_Mechanics/chapter_8.ipynb | 1699 | ||||
| -rw-r--r-- | Engineering_Mechanics/chapter_9.ipynb | 1623 |
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diff --git a/Engineering_Mechanics/chapter_1.ipynb b/Engineering_Mechanics/chapter_1.ipynb new file mode 100644 index 00000000..ea9d90ce --- /dev/null +++ b/Engineering_Mechanics/chapter_1.ipynb @@ -0,0 +1,866 @@ +{
+ "metadata": {
+ "name": "chapter_1.ipynb"
+ },
+ "nbformat": 3,
+ "nbformat_minor": 0,
+ "worksheets": [
+ {
+ "cells": [
+ {
+ "cell_type": "heading",
+ "level": 1,
+ "metadata": {},
+ "source": [
+ "Chapter 1:Fundamental Of Engineering Mechanics"
+ ]
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 1.1,Page No.8"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "from math import sin, cos, tan, radians, pi\n",
+ "\n",
+ "#Declaration of Variables\n",
+ "\n",
+ "P=10 #N #Force1\n",
+ "Q=8 #N #Force2\n",
+ "alpha=60 #Degrees #Angle Between Two Forces\n",
+ "\n",
+ "#Calculations\n",
+ "\n",
+ "#Magnitude of Resultant Force \n",
+ "R=(P**2+Q**2+2*P*Q*cos(alpha*pi*180**-1))**0.5 #N\n",
+ " \n",
+ "#Result\n",
+ "print\"Magnitude of Resultant Force\",round(R,2),\"N\""
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "Magnitude of Resultant Force 15.62 N\n"
+ ]
+ }
+ ],
+ "prompt_number": 2
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 1.2,Page No.8"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "\n",
+ "#Declaration of Variables\n",
+ "\n",
+ "alpha=60 #Degrees #Angle between Forces\n",
+ "R=20*(3)**0.5\n",
+ "\n",
+ "#Let P & Q be the Two forces\n",
+ "#As Two Forces are equal i.e P=Q\n",
+ "\n",
+ "#Magnitude of Resultant Force \n",
+ "#R=(P**2+Q**2+2*P*Q*cos(alpha*pi*180**-1))**0.5 #N\n",
+ "#After Sub values and Furhter simplifying above equations we get\n",
+ "#R=2*P*cos(alpha*2**-1*pi*180**-1)\n",
+ "\n",
+ "#Further on Simplifying we get\n",
+ "P=R*((3)**0.5)**-1 #N\n",
+ "\n",
+ "#Result\n",
+ "print\"Magnitude of Force is\",round(P,2),\"N\""
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "Magnitude of Force is 20.0 N\n"
+ ]
+ }
+ ],
+ "prompt_number": 3
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 1.3,Page No.9"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "import numpy as np\n",
+ "\n",
+ "#Declaration of Variables\n",
+ "\n",
+ "#Case-1\n",
+ "R1=14 #N #Resultant1\n",
+ "alpha1=60 #Degrees #Angle between two forces\n",
+ "\n",
+ "#Case-2\n",
+ "R2=(136)**0.5\n",
+ "alpha2=90 #Degrees #Angle between two Forces\n",
+ "\n",
+ "#Let P And Q be the two forces\n",
+ "#R=(P**2+Q**2+2*P*Q**cos(alpha))\n",
+ "\n",
+ "#Now For case-1,we get Resultant as\n",
+ "#P**2+Q**2+P*Q=196 ............................(1)\n",
+ "\n",
+ "#For case-2,we get Resultant as\n",
+ "#P**2+Q**2=136 ...................................(2)\n",
+ "\n",
+ "#Subtracting Equation 2 from equation 1 we get\n",
+ "#P*Q=60 .........................................(3)\n",
+ "\n",
+ "#Multiplying abovw equation by 2 we get\n",
+ "#2*P*Q=120 .......................................(4)\n",
+ "\n",
+ "#Adding equation 4 to equation 2 we get\n",
+ "#P**2+Q**2+2*P*Q=256\n",
+ "#After Further simplifying we get\n",
+ "#P=16-Q ..........................(5)\n",
+ "\n",
+ "#Sub value of P in equation 3 we get\n",
+ "#Q**2-16*Q+60=0\n",
+ "a=1\n",
+ "b=-16\n",
+ "c=60\n",
+ "\n",
+ "X=b**2-4*a*c\n",
+ "\n",
+ "Q1=(-b+X**0.5)*(2*a)**-1\n",
+ "Q2=(-b-X**0.5)*(2*a)**-1\n",
+ "\n",
+ "#Now sub value of Q in equation 5 we get\n",
+ "P1=16-Q1\n",
+ "P2=16-Q2\n",
+ "\n",
+ "\n",
+ "#Result\n",
+ "print\"Magnitude of two Forces is:P2\",round(P2,2),\"N\"\n",
+ "print\" :Q1\",round(Q2,2),\"N\""
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "Magnitude of two Forces is:P2 10.0 N\n",
+ " :Q1 6.0 N\n"
+ ]
+ }
+ ],
+ "prompt_number": 4
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 1.4,Page No.10 "
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "from math import sin, cos, tan, radians, pi\n",
+ "import numpy as np\n",
+ "\n",
+ "P=50 #N #Force acting at pt O\n",
+ "Q=100 #N #force acting at pt O\n",
+ "alpha=30 #DEgree #Angle Between Two Forces\n",
+ "\n",
+ "#Calculations\n",
+ "\n",
+ "#MAgnitude of Resultant\n",
+ "R=(P**2+Q**2+2*P*Q*cos(alpha*pi*180**-1))**0.5 #N\n",
+ "\n",
+ "#Angle Made by resultant with the direction of P\n",
+ "X=(Q*sin(alpha*180**-1*pi)*(P+(Q*cos(alpha*pi*180**-1)))**-1)\n",
+ "theta=np.arctan(X)*(180*pi**-1) #Degrees\n",
+ "\n",
+ "#Angle made by resultant with x-axis is\n",
+ "Y=theta+alpha*2**-1 #Degrees\n",
+ "\n",
+ "#Result\n",
+ "print\"Resultant in the Magnitude is\",round(R,2),\"N\"\n",
+ "print\"Resultant in the Direction is\",round(Y,2),\"Degrees\""
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "Resultant in the Magnitude is 145.47 N\n",
+ "Resultant in the Direction is 35.1 Degrees\n"
+ ]
+ }
+ ],
+ "prompt_number": 2
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 1.5,Page No.10 "
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "\n",
+ "#Declaration of Variables\n",
+ "\n",
+ "R=1500 #N #REsultant of two Forces\n",
+ "alpha=90 #Degrees #Angle between two Forces\n",
+ "theta=36 #Degrees #Angle Made by Resultant with one Force\n",
+ "\n",
+ "#Calculations\n",
+ "\n",
+ "#Now From Equation of Direction of Resultant,we get\n",
+ "#tan(theta)=(Q*sin(alpha))*(P+Q*sin(alpha))**-1\n",
+ "#After Further sub values and simplifying we get\n",
+ "#Q=0.726*P .......................................(1)\n",
+ "\n",
+ "#Now From Equation of Resultant\n",
+ "#R=(P**2+Q**2+2*P*Q*cos(alpha))\n",
+ "#After sub values and further simplifying we get\n",
+ "#R=1.527*P**2 \n",
+ "#Therefore,we get value of P After simplifying above equation\n",
+ "P=(R**2*(1.527)**-1)**0.5\n",
+ "\n",
+ "#Sub value of P in equation 1 we get\n",
+ "Q=0.726*P \n",
+ "\n",
+ "#Result\n",
+ "print\"Magnitude Of Forces:P\",round(P,2),\"N\"\n",
+ "print\" :Q\",round(Q,2),\"N\""
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "Magnitude Of Forces:P 1213.87 N\n",
+ " :Q 881.27 N\n"
+ ]
+ }
+ ],
+ "prompt_number": 6
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 1.6,Page No.11"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "from math import sin, cos, tan, radians, pi\n",
+ "import numpy as np\n",
+ "\n",
+ "#Declaration of Variables\n",
+ "#P+Q=120\n",
+ "R=180 #N #Resultant of two Forces\n",
+ "theta=90 #Degrees #Angle between force and Resultant\n",
+ "\n",
+ "#Calculations\n",
+ "\n",
+ "#Now From Equation of Direction of Resultant,we get\n",
+ "#Tan(theta)=Q*sin(alpha)*(P+Q*sin(alpha))**-1\n",
+ "#After Further ssub values a in above equation and further simplifying we get\n",
+ "#P=-Q*cos(alpha) ..........(1)\n",
+ "\n",
+ "#Now From equation of Resultant we get\n",
+ "#R=(P**2++Q**2+2*P*Q*cos(alpha))**0.5\n",
+ "#After sub values and further simplifying\n",
+ "#Q-P=120 ......................................(1)\n",
+ "#P+Q=270 ......................................(2)\n",
+ "\n",
+ "#After Adding above equations i.e equations 1 and 2 we get\n",
+ "Q=390*2**-1 #N\n",
+ "\n",
+ "P=270-Q #N\n",
+ "\n",
+ "#Value of angle alpha\n",
+ "alpha=np.arccos(-P*Q**-1)*(180*pi**-1) #Degrees\n",
+ "\n",
+ "#Result\n",
+ "print\"Magnitude of Each Force:P\",round(P,2),\"N\"\n",
+ "print\" :Q\",round(Q,2),\"N\"\n",
+ "print\"Angle between Two Forces\",round(alpha,2),\"Degrees\""
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "Magnitude of Each Force:P 75.0 N\n",
+ " :Q 195.0 N\n",
+ "Angle between Two Forces 112.62 Degrees\n"
+ ]
+ }
+ ],
+ "prompt_number": 7
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 1.7,Page No.13"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "from math import sin, cos, tan, radians, pi\n",
+ "\n",
+ "#Declaration of Variables\n",
+ "\n",
+ "W=1000 #N #Weight\n",
+ "#Angles\n",
+ "CAB=30 #Degrees\n",
+ "CBA=CBD=60 #Degrees\n",
+ "ACB=90 #Degrees\n",
+ "\n",
+ "#Calculations\n",
+ "#Angle\n",
+ "CAD=30 #Degrees\n",
+ "\n",
+ "#In Right-Angle Triangle,Angle ADC\n",
+ "ACD=90-CAD #Degrees\n",
+ "\n",
+ "#In Right-Angle Triangle,Angle BDC\n",
+ "#Angle\n",
+ "BCD=90-CBD #Degrees\n",
+ "ACE=180-ACB-90-60 #DEgrees\n",
+ "BCE=180-ACE-ACB #DEGrees\n",
+ "\n",
+ "#Applying LAmi's Theorem at Point C\n",
+ "#T1*(sin150)**-1=T2*(sin(120)**-1=1000*sin(90)**-1\n",
+ "\n",
+ "#After Further simp;ifying we get\n",
+ "T1=W*sin(150*pi*180**-1) #N\n",
+ "T2=W*sin(120*pi*180**-1) #N\n",
+ "\n",
+ "#Result\n",
+ "print\"Tension in Chain is:T1\",round(T1,2),\"N\"\n",
+ "print\" :T2\",round(T2,2),\"N\""
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "Tension in Chain is:T1 500.0 N\n",
+ " :T2 866.03 N\n"
+ ]
+ }
+ ],
+ "prompt_number": 8
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 1.8,Page No.18"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "from math import sin, cos, tan, radians, pi\n",
+ "import numpy as np\n",
+ "\n",
+ "#Declaration of Variables\n",
+ "W=900 #N #Weight at C\n",
+ "#Length\n",
+ "AC=4 #m \n",
+ "BC=3 #m\n",
+ "AB=5 #m\n",
+ "\n",
+ "\n",
+ "#Calculations\n",
+ "\n",
+ "#In Triangle ABC\n",
+ "X=AC**2+BC**2 \n",
+ "Y=AB**2 \n",
+ "\n",
+ "#Therefore,\n",
+ "#X=Y\n",
+ "\n",
+ "#Therefore,\n",
+ "#Triangle ABC is Right Angle Triangle,In Which Angle ACB=90 Degrees\n",
+ "alpha=np.arcsin(BC*AB**-1)*(180*pi**-1)\n",
+ "Beta=90-alpha\n",
+ "\n",
+ "#In Right Angle Triangle ADC,\n",
+ "theta1=90-alpha\n",
+ "\n",
+ "#In Right Angle Triangle BDC,\n",
+ "theta2=90-Beta\n",
+ "\n",
+ "#Now,Angles\n",
+ "ACE=180-theta1\n",
+ "BCE=180-theta2\n",
+ "\n",
+ "#Now applying ami's Theorem\n",
+ "#T1*(sin(BCE))**-1=T2*(sin(ACE))**-1=W*(sin(90))**-1\n",
+ "\n",
+ "#Tensions in chains \n",
+ "T1=W*sin(BCE*180**-1*pi) #N\n",
+ "T2=W*sin(ACE*180**-1*pi) #N\n",
+ "\n",
+ "#Result\n",
+ "print\"Tension in Chains are:T1\",round(T1,2),\"N\"\n",
+ "print\" :T2\",round(T2,2),\"N\"\n",
+ "\n",
+ "#Answer in hte book For T2 is incorrect"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "Tension in Chains are:T1 540.0 N\n",
+ " :T2 720.0 N\n"
+ ]
+ }
+ ],
+ "prompt_number": 9
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 1.9,Page No.18"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "from math import sin, cos, tan, radians, pi\n",
+ "\n",
+ "#Declaration of Variables\n",
+ "\n",
+ "W=15 #N #Weight at Pt C\n",
+ "OAC=FAC=60 #Degrees\n",
+ "CBD=BCF=45 #Degrees\n",
+ "FCA=90-FAC #Degrees\n",
+ "\n",
+ "#Calculations\n",
+ "\n",
+ "#Using Lami's theorem,\n",
+ "#W*(sin(BCA))**-1=T1*(sin(ACE))**-1=T2*(sin(ACE))**-1\n",
+ "\n",
+ "#Angles\n",
+ "BCA=BCF+FCA #Degrees\n",
+ "ACE=180-FCA #Degrees\n",
+ "BCE=180-BCF #Degrees\n",
+ "\n",
+ "#Force's in the string AC\n",
+ "T1=W*sin(ACE*180**-1*pi)*(sin(BCA*180**-1*pi))**-1 #N\n",
+ "T2=W*sin(BCE*180**-1*pi)*(sin(BCA*180**-1*pi))**-1 #N\n",
+ "\n",
+ "#Result\n",
+ "print\"Force's in the string:T1\",round(T1,2),\"N\"\n",
+ "print\" :T2\",round(T2,2),\"N\""
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "Force's in the string:T1 7.76 N\n",
+ " :T2 10.98 N\n"
+ ]
+ }
+ ],
+ "prompt_number": 10
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 1.10,Page No.16"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "from math import sin, cos, tan, radians, pi\n",
+ "import numpy as np\n",
+ "\n",
+ "#Declaration of Variables\n",
+ "\n",
+ "#Forces\n",
+ "P=50 #N\n",
+ "Q=100 #N\n",
+ "alpha=30 #Angle Between Two Forces\n",
+ "theta=15 #Degrees #Angle Made By Force P with x-axis\n",
+ "theta2=alpha+theta #Degrees\n",
+ "\n",
+ "#Calculations\n",
+ "\n",
+ "#Sum Of COmponents of forces along X-Axis is\n",
+ "H=P*cos(theta*pi*180**-1)+Q*cos(theta2*pi*180**-1) #N\n",
+ "\n",
+ "#Sum Of COmponents of forces along Y-Axis is\n",
+ "V=P*sin(theta*pi*180**-1)+Q*sin(theta2*pi*180**-1) #N\n",
+ "\n",
+ "#MAgnitude Of Resultant Force is\n",
+ "R=(H**2+V**2)**0.5 #N\n",
+ "\n",
+ "#Let Direction Of Resultant Force be beta\n",
+ "#Direction Of Resultant Force is\n",
+ "beta=np.arctan(V*H**-1)*(180*pi**-1) #Degrees\n",
+ "\n",
+ "#Result\n",
+ "print\"Magnitude of Resultant Force is\",round(R,2),\"N\"\n",
+ "print\"Direction of Resultant Force is\",round(beta,2),\"Degrees\""
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "Magnitude of Resultant Force is 145.47 N\n",
+ "Direction of Resultant Force is 35.1 Degrees\n"
+ ]
+ }
+ ],
+ "prompt_number": 11
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 1.11,Page No.17"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "from math import sin, cos, tan, radians, pi\n",
+ "import numpy as np\n",
+ "\n",
+ "#Declaration of Variables\n",
+ "\n",
+ "#Let 3Forces Be\n",
+ "R1=40 #KN\n",
+ "R2=15 #KN\n",
+ "R3=20 #KN\n",
+ "\n",
+ "#Angles Made by respective forces with X-Axis\n",
+ "theta1=60 #Degrees\n",
+ "theta2=120 #Degrees\n",
+ "theta3=240 #Degrees\n",
+ "\n",
+ "#Calculations\n",
+ "\n",
+ "#Now sum of components of all forces along X-Axis\n",
+ "H=R1*cos(theta1*pi*180**-1)+R2*cos(theta2*pi*180**-1)+R3*cos(theta3*pi*180**-1)\n",
+ "\n",
+ "#Now sum of components of all forces along Y-Axis\n",
+ "V=R1*sin(theta1*pi*180**-1)+R2*sin(theta2*pi*180**-1)+R3*sin(theta3*pi*180**-1)\n",
+ "\n",
+ "#MAgnitude of Resultant Force is\n",
+ "R=(H**2+V**2)**0.5 #N\n",
+ "\n",
+ "#Direction of Resultant Force is\n",
+ "theta=np.arctan(V*H**-1)*(pi**-1*180)\n",
+ "\n",
+ "#Result\n",
+ "print\"Magnitude of Resultant Force is\",round(R,2),\"KN\"\n",
+ "print\"Direction of Resultant Force is\",round(theta,2),\"Degrees\"\n",
+ "\n",
+ "#Declaration of Variables\n",
+ "\n",
+ "#Let 3Forces Be\n",
+ "R1=40 #KN\n",
+ "R2=15 #KN\n",
+ "R3=20 #KN\n",
+ "\n",
+ "#Angles Made by respective forces with X-Axis\n",
+ "theta1=60 #Degrees\n",
+ "theta2=120 #Degrees\n",
+ "theta3=240 #Degrees\n",
+ "\n",
+ "#Calculations\n",
+ "\n",
+ "#Now sum of components of all forces along X-Axis\n",
+ "H=R1*cos(theta1*pi*180**-1)+R2*cos(theta2*pi*180**-1)+R3*cos(theta3*pi*180**-1)\n",
+ "\n",
+ "#Now sum of components of all forces along Y-Axis\n",
+ "V=R1*sin(theta1*pi*180**-1)+R2*sin(theta2*pi*180**-1)+R3*sin(theta3*pi*180**-1)\n",
+ "\n",
+ "#MAgnitude of Resultant Force is\n",
+ "R=(H**2+V**2)**0.5 #N\n",
+ "\n",
+ "#Direction of Resultant Force is\n",
+ "theta=np.arctan(V*H**-1)*(pi**-1*180)\n",
+ "\n",
+ "#Result\n",
+ "print\"Magnitude of Resultant Force is\",round(R,2),\"KN\"\n",
+ "print\"Direction of Resultant Force is\",round(theta,2),\"Degrees\""
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "Magnitude of Resultant Force is 30.41 KN\n",
+ "Direction of Resultant Force is 85.28 Degrees\n",
+ "Magnitude of Resultant Force is 30.41 KN\n",
+ "Direction of Resultant Force is 85.28 Degrees\n"
+ ]
+ }
+ ],
+ "prompt_number": 3
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 1.12,Page No.18"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "from math import sin, cos, tan, radians, pi\n",
+ "import numpy as np\n",
+ "\n",
+ "#Declaration of Variables\n",
+ "\n",
+ "#Let 4 Forces Be\n",
+ "R1=10 #KN\n",
+ "R2=15 #KN\n",
+ "R3=20 #KN\n",
+ "R4=40 #KN\n",
+ "\n",
+ "#Angles Made by respective forces with X-Axis\n",
+ "theta1=30 #Degrees\n",
+ "theta2=60 #Degrees\n",
+ "theta3=90 #Degree\n",
+ "theta4=120 #Degrees\n",
+ "\n",
+ "#Calculations\n",
+ "\n",
+ "#Now sum of components of all forces along X-Axis\n",
+ "H=R1*cos(theta1*pi*180**-1)+R2*cos(theta2*pi*180**-1)+R3*cos(theta3*pi*180**-1)+R4*cos(theta4*pi*180**-1)\n",
+ "\n",
+ "#Now sum of components of all forces along Y-Axis\n",
+ "V=R1*sin(theta1*pi*180**-1)+R2*sin(theta2*pi*180**-1)+R3*sin(theta3*pi*180**-1)+R4*sin(theta4*pi*180**-1)\n",
+ "\n",
+ "#MAgnitude of Resultant Force is\n",
+ "R=(H**2+V**2)**0.5 #N\n",
+ "\n",
+ "#Direction of Resultant Force is\n",
+ "theta4=np.arctan(V*H**-1)*(pi**-1*180)\n",
+ "theta=180+theta4 #Degrees\n",
+ "\n",
+ "#Result\n",
+ "print\"Magnitude of Resultant Force is\",round(R,2),\"KN\"\n",
+ "print\"Direction of Resultant Force is\",round(theta,2),\"Degrees\""
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "Magnitude of Resultant Force is 72.73 KN\n",
+ "Direction of Resultant Force is 93.03 Degrees\n"
+ ]
+ }
+ ],
+ "prompt_number": 13
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 1.13,Page No.19"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "\n",
+ "#Declaration of Variables\n",
+ "\n",
+ "L=10 #m #Length of beam\n",
+ "W=200 #N #Pt Load\n",
+ "\n",
+ "#Distances\n",
+ "L_AC=4 #m\n",
+ "L_CB=6 #m\n",
+ "\n",
+ "#Calculations\n",
+ "\n",
+ "#Let R_A & R_B be the forces acting at A & B\n",
+ "#Taking Moment at A\n",
+ "R_B=(W*L_CB)*L**-1 #N\n",
+ "R_A=W-R_B #N\n",
+ "\n",
+ "#Result\n",
+ "print\"Beam Reactions are:R_A\",round(R_A,2),\"N\"\n",
+ "print\" :R_B\",round(R_B,2),\"N\""
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "Beam Reactions are:R_A 80.0 N\n",
+ " :R_B 120.0 N\n"
+ ]
+ }
+ ],
+ "prompt_number": 14
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 1.14,Page No.20"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "from math import sin, cos, tan, radians, pi\n",
+ "import numpy as np\n",
+ "\n",
+ "#Declaration of Variables\n",
+ "\n",
+ "#Let 4 Forces be\n",
+ "F1=10 #N\n",
+ "F2=20 #N\n",
+ "F3=30 #N\n",
+ "F4=40 #N\n",
+ "\n",
+ "#Calculations\n",
+ "\n",
+ "#Net Forces in Horizontal direction is\n",
+ "H=F1-F3 #N\n",
+ "\n",
+ "#Net Forces in Vertical direction is\n",
+ "V=F2-F4 #N\n",
+ "\n",
+ "#Resultant Force is given by\n",
+ "R=(H**2+V**2)**0.5 #N\n",
+ "\n",
+ "#Direction of resultant Forces\n",
+ "theta=np.arctan(V*H**-1)*(pi**-1*180) #Degrees\n",
+ "\n",
+ "#Since H & V are negative theta lies between 180 & 270\n",
+ "theta2=180+theta #Degrees\n",
+ "\n",
+ "#Result\n",
+ "print\"Magnitude of Force is\",round(R,2),\"N\"\n",
+ "print\"Direction of Force is\",round(theta2,2),\"Degrees\""
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "Magnitude of Force is 28.28 N\n",
+ "Direction of Force is 225.0 Degrees\n"
+ ]
+ }
+ ],
+ "prompt_number": 15
+ }
+ ],
+ "metadata": {}
+ }
+ ]
+}
\ No newline at end of file diff --git a/Engineering_Mechanics/chapter_11.ipynb b/Engineering_Mechanics/chapter_11.ipynb new file mode 100644 index 00000000..47d411ff --- /dev/null +++ b/Engineering_Mechanics/chapter_11.ipynb @@ -0,0 +1,1353 @@ +{
+ "metadata": {
+ "name": "chapter_11.ipynb"
+ },
+ "nbformat": 3,
+ "nbformat_minor": 0,
+ "worksheets": [
+ {
+ "cells": [
+ {
+ "cell_type": "heading",
+ "level": 1,
+ "metadata": {},
+ "source": [
+ "Chapter 11:Belts,Ropes And Chain Drives"
+ ]
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 11.1,Page No.386"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "\n",
+ "#Initilization of Variables\n",
+ "\n",
+ "N1=200 #r.p.m\n",
+ "d1=51 #cm #Dia. of engine\n",
+ "d2=30 #cm #Dia. of driven shaft\n",
+ "\n",
+ "#Calculations\n",
+ "\n",
+ "#Speed of driven shaft\n",
+ "N2=d1*d2**-1*N1 #r.p.m\n",
+ "\n",
+ "#Result\n",
+ "print\"Speed of driven shaft is\",round(N2,2),\"r.p.m\""
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "Speed of driven shaft is 340.0 r.p.m\n"
+ ]
+ }
+ ],
+ "prompt_number": 1
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 11.2,Page No.386"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "\n",
+ "#Initilization of Variables\n",
+ "\n",
+ "t=1 #cm #thickness\n",
+ "N1=200 #r.p.m\n",
+ "d1=51 #cm\n",
+ "d2=30 #cm\n",
+ "\n",
+ "#Calculations\n",
+ "\n",
+ "#Speed of shaft\n",
+ "N2=(d1+t)*(d2+t)**-1*N1 #r.p.m\n",
+ "\n",
+ "#Result\n",
+ "print\"speed of shaft is\",round(N2,2),\"r.p.m\""
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "speed of shaft is 335.48 r.p.m\n"
+ ]
+ }
+ ],
+ "prompt_number": 2
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 11.3,Page No.388"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "\n",
+ "#Initilization of Variables\n",
+ "\n",
+ "N1=200 #r.p.m\n",
+ "N2=300\n",
+ "d1=60 #cm\n",
+ "t=0.5 #cm\n",
+ "s=4 #%\n",
+ "\n",
+ "#Calculations\n",
+ "\n",
+ "#Diameter of pulley\n",
+ "d2=N1*N2**-1*d1 #cm\n",
+ "\n",
+ "#Taking belt thickness\n",
+ "d2_2=(d1+t)*N1*N2**-1-t\n",
+ "\n",
+ "#Also considering slip\n",
+ "d2_3=(d1+t)*N1*N2**-1*(1-s*100**-1)-t #cm\n",
+ "\n",
+ "#Result\n",
+ "print\"Diameter of belt is:Neglecting belt thickness\",round(d2,2),\"cm\"\n",
+ "print\" :Belt thickness only\",round(d2_2,2),\"cm\"\n",
+ "print\" :Considering belt thickness and slip\",round(d2_3,2),\"cm\""
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "Diameter of belt is:Neglecting belt thickness 40.0 cm\n",
+ " :Belt thickness only 39.83 cm\n",
+ " :Considering belt thickness and slip 38.22 cm\n"
+ ]
+ }
+ ],
+ "prompt_number": 3
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 11.4,Page No.389"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "\n",
+ "#Initilization of Variables\n",
+ "\n",
+ "d1=1 #m #dia. of driver pulley\n",
+ "N1=200 #r.p.m #Speed of driver pulley\n",
+ "d2=2.5 #m #Dia. of driven pulley\n",
+ "f1=1.44 #N/mm**2 #strress\n",
+ "f2=0.49 #N/mm**2 \n",
+ "E=100 #N/mm**2 #Young's Modulus\n",
+ "\n",
+ "#Calculations\n",
+ "\n",
+ "#Speed of driven pulley\n",
+ "N2=d1*d2**-1*(E+round((f2)**0.5,2))*(E+round((f1)**0.5,2))**-1*N1\n",
+ "\n",
+ "#Speed if creep is neglected\n",
+ "N2_2=d1*d2**-1*N1 #r.p.m\n",
+ "\n",
+ "#Speed lost by driven pulley due to creep\n",
+ "N=N2_2-N2\n",
+ "\n",
+ "#Result\n",
+ "print\"speed Lost by driven pulley due to creep is\",round(N,3),\"r.p.m\""
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "speed Lost by driven pulley due to creep is 0.395 r.p.m\n"
+ ]
+ }
+ ],
+ "prompt_number": 4
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 11.5,Page No.390"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "\n",
+ "#Initilization of Variables\n",
+ "\n",
+ "d1=1 #m #Diameter\n",
+ "N1=200 #r.p.m\n",
+ "d2=2.5 #m\n",
+ "b=500 #mm #width\n",
+ "t=10 #mm #thickness\n",
+ "E=100 #N/mm**2\n",
+ "\n",
+ "#Calculations\n",
+ "\n",
+ "#Area\n",
+ "A=b*t #mm**2\n",
+ "\n",
+ "#Tension on tight side\n",
+ "T1=10*b\n",
+ "\n",
+ "#Tension on slack side\n",
+ "T2=4*b #N\n",
+ "\n",
+ "#Stress on tight side\n",
+ "f1=T1*A**-1 #N/mm**2\n",
+ "\n",
+ "#Stress on slack side\n",
+ "f2=T2*A**-1 #N/mm**2\n",
+ "\n",
+ "#Speed of driven pulley\n",
+ "N2=d1*d2**-1*(E+(f2)**0.5)*(E+(f1)**0.5)**-1*N1\n",
+ "\n",
+ "#Speed if creep is neglected\n",
+ "N2_2=d1*d2**-1*N1 #r.p.m\n",
+ "\n",
+ "#Speed lost by driven pulley due to creep\n",
+ "N=N2_2-N2\n",
+ "\n",
+ "#Result\n",
+ "print\"speed Lost by driven pulley due to creep is\",round(N,2),\"r.p.m\""
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "speed Lost by driven pulley due to creep is 0.29 r.p.m\n"
+ ]
+ }
+ ],
+ "prompt_number": 5
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 11.7,Page No.397"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "from math import sin, cos, tan, radians, pi\n",
+ "\n",
+ "#Initilization of Variables\n",
+ "\n",
+ "x=600 #cm #Distance between shafts\n",
+ "r1=30 #cm #radius\n",
+ "r2=20 #cm \n",
+ "\n",
+ "#Calculations\n",
+ "\n",
+ "#If belt is open \n",
+ "L1=pi*(r1+r2)+(r1-r2)**2*x**-3+2*x #cm \n",
+ "\n",
+ "#If belt is crossed\n",
+ "L2=pi*(r1+r2)+(r1+r2)**2*x**-1+2*x #cm\n",
+ "\n",
+ "#Result\n",
+ "print\"If belt is open Length is\",round(L1,2),\"cm\"\n",
+ "print\"If belt is crossed length is\",round(L2,2),\"cm\""
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "If belt is open Length is 1357.08 cm\n",
+ "If belt is crossed length is 1361.25 cm\n"
+ ]
+ }
+ ],
+ "prompt_number": 2
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 11.8,Page No.397"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "from math import sin, cos, tan, radians, pi\n",
+ "\n",
+ "#Initilization of Variables\n",
+ "\n",
+ "#speed of shafts\n",
+ "N1=N3=N5=160 #r.p.m\n",
+ "N2=60 #r.p.m\n",
+ "N4=80 #r.p.m\n",
+ "N6=100 #r.p.m\n",
+ "x=180 #cm #Distance between shafts\n",
+ "r1=15 #cm #Radius of smallest pulley\n",
+ "\n",
+ "#Calculations\n",
+ "\n",
+ "#Radii of pulley 2\n",
+ "r2=r1*N1*N2**-1 #cm\n",
+ "\n",
+ "#using same above equation for radii of pulley 3 we get and further simplifying we get\n",
+ "#r4=2*r3 ..................1\n",
+ "\n",
+ "#but for crossed belt equation is\n",
+ "#r1+r2=r3+r4=r5+r6 .................2\n",
+ "#After further simplifying we get\n",
+ "r3=(r1+r2)*3**-1 #cm\n",
+ "r4=2*r3 #cm\n",
+ "\n",
+ "#Using same above equation and further simplifying we get\n",
+ "#r6=1.6*r5 ...............3\n",
+ "\n",
+ "#sub value of r6 in equation we get\n",
+ "r5=(r1+r2)*2.6**-1 #cm\n",
+ "r6=1.6*r5 #cm\n",
+ "\n",
+ "#Length of open belt\n",
+ "L=pi*(r1+r2)+(r1-r2)**2*x**-1+2*x #cm\n",
+ "\n",
+ "#For pulley 3 and 4 equation is\n",
+ "#L=pi*(r3+r4)+(r3-r4)**2*x**-1+2*x\n",
+ "#sub value in above equation we get an equation as\n",
+ "#r3**2+1696.5*r3-31710.6=0\n",
+ "a=1\n",
+ "b=1696.5\n",
+ "c=-31710.6\n",
+ "\n",
+ "X=b**2-4*a*c\n",
+ "\n",
+ "r3_2=(-b+X**0.5)*2**-1 #cm\n",
+ "r4_2=2*r3_2 #cm\n",
+ "\n",
+ "#Sim for r5 & r6 \n",
+ "\n",
+ "#L=pi*(r6+r5)+(r6-r5)**2*x**-1+2*x\n",
+ "#sub value in above equation we get an equation as\n",
+ "#r5**2+4084*r5-88085=0\n",
+ "a=1\n",
+ "b=4084\n",
+ "c=-88085\n",
+ "\n",
+ "X=b**2-4*a*c\n",
+ "\n",
+ "r5_2=(-b+X**0.5)*2**-1 #cm\n",
+ "r6_2=1.6*r5_2 #cm\n",
+ "\n",
+ "#Result\n",
+ "print\"Radii of two stepped pulleys is:For crossed belt:r3\",round(r3,2),\"cm\"\n",
+ "print\" :r4\",round(r4,2),\"cm\"\n",
+ "print\" :r5\",round(r5,2),\"cm\"\n",
+ "print\" :r6\",round(r6,2),\"cm\"\n",
+ "print\"Radii of two stepped pulleys is:For open belt:r3_2\",round(r3_2,2),\"cm\"\n",
+ "print\" :r4_2\",round(r4_2,2),\"cm\"\n",
+ "print\" :r5_2\",round(r5_2,2),\"cm\"\n",
+ "print\" :r6_2\",round(r6_2,2),\"cm\""
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "Radii of two stepped pulleys is:For crossed belt:r3 18.33 cm\n",
+ " :r4 36.67 cm\n",
+ " :r5 21.15 cm\n",
+ " :r6 33.85 cm\n",
+ "Radii of two stepped pulleys is:For open belt:r3_2 18.49 cm\n",
+ " :r4_2 36.98 cm\n",
+ " :r5_2 21.46 cm\n",
+ " :r6_2 34.33 cm\n"
+ ]
+ }
+ ],
+ "prompt_number": 8
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 11.9,Page No.403"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "from math import sin, cos, tan, radians, pi\n",
+ "\n",
+ "#Initilization of Variables\n",
+ "\n",
+ "d=1.2 #m #Diameter\n",
+ "N=200 #r.p.m #Speed\n",
+ "theta=165*pi*180**-1 #radians\n",
+ "mu=0.3 #Coefficient of friction\n",
+ "T1=3000 #N #MAx Tension\n",
+ "\n",
+ "\n",
+ "#Calculations\n",
+ "\n",
+ "#Velocity\n",
+ "v=pi*d*N*60**-1 #m/s\n",
+ "\n",
+ "#From ration of tensions we get\n",
+ "#T1*T2=e**mu*theta \n",
+ "#After simplifying we get\n",
+ "#e**mu*theta =2.3714\n",
+ "T2=T1*2.3714**-1 #N\n",
+ "\n",
+ "#Power transmitted\n",
+ "P=(T1-T2)*v*1000**-1 #KW\n",
+ "\n",
+ "#Result\n",
+ "print\"Power transmitted is\",round(P,2),\"KW\""
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "Power transmitted is 21.8 KW\n"
+ ]
+ }
+ ],
+ "prompt_number": 3
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 11.10,Page No.403"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "from math import sin, cos, tan, radians, pi\n",
+ "import numpy as np\n",
+ "\n",
+ "#Initilization of Variables\n",
+ "\n",
+ "d1=1.20 #m #Diameter\n",
+ "r1=0.6 #m #Radius\n",
+ "r2=0.25 #m \n",
+ "x=4 #m #Distance between shafts\n",
+ "T1=1855.3 #N #Max TRension\n",
+ "mu=0.3 #Coefficient of friction\n",
+ "N1=200 #r.p.m\n",
+ "\n",
+ "#Calculations\n",
+ "\n",
+ "#Velocity\n",
+ "v=pi*d1*N1*60**-1 #m/s\n",
+ "\n",
+ "##Let sin(alpha)=X\n",
+ "X=(r1-r2)*x**-1\n",
+ "alpha=np.arcsin(X)*(pi**-1*180)\n",
+ "\n",
+ "#Angle of contact\n",
+ "theta=180-2*alpha\n",
+ "\n",
+ "#From equation of max tension and further simplifying we get\n",
+ "T2=1855.3*2.435**-1 #N\n",
+ "\n",
+ "#Power transmitted\n",
+ "P=(T1-T2)*v*1000**-1 #KW\n",
+ "\n",
+ "#Torque\n",
+ "t1=(T1-T2)*r1 #N*m\n",
+ "t2=(T1-T2)*r2 #Nm\n",
+ "\n",
+ "\n",
+ "#Result\n",
+ "print\"Power transmitted is\",round(P,2),\"KN\"\n",
+ "print\"Torque Exerted on driving shaft is:t1\",round(t1,2),\"N*m\"\n",
+ "print\" :t2\",round(t2,2),\"N*m\""
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "Power transmitted is 13.74 KN\n",
+ "Torque Exerted on driving shaft is:t1 656.02 N*m\n",
+ " :t2 273.34 N*m\n"
+ ]
+ }
+ ],
+ "prompt_number": 5
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 11.11,Page No.407"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "\n",
+ "#Initilization of Variables\n",
+ "\n",
+ "theta=2.88\n",
+ "v=28.33 #m/s #velocity\n",
+ "b=20 #cm #Width\n",
+ "t=0.8 #cm #thickness\n",
+ "rho=10**-3 #Kg/cm**3 #density\n",
+ "f=250 #N/cm**2 #Stress\n",
+ "mu=0.25 #coefficient of friction\n",
+ "\n",
+ "#Calculations\n",
+ "\n",
+ "#Max Tension\n",
+ "Tm=f*b*t #N\n",
+ "\n",
+ "#mass\n",
+ "m=rho*b*t*100 #Kg\n",
+ "\n",
+ "#Centrifugal Tension\n",
+ "Tc=m*v**2 #N\n",
+ "\n",
+ "#Tension on tight side\n",
+ "T1=Tm-Tc #N\n",
+ "\n",
+ "#From ratio of tension equation we get\n",
+ "T2=T1*2.056**-1 #N\n",
+ "\n",
+ "#MAx Power\n",
+ "P=(T1-T2)*v*1000**-1 #KW\n",
+ "\n",
+ "#Result\n",
+ "print\"Max Power transmitted is\",round(P,2),\"KW\""
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "Max Power transmitted is 39.52 KW\n"
+ ]
+ }
+ ],
+ "prompt_number": 11
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 11.12,Page No.408"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "\n",
+ "#Initilization of Variables\n",
+ "\n",
+ "rho=10**-3 #kg/cm**3 #density\n",
+ "f=250 #N/cm**2 #stress\n",
+ "b=20 #cm #width\n",
+ "t=1.2 #cm #thickness\n",
+ "\n",
+ "\n",
+ "#Calculations\n",
+ "\n",
+ "#MAss\n",
+ "m=rho*b*t*100\n",
+ "\n",
+ "#MAx tension\n",
+ "Tm=f*b*t #N\n",
+ "\n",
+ "#Velocity\n",
+ "v=(Tm*(3*m)**-1)**0.5 #m/s\n",
+ "\n",
+ "#From equation of max tension and further simplifying we get\n",
+ "T1=2*3**-1*Tm #N\n",
+ "T2=T1*2**-1 #N\n",
+ "\n",
+ "#Power \n",
+ "P=(T1-T2)*v*(1000)**-1 #KW\n",
+ "\n",
+ "#Result\n",
+ "print\"Max Power transmitted is\",round(P,2),\"KW\""
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "Max Power transmitted is 57.74 KW\n"
+ ]
+ }
+ ],
+ "prompt_number": 12
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 11.13,Page No.409"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "from math import sin, cos, tan, radians, pi\n",
+ "\n",
+ "#Initilization of Variables\n",
+ "\n",
+ "P=9 #KW #Power\n",
+ "d1=1.2 #m #Diameter\n",
+ "N1=200 #r.p.m\n",
+ "theta=165*pi*180**-1 #radians\n",
+ "mu=0.3 #Coefficient of friction\n",
+ "f=140 #N/cm**2 #Stress\n",
+ "rho=10**-3 #kg/cm**3\n",
+ "t=1 #cm #thickness\n",
+ "\n",
+ "\n",
+ "#Calculations\n",
+ "\n",
+ "#From Ratio of tension equation we get\n",
+ "#T1*T2=e**mu*theta \n",
+ "#After simplifying we get\n",
+ "#e**mu*theta =2.3714\n",
+ "#T1=2.3714*T2 ................1\n",
+ "\n",
+ "#Max tension in belt\n",
+ "#Tm=f*b*t ..............2\n",
+ "\n",
+ "#Centrifugal tension\n",
+ "#Tc=m*v**2 .....................3\n",
+ "\n",
+ "#Velocity\n",
+ "v=pi*d1*N1*60**-1 #m/s\n",
+ "\n",
+ "#mass\n",
+ "#m=rho*b*t*100\n",
+ "#After simplifying we get\n",
+ "#m=b*10**-1\n",
+ "\n",
+ "#Sub value of m in equation 2 and further simplfying we get\n",
+ "#T1-T2=716.5\n",
+ "\n",
+ "#After further simplifying equations 1,2,3 we get\n",
+ "T2=716.5*1.3714**-1 #N\n",
+ "T1=2.3714*T2 #N\n",
+ "\n",
+ "#sub value in MAx tension and further simplifying we get\n",
+ "b=1238.96*124**-1 #cm\n",
+ "\n",
+ "#Result\n",
+ "print\"Width of belt is\",round(b,2),\"cm\""
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "Width of belt is 9.99 cm\n"
+ ]
+ }
+ ],
+ "prompt_number": 6
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 11.14,Page No.411"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "\n",
+ "#Initilization of Variables\n",
+ "b=100 #mm #Width\n",
+ "t=10 #mm #thickness\n",
+ "theta=2.79 #radians\n",
+ "rho=10**-6 #kg/mm**3\n",
+ "mu=0.25 #coefficient of friction\n",
+ "f=1.5 #N/mm**2\n",
+ "g=9.81 \n",
+ "\n",
+ "#Calculations\n",
+ "\n",
+ "#MAx tension\n",
+ "Tm=f*b*t #N\n",
+ "\n",
+ "#From Ratio of tension equation we get\n",
+ "#T1*T2=e**mu*theta \n",
+ "#After simplifying we get\n",
+ "#e**mu*theta =2\n",
+ "\n",
+ "#For Max power\n",
+ "Tc=Tm*3**-1 #N\n",
+ "\n",
+ "#From max transmissiom equation\n",
+ "T1=Tm-Tc\n",
+ "T2=T1*2**-1 #N\n",
+ "\n",
+ "#MAss\n",
+ "m=rho*b*t*1000 #Kg\n",
+ "\n",
+ "#Weight\n",
+ "W=m*g #N\n",
+ "\n",
+ "#Velocity\n",
+ "v=(Tm*(3*m)**-1)**0.5 #m/s\n",
+ "\n",
+ "#Power transmitted\n",
+ "P=(T1-T2)*v*10**-3 #KW\n",
+ "\n",
+ "#Result\n",
+ "print\"Max Power that can be transmitted is\",round(P,2),\"KW\""
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "Max Power that can be transmitted is 11.18 KW\n"
+ ]
+ }
+ ],
+ "prompt_number": 14
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 11.15,Page No.412"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "from math import sin, cos, tan, radians, pi\n",
+ "import numpy as np\n",
+ "\n",
+ "#Initilization of Variables\n",
+ "\n",
+ "d1=60 #cm #diameter\n",
+ "r1=30 #cm #Radius\n",
+ "d2=24 #cm \n",
+ "r2=12 #cm\n",
+ "x=300 #cm #dist between two shafs\n",
+ "N2=300 #r.p.m #speed of small pulley\n",
+ "mu=0.3 #coefficient of friction\n",
+ "m=0.6703 #kg\n",
+ "t=100 #N per cm width #Safe working tension\n",
+ "\n",
+ "#Calculations\n",
+ "\n",
+ "#LEt sin(Alpha)=X\n",
+ "alpha=np.arcsin((r1-r2)*x**-1)*(180*pi**-1)\n",
+ "\n",
+ "#Using equation of ratio of tension\n",
+ "#T1*T2**-1=e**mu*theta ...........1\n",
+ "#Simplifying furter we get value of\n",
+ "#e**mu*theta=2.474\n",
+ "#T1=2.474*T2 ...................1\n",
+ "\n",
+ "#Velocity\n",
+ "v=pi*d2*N2*60**-1*10**-2 #m/s\n",
+ "\n",
+ "#Sub value of v and P in equation of power transmited and further simplifying we get\n",
+ "#(T1-T2)=994.7 .....................2\n",
+ "#Sub value of T1 from equation 1 we get\n",
+ "T2=994.7*1.474**-1 #N\n",
+ "T1=2.474*T2 #N\n",
+ "\n",
+ "#Min width\n",
+ "b=T1*t**-1 #cm\n",
+ "\n",
+ "#Initial belt tension\n",
+ "To=(T1+T2)*2**-1 #N\n",
+ "\n",
+ "#Length of belt required\n",
+ "L=(pi*(r1+r2)+(r1+r2)**2*x**-1+2*x)*100**-1 #m\n",
+ "\n",
+ "#Result\n",
+ "print\"Minimum width of belt is\",round(b,2),\"cm\"\n",
+ "print\"Initial belt tension is\",round(To,2),\"N\"\n",
+ "print\"Length of belt required is\",round(L,2),\"m\""
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "Minimum width of belt is 16.7 cm\n",
+ "Initial belt tension is 1172.18 N\n",
+ "Length of belt required is 7.38 m\n"
+ ]
+ }
+ ],
+ "prompt_number": 7
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 11.16,Page No.414"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "from math import sin, cos, tan, radians, pi\n",
+ "import numpy as np\n",
+ "\n",
+ "#Initilization of Variables\n",
+ "\n",
+ "d1=1.5 #m #diameter\n",
+ "r1=0.75 #m #Radius\n",
+ "d2=1 #m \n",
+ "r2=0.5 #m\n",
+ "x=4.80 #dist between two shafs\n",
+ "To=3000 #N #Initial tension\n",
+ "N2=600 #r.p.m #speed of small pulley\n",
+ "mu=0.3 #coefficient of friction\n",
+ "m=0.6703 #kg\n",
+ "\n",
+ "#Calculation\n",
+ "\n",
+ "#Velocity\n",
+ "v=pi*d2*N2*60**-1 #m/s\n",
+ "\n",
+ "#Centrifugal tension\n",
+ "Tc=m*v**2\n",
+ "\n",
+ "#from Initial Tensiom\n",
+ "#T1+T2=4677 ..........1\n",
+ "\n",
+ "#Let sin(alpha)=X\n",
+ "X=(r1-r2)*x**-1\n",
+ "alpha=np.arcsin(X)*(pi**-1*180)\n",
+ "\n",
+ "#Angle of contact\n",
+ "theta=(180-2*alpha)*pi*180**-1\n",
+ "\n",
+ "#From equation of ratio of tension we get\n",
+ "#t1=2.5*T2 ...................2\n",
+ "\n",
+ "#sub value in equation 1 we get\n",
+ "T2=4677*3.5**-1 #N\n",
+ "T1=2.5*T2\n",
+ "\n",
+ "#Power transmitted\n",
+ "P2=(T1-T2)*v*10**-3\n",
+ "\n",
+ "#Result\n",
+ "print\"Power transmitted is\",round(P2,2),\"KW\""
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "Power transmitted is 62.97 KW\n"
+ ]
+ }
+ ],
+ "prompt_number": 8
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 11.18,Page No.418"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "from math import sin, cos, tan, radians, pi\n",
+ "\n",
+ "#Initilization of Variables\n",
+ "\n",
+ "alpha=25 #degrees #Angle of groove\n",
+ "Tmax=T1=1500 #N #Max tension\n",
+ "theta=170*pi*180**-1 #radians\n",
+ "mu=0.27 #coefficient of friction\n",
+ "v=2 #m/s #belt speed\n",
+ "\n",
+ "#Calculations\n",
+ "\n",
+ "#From ratio of tension\n",
+ "#T1*T2**-1=e**mu*cosec(alpha)\n",
+ "#AFter further simplifying we get\n",
+ "#e**mu*cosec(alpha)=8.109\n",
+ "T2=T1*8.109**-1 \n",
+ "\n",
+ "#Net driving tension\n",
+ "T3=(T1-T2) #N\n",
+ "\n",
+ "#Power transmitted\n",
+ "P=T3*v*10**-3 #W\n",
+ "\n",
+ "#Result\n",
+ "print\"Net driving tension is\",round(T3,2),\"N\"\n",
+ "print\"Power transmitted by the pulley is\",round(P,2),\"W\""
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "Net driving tension is 1315.02 N\n",
+ "Power transmitted by the pulley is 2.63 W\n"
+ ]
+ }
+ ],
+ "prompt_number": 9
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 11.19,Page No.418"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "from math import sin, cos, tan, radians, pi\n",
+ "\n",
+ "#Initilization of Variables\n",
+ "\n",
+ "alpha=15 #Degrees\n",
+ "t=2 #cm #Depth pf belt\n",
+ "m=3.5*100*1000 #gm/l #mass\n",
+ "f=140 #N/cm**2 #Allowable stress\n",
+ "theta=140*pi*180**-1\n",
+ "mu=0.15 #coefficient of friction\n",
+ "\n",
+ "#Calculations\n",
+ "\n",
+ "CF=2*tan(15*pi*180**-1)\n",
+ "GC=1-2*tan(15*pi*180**-1)\n",
+ "BC=2*GC\n",
+ "ED=2\n",
+ "DF=2\n",
+ "\n",
+ "#Area of v-belt\n",
+ "A=(ED+BC)*2**-1*DF\n",
+ "\n",
+ "#MAx permissible tension\n",
+ "Tmax=f*A #N\n",
+ "\n",
+ "#Centrifugal tension\n",
+ "Tc=Tmax*3**-1 #N\n",
+ "\n",
+ "#Velocity\n",
+ "v=(Tc*m**-1)**0.5*1000 #m/s\n",
+ "\n",
+ "#tension on tight side\n",
+ "T1=Tmax-Tc #N\n",
+ " \n",
+ "#From ratio of tensions \n",
+ "#T1*T2**-1=e*mu*thta*cosec(alpha)\n",
+ "#After substituting values and furter simplifying we get value of\n",
+ "#e*mu*thta*cosec(alpha)=4.12\n",
+ "T2=T1*4.12**-1 #N\n",
+ "\n",
+ "#Power\n",
+ "P2=(T1-T2)*v*1000**-1\n",
+ "\n",
+ "#Result\n",
+ "print\"Max Power transmitted is\",round(P2,2),\"KW\""
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "Max Power transmitted is 4.09 KW\n"
+ ]
+ }
+ ],
+ "prompt_number": 18
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 11.20,Page No.420"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "from math import sin, cos, tan, radians, pi\n",
+ "\n",
+ "#Initilization of Variables\n",
+ "\n",
+ "P=75 #KW #Power\n",
+ "d1=1.50 #m #Dia. of driver pulley\n",
+ "N1=200 #r.p.m\n",
+ "alpha=22.5 #Angle of groove\n",
+ "mu=0.3 #coefficient of friction\n",
+ "theta=160*pi*180**-1\n",
+ "m=0.6 #kg #Mass\n",
+ "Tmax=800 #N #Max safe\n",
+ "\n",
+ "#Calculations\n",
+ "\n",
+ "#Velocity of rope\n",
+ "v=pi*d1*N1*60**-1 #m/s\n",
+ "\n",
+ "#centrifugal Tension\n",
+ "Tc=m*v**2 #N\n",
+ "\n",
+ "#Tension in tight side of rope\n",
+ "T1=Tmax-Tc #N\n",
+ "\n",
+ "#Ratio of tension in rope\n",
+ "#T1*T2=e**mu*theta*cosec(alpha)\n",
+ "#After further simplifying we get value of e**mu*theta*cosec(alpha\n",
+ "#e**mu*theta*cosec(alpha=8.95\n",
+ "T2=T1*8.95**-1\n",
+ "\n",
+ "#Power Transmitted by onr rope\n",
+ "P2=(T1-T2)*v*1000**-1 #KW\n",
+ "\n",
+ "#No. of ropes required\n",
+ "n=P*P2**-1 \n",
+ "\n",
+ "#Initial rope tensuion\n",
+ "To=(T1+T2+2*Tc)*2**-1\n",
+ "\n",
+ "#Result\n",
+ "print\"No. of ropes required for drive is\",round(n,2)\n",
+ "print\"Initial Rope tension is\",round(To,2),\"N\""
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "No. of ropes required for drive is 8.24\n",
+ "Initial Rope tension is 510.44 N\n"
+ ]
+ }
+ ],
+ "prompt_number": 19
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 11.21,Page No.421"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "from math import sin, cos, tan, radians, pi\n",
+ "\n",
+ "#Initilization of Variables\n",
+ "\n",
+ "d1=0.40 #Dia. of pulley\n",
+ "N1=110 #speed #r.p.m\n",
+ "alpha=22.5 #Angle of groove\n",
+ "mu=0.28 #coefficient of friction\n",
+ "N=10 #No.of ropes\n",
+ "P=23.628 #KW #Power\n",
+ "theta=160*pi*180**-1 #radians\n",
+ "\n",
+ "#Calculations\n",
+ "\n",
+ "#velocity\n",
+ "v=pi*d1*N1*60**-1 #m/s\n",
+ "\n",
+ "#Power transmited by one rope\n",
+ "P2=P*N**-1 #KW\n",
+ "\n",
+ "#Centrifugal Tension\n",
+ "#Tc=0.0281*C**2 ................1\n",
+ "\n",
+ "#Ratio of tension in rope\n",
+ "#T1=7.71*T2 ...........................2\n",
+ "\n",
+ "#From other formula of power transmited by one rope \n",
+ "#P2=(T1-T2)*v*1000**-1 \n",
+ "#After further substituting and simplifying we get\n",
+ "T2=1026*6.71**-1 #N\n",
+ "T1=7.71*T2 #N\n",
+ "\n",
+ "#Tmax=T1+T2\n",
+ "#After sub values and further simplifying we get\n",
+ "C=(96.86)**0.5 #cm #girth of rope\n",
+ "\n",
+ "Tc=0.0281*C**2 #N\n",
+ "\n",
+ "#Initial Tension\n",
+ "To=(T1+T2+2*Tc)*2**-1 #N\n",
+ "\n",
+ "#Dia. of each rope\n",
+ "d=C*pi**-1 #cm\n",
+ "\n",
+ "#Result\n",
+ "print\"Initial Tension is\",round(To,2),\"N\"\n",
+ "print\"Dia. of each rope is\",round(d,2),\"cm\""
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "Initial Tension is 668.63 N\n",
+ "Dia. of each rope is 3.13 cm\n"
+ ]
+ }
+ ],
+ "prompt_number": 20
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 11.22,Page No.422"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "from math import sin, cos, tan, radians, pi\n",
+ "\n",
+ "#Initilization of Variables\n",
+ "\n",
+ "D=3.6 #m #Dia. of pulley\n",
+ "n=15 #No. of ropes\n",
+ "alpha=22.5 #Degrees\n",
+ "theta=170*pi*180**-1 #Angle of contact\n",
+ "mu=0.28 #angle of friction\n",
+ "Tmax=960 #N #MAx tension\n",
+ "m=1.5 #kg/l #mass of rope\n",
+ "\n",
+ "#Calculations\n",
+ "\n",
+ "#Centrifugal tension\n",
+ "Tc=Tmax*3**-1 #N\n",
+ "\n",
+ "#Velocity\n",
+ "v=(Tmax*(3*m)**-1)**0.5 #m\n",
+ "N=60*v*(pi*D)**-1 #r.p.m\n",
+ "\n",
+ "#equation\n",
+ "#T1*T2**-1=e**mu*theta*cosec(alpha)\n",
+ "#After simlifying further we get \n",
+ "#e**mu*theta*cosec(alpha)=8.756\n",
+ "\n",
+ "#Tension in tight side of rope\n",
+ "T1=Tmax-Tc #N\n",
+ "\n",
+ "#Tension in slack side\n",
+ "T2=T1*8.756**-1\n",
+ "\n",
+ "#Max Power\n",
+ "P=(T1-T2)*v*1000**-1\n",
+ "\n",
+ "#Total max power\n",
+ "P2=P*n\n",
+ "\n",
+ "#Result\n",
+ "print\"Speed of the pulley in r.p.m is\",round(N,2),\"r.p.m\"\n",
+ "print\"Total max power is\",round(P2,2),\"KW\""
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "Speed of the pulley in r.p.m is 77.49 r.p.m\n",
+ "Total max power is 124.2 KW\n"
+ ]
+ }
+ ],
+ "prompt_number": 21
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 11.23,Page No.423"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "from math import sin, cos, tan, radians, pi\n",
+ "\n",
+ "#Initilization of Variables\n",
+ "\n",
+ "W=9000 #N #Weight of casting\n",
+ "n=2.5 #turns\n",
+ "theta=5*pi #Total angle covered\n",
+ "D=0.3 #m #diameter\n",
+ "N=20 #Speed\n",
+ "mu=0.25 #Coefficient of friction\n",
+ "\n",
+ "#Calculations\n",
+ "\n",
+ "#equation\n",
+ "#W*P**-1=e**mu*theta\n",
+ "#After simlifying further we get \n",
+ "P=W*50.65**-1 #Tension in slack side of rope #N\n",
+ "\n",
+ "#Velocity\n",
+ "v=pi*D*N*60**-1 #m/s\n",
+ "\n",
+ "#Power to raise casting\n",
+ "P2=(W-P)*v*1000**-1\n",
+ "\n",
+ "#Result\n",
+ "print\"Force Required by the man is\",round(P,2),\"N\"\n",
+ "print\"Power to raise the casting is\",round(P2,2),\"N\""
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "Force Required by the man is 177.69 N\n",
+ "Power to raise the casting is 2.77 N\n"
+ ]
+ }
+ ],
+ "prompt_number": 6
+ }
+ ],
+ "metadata": {}
+ }
+ ]
+}
\ No newline at end of file diff --git a/Engineering_Mechanics/chapter_12.ipynb b/Engineering_Mechanics/chapter_12.ipynb new file mode 100644 index 00000000..212f421c --- /dev/null +++ b/Engineering_Mechanics/chapter_12.ipynb @@ -0,0 +1,1392 @@ +{
+ "metadata": {
+ "name": "chapter_12.ipynb"
+ },
+ "nbformat": 3,
+ "nbformat_minor": 0,
+ "worksheets": [
+ {
+ "cells": [
+ {
+ "cell_type": "heading",
+ "level": 1,
+ "metadata": {},
+ "source": [
+ "Chapter 12:Kinematics of Linear Motion"
+ ]
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 12.1,Page No.437"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "\n",
+ "#Initilization of Variables\n",
+ "\n",
+ "u=2 #m/s #Initial velocity\n",
+ "v=5 #m/s #Final Velocity\n",
+ "t=4 #sec\n",
+ "\n",
+ "#Calculations\n",
+ "\n",
+ "a=(v-u)*t**-1 #m/s**2\n",
+ "\n",
+ "#Result\n",
+ "print\"Acceleration of the body is\",round(a,2),\"m/s**2\""
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "Acceleration of the body is 0.75 m/s**2\n"
+ ]
+ }
+ ],
+ "prompt_number": 1
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 12.2,Page No.437"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "\n",
+ "#Initilization of Variables\n",
+ "\n",
+ "u=15 #m/s #Intital velocity\n",
+ "v=0 #m/s #Final velocity\n",
+ "t=5 #sec\n",
+ "\n",
+ "#Calculations\n",
+ "\n",
+ "#acceleration\n",
+ "a=u*t**-1 #m/s**2\n",
+ "\n",
+ "#Distance\n",
+ "S=u*t-a*t**2*0.5\n",
+ "\n",
+ "#Result\n",
+ "print\"Retardation is\",round(a,2),\"m/s**2\"\n",
+ "print\"Distance travelled by the car is\",round(S,2),\"m\""
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "Retardation is 3.0 m/s**2\n",
+ "Distance travelled by the car is 37.5 m\n"
+ ]
+ }
+ ],
+ "prompt_number": 2
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 12.3,Page No.437"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "\n",
+ "#Initilization of Variables\n",
+ "\n",
+ "u=250 #m/s #Initial Velocity\n",
+ "v=0 #m/s #final Velocity\n",
+ "s1=0.40 #m #Distance\n",
+ "s2=0.20 #m #distance moved\n",
+ "\n",
+ "#Calculations\n",
+ "\n",
+ "#acceleration\n",
+ "a=u**2*(2*s1)**-1 #m/s**2\n",
+ "\n",
+ "#velocity\n",
+ "v=(u**2-2*a*s2)**0.5 #m/s\n",
+ "\n",
+ "\n",
+ "#Result\n",
+ "print\"Acceleration is\",round(a,2),\"m/s**2\"\n",
+ "print\"Velocity is\",round(v,2),\"m/s\""
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "Acceleration is 78125.0 m/s**2\n",
+ "Velocity is 176.78 m/s\n"
+ ]
+ }
+ ],
+ "prompt_number": 3
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 12.4,Page No.438"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "\n",
+ "#Initilization of Variables\n",
+ "\n",
+ "L_AB=100 #m #Distance AB\n",
+ "L_BC=100 #m #distance BC\n",
+ "t1=10 #s #Time taken by car from A to B\n",
+ "t2=8 #s #Time taken by car from B to C\n",
+ "s=100 #m #Distance\n",
+ "L_AC=L_AB+L_BC #m\n",
+ "\n",
+ "#Calculations\n",
+ "\n",
+ "#From equation of distance we get value of velocity\n",
+ "#s=10*V_A+50*a ...........................1\n",
+ "\n",
+ "#again using equation of distance we get\n",
+ "#L_AC=18*V_A+162*a .........................2\n",
+ "\n",
+ "#After simplifying above equations we get equations like\n",
+ "#900=90*V_A+450*a ......................3\n",
+ "#1000=90*V_A+810*a ..............4\n",
+ "\n",
+ "#Subtracting equations 3 by 4 we get\n",
+ "a=100*360**-1 #m/s**2\n",
+ "\n",
+ "#Velocity of car A\n",
+ "V_A=(100-13.9)*10**-1 #m/s\n",
+ "\n",
+ "#Velocity of car B\n",
+ "V_B=(L_BC-(a*t2**2*0.5))*t2**-1 #m/s\n",
+ "\n",
+ "#Distance OA\n",
+ "s3=V_A**2*(2*a)**-1 #m/s\n",
+ "\n",
+ "#Result\n",
+ "print\"Acceleration of car is\",round(a,2),\"m/s**2\"\n",
+ "print\"Velocity of car A\",round(V_A,2),\"m/s\"\n",
+ "print\"Velocity of car B\",round(V_B,2),\"m/s\"\n",
+ "print\"distance of mark A from starting point is\",round(s3,2),\"m\""
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "Acceleration of car is 0.28 m/s**2\n",
+ "Velocity of car A 8.61 m/s\n",
+ "Velocity of car B 11.39 m/s\n",
+ "distance of mark A from starting point is 133.44 m\n"
+ ]
+ }
+ ],
+ "prompt_number": 4
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 12.5,Page No.440"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "\n",
+ "#Initilization of Variables\n",
+ "\n",
+ "u=0 #m/s #Initial velocity\n",
+ "a=2 #m/s**2 #Acceleration\n",
+ "u2=40 #m/s #Uniform velocity\n",
+ "\n",
+ "#Calculations\n",
+ "\n",
+ "#after simplifying Distance travelled we get\n",
+ "#t**2+20t+100=0 .................1\n",
+ "\n",
+ "#Distance travelled by police party=40*t ..........2\n",
+ "\n",
+ "#Equating equations 1 and 2 we get\n",
+ "#t**2-20*t+100\n",
+ "a=1\n",
+ "b=-20\n",
+ "c=100\n",
+ "\n",
+ "X=b**-4*a*c\n",
+ "\n",
+ "t=(-b+X**0.5)*(2*a)**-1 #s\n",
+ "\n",
+ "#Result\n",
+ "print\"TIme taken in which police van will overtake the car is\",round(t,2),\"s\""
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "TIme taken in which police van will overtake the car is 10.01 s\n"
+ ]
+ }
+ ],
+ "prompt_number": 5
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 12.6,Page No.440"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "\n",
+ "#Initilization of Variables\n",
+ "\n",
+ "v=10 #m/s #uniform Velocity\n",
+ "a=1 #m/s**2 #Uniform acceleration\n",
+ "u=10 #m/s #uniform velocity\n",
+ "\n",
+ "#Calculations\n",
+ "\n",
+ "#From distance equation and further simplifying we get\n",
+ "#S=(t**2+100-20*t) .................1\n",
+ "\n",
+ "#again sub value in distance we get\n",
+ "#S=u*t ............2\n",
+ "\n",
+ "#Equating two equations and further simplifying we get\n",
+ "#t**2-40*t+100=0\n",
+ "a=1\n",
+ "b=-40\n",
+ "c=100\n",
+ "\n",
+ "X=b**2-4*a*c\n",
+ "\n",
+ "t1=(-b+X**0.5)*(2*a)**-1 #s\n",
+ "t2=(-b-X**0.5)*(2*a)**-1 #s\n",
+ "\n",
+ "#time required to catch smugglers car is\n",
+ "t3=(t1-10)\n",
+ "\n",
+ "#Result\n",
+ "print\"Time necesscary for the jeep to catch up with the smuggler's car is\",round(t3,2),\"s\""
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "Time necesscary for the jeep to catch up with the smuggler's car is 27.32 s\n"
+ ]
+ }
+ ],
+ "prompt_number": 6
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 12.6(A),Page No.442"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "\n",
+ "#Initilization of Variables\n",
+ "\n",
+ "u=0\n",
+ "a=4 #m/s**2\n",
+ "t1=7 #s\n",
+ "t2=6 #s\n",
+ "\n",
+ "#Calculations\n",
+ "\n",
+ "#Distance travelled in 7 seconds\n",
+ "S7=u*t1+0.5*a*t1**2 #m\n",
+ "\n",
+ "#DistANCE TRAVELLED in 6 seconds\n",
+ "S6=u*t2+0.5*a*t2**2 #m\n",
+ "\n",
+ "#Distance travelled in 7th second\n",
+ "S7_2=S7-S6\n",
+ "\n",
+ "#Result\n",
+ "print\"Distance travelled in 7th second is\",round(S7_2,2),\"s\""
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "Distance travelled in 7th second is 26.0 s\n"
+ ]
+ }
+ ],
+ "prompt_number": 7
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 12.7,Page No.442"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "\n",
+ "#Initilization of Variables\n",
+ "\n",
+ "S5=15 #m #Distance travelled for 5 th seconds\n",
+ "S10=25 #m #Distance travelled for 10 th seconds\n",
+ "n1=10\n",
+ "n2=5\n",
+ "\n",
+ "#Calculations\n",
+ "\n",
+ "#Equation for distance covered for nth seconds\n",
+ "#S=u+a*2**-1\n",
+ "\n",
+ "#distance covered in 10 th second\n",
+ "#S10=u+a*2**-1*(2*n1-1) ...................1\n",
+ "\n",
+ "#distance covered in 5 th second\n",
+ "#S5=u+a*2**-1*(2*n2-1) .........................2\n",
+ "\n",
+ "#Subtracting equation 2 by 1 we get\n",
+ "a=10*(19-9)**-1*2\n",
+ "\n",
+ "u=S5-9*2**-1*2\n",
+ "\n",
+ "#Result\n",
+ "print\"Initial Velocity of the body is\",round(a,2),\"m/s**2\"\n",
+ "print\"Acceleration of the body is\",round(u,2),\"m/s**2\""
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "Initial Velocity of the body is 2.0 m/s**2\n",
+ "Acceleration of the body is 6.0 m/s**2\n"
+ ]
+ }
+ ],
+ "prompt_number": 8
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 12.8,Page No.443"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "\n",
+ "#Initilization of Variables\n",
+ "\n",
+ "h=90 #3mm Height of tower\n",
+ "h1=30 #m #Height at which both particles meet\n",
+ "S1=60 #m #Distance travelled by first particle\n",
+ "S2=30 #m \n",
+ "g2=-9.81 #m/s**2\n",
+ "\n",
+ "#For Initial Velocity\n",
+ "u1=0 \n",
+ "g=9.81 #m/s**2\n",
+ "\n",
+ "\n",
+ "#Calculations\n",
+ "\n",
+ "#Time\n",
+ "t1=((S1*2)*g**-1)**0.5 #s\n",
+ "\n",
+ "#For second particle\n",
+ "u2=(S2-0.5*g2*t1**2)*t1**-1\n",
+ "\n",
+ "#Result\n",
+ "print\"Velocity with which second particle projected is\",round(u2,2),\"m/s\""
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "Velocity with which second particle projected is 25.73 m/s\n"
+ ]
+ }
+ ],
+ "prompt_number": 9
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 12.9,Page No.443"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "\n",
+ "#Initilization of Variables\n",
+ "\n",
+ "h=800 #m #Height of aeroplane\n",
+ "U=166.67 #m/s \n",
+ "\n",
+ "#First case\n",
+ "u1=0\n",
+ "h2=800 #m #Height of bomb when released\n",
+ "g=9.81 #m/s**2\n",
+ "\n",
+ "#Calculations\n",
+ "\n",
+ "#Time required to reach the ground\n",
+ "t=(h*2*(g)**-1)**0.5\n",
+ "\n",
+ "#Horizontal distance travelled\n",
+ "S=U*t\n",
+ "\n",
+ "#Result\n",
+ "print\"Time required to reach the ground is\",round(t,2),\"s\"\n",
+ "print\"Horizontal distance travelled is\",round(S,2),\"m\""
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "Time required to reach the ground is 12.77 s\n",
+ "Horizontal distance travelled is 2128.55 m\n"
+ ]
+ }
+ ],
+ "prompt_number": 10
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 12.10,Page No.445"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "\n",
+ "#Initilization of Variables\n",
+ "\n",
+ "u=0 #m/s #Initial velocity\n",
+ "g=9.81 #m/s**2 #acceleration due to gravity\n",
+ "\n",
+ "#Calculations\n",
+ "\n",
+ "#t1+t2=4 ...........1\n",
+ "\n",
+ "#Depth of well after simplifying we get\n",
+ "#h=4.905*t1**2 ........2\n",
+ "\n",
+ "#Time taken by sound to reach from bottom of well\n",
+ "#t2=4.905*t1**2*350**-1 #s ...............3\n",
+ "\n",
+ "#Sub value in equation 1 and further simplifying we get\n",
+ "#4.905*t1**2+350*t1-1400=0\n",
+ "a=4.905 \n",
+ "b=350\n",
+ "c=-1400\n",
+ "\n",
+ "X=b**2-4*a*c\n",
+ "\n",
+ "t1=(-b+X**0.5)*(2*a)**-1 #s\n",
+ "\n",
+ "#Depth of well \n",
+ "h=4.905*t1**2 #m \n",
+ "\n",
+ "#Result\n",
+ "print\"Depth of well is\",round(h,2),\"m\""
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "Depth of well is 70.75 m\n"
+ ]
+ }
+ ],
+ "prompt_number": 11
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 12.11,Page No.446"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "\n",
+ "#Initilization of Variables\n",
+ "\n",
+ "u=19.6 #m/s #Initial velocity\n",
+ "h=24.5 #m #height of tower\n",
+ "g=9.80 #m/s**2 #acceleration de to gravity\n",
+ "\n",
+ "#Calculations\n",
+ "\n",
+ "#Max height of stone\n",
+ "h1=(u**2)*(2*g)**-1 #m\n",
+ "\n",
+ "#Time for stone to move from A to C\n",
+ "t1=u*g**-1\n",
+ "\n",
+ "#Time for stone to move from C to D\n",
+ "h2=h+h1 #m #Max height to which stone will rise\n",
+ "t2=((h2*4.9**-1))**0.5 #s\n",
+ "\n",
+ "#Total time for stone to reach the ground\n",
+ "t=t1+t2 #s\n",
+ "\n",
+ "#Result\n",
+ "print\"Total time for stone to reach the ground is\",round(t,2),\"s\"\n",
+ "print\"Velocity of stone in downward travel is\",round(u,2),\"m/s\"\n",
+ "print\"Max height to which the stone will rise is\",round(h2,2),\"m\""
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "Total time for stone to reach the ground is 5.0 s\n",
+ "Velocity of stone in downward travel is 19.6 m/s\n",
+ "Max height to which the stone will rise is 44.1 m\n"
+ ]
+ }
+ ],
+ "prompt_number": 12
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 12.12,Page No.447"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "\n",
+ "#Initilization of Variables\n",
+ "\n",
+ "u=0 #Initial Velocity\n",
+ "t=5 #s #time taken by stone in striking the glass pane\n",
+ "g=9.81 #m/s**2\n",
+ "\n",
+ "#Calculations\n",
+ "\n",
+ "#velocity\n",
+ "v1=u+g*t #m/s\n",
+ "\n",
+ "#Velocity lost in breaking stones\n",
+ "v2=20*100**-1*10\n",
+ "\n",
+ "#Velocity of the stone after breaking the glass pane\n",
+ "v3=v1-v2 #m/s \n",
+ "\n",
+ "#distance travelled in t2=1 s\n",
+ "t2=1 #s\n",
+ "s=v3*t2+0.5*g*t2**2 #m\n",
+ "\n",
+ "#Result\n",
+ "print\"Distance travelled by the stone in next second is\",round(s,2),\"m\""
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "Distance travelled by the stone in next second is 51.96 m\n"
+ ]
+ }
+ ],
+ "prompt_number": 13
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 12.13,Page No.448"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "\n",
+ "#Initilization of Variables\n",
+ "\n",
+ "u=0 #m/s\n",
+ "s=53.90 #m #Distance\n",
+ "g=9.80 #m/s**2 #Acceleration due to gravity\n",
+ "\n",
+ "#Calculations\n",
+ "\n",
+ "#Height \n",
+ "#After simplifying equation of distance we get\n",
+ "#h1=4.9*t**2 ..................................1\n",
+ "\n",
+ "#Distance travelleed in (t-1) s\n",
+ "#After simplifying equation of distance we get\n",
+ "#h2=4.9(t-1)**2 ..................................2\n",
+ "\n",
+ "#Distance travelled by object in last seconds\n",
+ "#h3=h-h2\n",
+ "#After substituting values in above equation we get\n",
+ "#h3=4.9(2*t-1)\n",
+ "\n",
+ "#Equating h3 to s we get after simplifying\n",
+ "t=12*2**-1 #m/s\n",
+ "\n",
+ "#height from which object falls\n",
+ "h1=4.9*t**2\n",
+ "\n",
+ "#Result\n",
+ "print\"height from which object falls is\",round(t,2),\"s\"\n",
+ "print\"Total time taken by object in falling is\",round(h1,2),\"m\""
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "height from which object falls is 6.0 s\n",
+ "Total time taken by object in falling is 176.4 m\n"
+ ]
+ }
+ ],
+ "prompt_number": 14
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 12.14,Page No.448"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "\n",
+ "#Initilization of Variables\n",
+ "\n",
+ "g=9.80 #m/s**2\n",
+ "u=0 #m/s\n",
+ "\n",
+ "#Calculations\n",
+ "\n",
+ "#Distance travelled in time t after simplifiying \n",
+ "#h=4.9*t**2\n",
+ "\n",
+ "#Distance travelled in (t-1)s\n",
+ "#h-h2=2*3**-1*h\n",
+ "\n",
+ "#Substituting value we get equation as\n",
+ "#2*t**2-6*t+3=0\n",
+ "a=2\n",
+ "b=-6\n",
+ "c=3\n",
+ "\n",
+ "X=b**2-4*a*c\n",
+ "\n",
+ "t=(-b+X**0.5)*(2*a)**-1 #s\n",
+ "t2=(-b-X**0.5)*(2*a)**-1 #s\n",
+ "\n",
+ "#Height of tower \n",
+ "h=4.9*t**2\n",
+ "\n",
+ "#Result\n",
+ "print\"Height of tower is\",round(h,2),\"m\""
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "Height of tower is 27.43 m\n"
+ ]
+ }
+ ],
+ "prompt_number": 15
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 12.15,Page No.449"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "\n",
+ "#Initilization of Variables\n",
+ "\n",
+ "u1=30 #m/s #Initial Vlocity of 1st object\n",
+ "u2=40 #m/s #Initial Velocity of2nd object\n",
+ "\n",
+ "#Calculations\n",
+ "\n",
+ "#For the first object\n",
+ "#After simplifying we get\n",
+ "#h1=30*t-4.905*t**2 ................1\n",
+ "\n",
+ "#For second object\n",
+ "##After simplifying we get\n",
+ "#h2=40*(t-4)-4.905(t-4)**2 ...........2\n",
+ "\n",
+ "#Equating equations 1 and 2 and further simplify we get\n",
+ "t=238.48*49.24**-1 #s\n",
+ "\n",
+ "#height\n",
+ "h=30*t-4.905*t**2 #m\n",
+ "\n",
+ "#Result\n",
+ "print\"Time whrn the two objects will meet each other is\",round(t,2),\"s\"\n",
+ "print\"Height from the earth at which the two objects will meet is\",round(h,2),\"m\""
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "Time whrn the two objects will meet each other is 4.84 s\n",
+ "Height from the earth at which the two objects will meet is 30.24 m\n"
+ ]
+ }
+ ],
+ "prompt_number": 16
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 12.16,Page No.450"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "\n",
+ "#Initilization of Variables\n",
+ "\n",
+ "h=100 #m #Height of tower\n",
+ "u1=0 #Initial velocity of 1st particle\n",
+ "S2=30 #m #Distace travelled by 2nd particle\n",
+ "S1=70 #m #Distance travelled by 1st paerticle\n",
+ "g=9.81 #m/s**2\n",
+ "\n",
+ "#Calculations\n",
+ "\n",
+ "#time of particle 1 \n",
+ "t=(S1*(g*2**-1)**-1)**0.5 #s\n",
+ "\n",
+ "#Initial velocity\n",
+ "u=((S2+(g*2**-1)*t**2)*t**-1) #m/s\n",
+ "\n",
+ "#Result\n",
+ "print\"Velocity with which the second particle is projected upward is\",round(u,2),\"m/s\""
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "Velocity with which the second particle is projected upward is 26.47 m/s\n"
+ ]
+ }
+ ],
+ "prompt_number": 17
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 12.16(A),Page No.451"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "\n",
+ "#Initilization of Variables\n",
+ "\n",
+ "n=5 #Rate of drops\n",
+ "u=0 #Initial Velocity\n",
+ "v=3 #m/s #Final Velocity\n",
+ "g=9.81 #m/s**2\n",
+ "t=3*9.81**-1 #s\n",
+ "\n",
+ "#Calculations\n",
+ "\n",
+ "#Vertical Distance \n",
+ "Sb=u*t+0.5*g*t**2 #m\n",
+ "\n",
+ "#time taken by drop A \n",
+ "t2=3*9.81**-1-0.2 #s\n",
+ "\n",
+ "#Vertical Distance travelled from mouth of faucet by drop A\n",
+ "Sa=u*t2+0.5*g*t2**2 #m\n",
+ "\n",
+ "#Vertical Separation between drops A and B\n",
+ "S=Sb-Sa #m\n",
+ "\n",
+ "#Result\n",
+ "print\"Vertical separation between two drops is\",round(S,3),\"m\""
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "Vertical separation between two drops is 0.404 m\n"
+ ]
+ }
+ ],
+ "prompt_number": 18
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 12.18,Page No.453"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "\n",
+ "#Initilization of Variables\n",
+ "\n",
+ "u=0 #m/s**2 #Initial Velocity\n",
+ "#S=(x+20) #m #distance\n",
+ "g=9.81 #m/s**2\n",
+ "\n",
+ "#Calculations\n",
+ "\n",
+ "#Distance travelled by Body in time t\n",
+ "#x=0.5*g*t**2 .................................1\n",
+ "\n",
+ "#Distance travelled by body in time (t+0.4)s\n",
+ "#S2=0.5(t**2+0.**t+0.16) ........................2\n",
+ "\n",
+ "#Subtracting equation 2 from 1 we get\n",
+ "t=3.92*0.80**-1\n",
+ "\n",
+ "#Distance travelled by Body in time t is given by\n",
+ "x=0.5*g*t**2 #m\n",
+ "\n",
+ "#Result\n",
+ "print\"Distance travelled by Body in time t is\",round(x,2),\"m\""
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "Distance travelled by Body in time t is 117.77 m\n"
+ ]
+ }
+ ],
+ "prompt_number": 19
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 12.19,Page No.454"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "\n",
+ "#Initilization of Variables\n",
+ "\n",
+ "#Equation of displacement\n",
+ "#s=t**3+3*t**2+4*t+5\n",
+ "\n",
+ "#Calculations\n",
+ "\n",
+ "#After differentiating displacement equation we get velocity at t=0\n",
+ "#At \n",
+ "t=0\n",
+ "v=3*t**2+6*t+4 #m/s\n",
+ "\n",
+ "#Velocity at t=4 seconds\n",
+ "t2=4\n",
+ "v2=3*t2**2+6*t2+4 #m/s\n",
+ "\n",
+ "#After differentiating w.r.to t we get equation of acceleration as\n",
+ "#a=6*t+6\n",
+ "\n",
+ "#at t=0\n",
+ "t3=0\n",
+ "a=6*t3+6 #m/s**2\n",
+ "\n",
+ "#at t=4\n",
+ "t4=4\n",
+ "a2=6*t4+6 #m/s**2\n",
+ "\n",
+ "\n",
+ "#Result\n",
+ "print\"Velocity at start of 4seconds is\",round(v,2),\"m/s\"\n",
+ "print\"Velocity after 4seconds is\",round(v2,2),\"m/s\"\n",
+ "print\"Acceleration at start is\",round(a,2),\"m/s**2\"\n",
+ "print\"Acceleration after four seconds is\",round(a2,2),\"m/s**2\""
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "Velocity at start of 4seconds is 4.0 m/s\n",
+ "Velocity after 4seconds is 76.0 m/s\n",
+ "Acceleration at start is 6.0 m/s**2\n",
+ "Acceleration after four seconds is 30.0 m/s**2\n"
+ ]
+ }
+ ],
+ "prompt_number": 20
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 12.20,Page No.455"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "\n",
+ "#Initilization of Variables\n",
+ "\n",
+ "#Equation of particle motion\n",
+ "#s=18*t+3*t**2-2*t**3\n",
+ "\n",
+ "#Calculations\n",
+ "\n",
+ "#After differentiating w.r.to t to above equation we get\n",
+ "#6*t**2-6*t-18\n",
+ "\n",
+ "#at \n",
+ "t=0\n",
+ "#Velocity\n",
+ "v=6*t**2+6*t+18\n",
+ "\n",
+ "#After differentiating above equation again we get equation of acceleration\n",
+ "#at \n",
+ "t2=0\n",
+ "a=6-12*t2\n",
+ "\n",
+ "#After differentiating equation of velocity we get value of \n",
+ "t2=6*12**-1\n",
+ "\n",
+ "vmax=18+6*t2-6*t2**2 #m/s\n",
+ "\n",
+ "#Result\n",
+ "print\"Velocity at start is\",round(v,2),\"m/s\"\n",
+ "print\"Acceleration at start is\",round(a,2),\"m/s**2\"\n",
+ "print\"Time when it reaches max velocity is\",round(t2,2),\"s\"\n",
+ "print\"MAx velocity of particle is\",round(vmax,2),\"m/s\""
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "Velocity at start is 18.0 m/s\n",
+ "Acceleration at start is 6.0 m/s**2\n",
+ "Time when it reaches max velocity is 0.5 s\n",
+ "MAx velocity of particle is 19.5 m/s\n"
+ ]
+ }
+ ],
+ "prompt_number": 21
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 12.21,Page No.457"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "\n",
+ "#Initilization of Variables\n",
+ "\n",
+ "#a=-**s**-2 #m/s**2\n",
+ "t=1 #s #time\n",
+ "s=4 #m #Distance\n",
+ "v=2 #m/s #Velocity\n",
+ "t2=2 #s #time\n",
+ "\n",
+ "#Calculations\n",
+ "\n",
+ "#Acceleration equation\n",
+ "#a=v*(dv*ds**-1)\n",
+ "#After sub values and further simplifying and integrating the obtained equation we get\n",
+ "#v**2=8*s**-1+C1 ...................1\n",
+ "#Sub equation in above equations we get\n",
+ "C1=v**2*2**-1-8*s**-1\n",
+ "\n",
+ "#Sub value in equation 1 and furter simplifying and integrating obtained equation we get\n",
+ "#2*3**-1*s**(3*2**_1)=4*t+c2\n",
+ "#Sub values\n",
+ "C2=2*3**-1*s**(3*2**-1)-4*t\n",
+ "\n",
+ "#Sub value of C2 and further sub values we get\n",
+ "s=14**(2*3**-1) \n",
+ "\n",
+ "#Acceleration\n",
+ "a=8*s**-2 #m/s**2\n",
+ "\n",
+ "#Result\n",
+ "print\"Acceleration when t=2 is\",round(a,4),\"m/s**2\""
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "Acceleration when t=2 is 0.2371 m/s**2\n"
+ ]
+ }
+ ],
+ "prompt_number": 22
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 12.22,Page No.458"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "\n",
+ "#Initilization of Variables\n",
+ "\n",
+ "#a=4*t**2-2 \n",
+ "t1=0 \n",
+ "s1=-2 #m\n",
+ "\n",
+ "t2=2 #s\n",
+ "s2=-20 #m\n",
+ "\n",
+ "t3=4 #s\n",
+ "\n",
+ "#Calculations\n",
+ "\n",
+ "#a=4*t**2-2\n",
+ "#After integrating above equations we getand further simplifying we get equation of distance as\n",
+ "#s=t**4*3**-1-t**2+C1*t+C2\n",
+ "C2=s1-t1**4*3**-1 \n",
+ "\n",
+ "#s=t**4*3**-1-t**2+C1*t-2 ...............3\n",
+ "#Now after sub in equation and further simplifying the equation we get\n",
+ "C1=(s2-t2**4*3**-1+t2**2+2)*t2**-1\n",
+ "#Sub in above equation 3 we get\n",
+ "\n",
+ "#when t=4\n",
+ "t4=4\n",
+ "s3=t4**4*3**-1-t4**2+C1*t4-2\n",
+ "\n",
+ "\n",
+ "#Result\n",
+ "print\"Position of particle when t=4 s is\",round(s3,2),\"s\""
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "Position of particle when t=4 s is 28.67 s\n"
+ ]
+ }
+ ],
+ "prompt_number": 23
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 12.23,Page No.460"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "\n",
+ "#Initilization of Variables\n",
+ "\n",
+ "#v=2*t**3-t**2-2*t**2-2*t+4\n",
+ "t=2 #s\n",
+ "s=10 #m\n",
+ "t2=6 #s\n",
+ "\n",
+ "#Calculations\n",
+ "\n",
+ "#acceleration\n",
+ "a=6*t2**2-2*t2-2 #m/s**2\n",
+ "\n",
+ "#Displacement when t=6s \n",
+ "#After integrating and further simplifying the equation of velocity we get equation of displacement as\n",
+ "#s=2*t**4*4**-1-t**3*3**-1-t**2+4*t+C ...............1\n",
+ "#After sub values we get \n",
+ "C=s-(2*t**4*4**-1-t**3*3**-1-t**2+4*t)\n",
+ "\n",
+ "#Sub value of C in equation \n",
+ "s2=2*t2**4*4**-1-t2**3*3**-1-t2**2+4*t2+C #m \n",
+ "\n",
+ "#Result\n",
+ "print\"Acceleration is\",round(a,2),\"m/s**2\"\n",
+ "print\"Displacement of particle when t=6 s is\",round(s2,2),\"m\""
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "Acceleration is 202.0 m/s**2\n",
+ "Displacement of particle when t=6 s is 564.67 m\n"
+ ]
+ }
+ ],
+ "prompt_number": 24
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 12.24,Page No.461"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "\n",
+ "#Initilization of Variables\n",
+ "\n",
+ "#a=2-3*t\n",
+ "t=5 #s \n",
+ "t2=10 #s\n",
+ "v=20 #m/s #velocity\n",
+ "s=85 #m #displacement\n",
+ "\n",
+ "#Calculations\n",
+ "\n",
+ "#Acceleration at start when t=0 \n",
+ "a=2-3*t \n",
+ "\n",
+ "#Equation of acceleration after integrating and further simplifying we get\n",
+ "C1=v-(2*t-3*t**2*2**-1)\n",
+ "\n",
+ "#After substituting in equation and further simplifying we get\n",
+ "#At t3=0\n",
+ "t3=0\n",
+ "v=2*t3-3*t3**2*2**-1+C1\n",
+ "\n",
+ "#After differentiating equation of velocity and integrating it we get equation of displacement as\n",
+ "#s=t**2-3*t**3*6**-1+47.5*t+C2 \n",
+ "C2=s-(t2**2-3*t2**3*6**-1+47.5*t2)\n",
+ "#sub value of C2 in above equation we get\n",
+ "s2=t3**2-3*t3**3*6**-1+47.5*t3+C2 \n",
+ "\n",
+ "#Sub v=0 in equation 3 we get an duaqratic equation as\n",
+ "#3*t**2-4*t-95=0\n",
+ "a=3\n",
+ "b=-4\n",
+ "c=-95\n",
+ "\n",
+ "X=b**2-4*a*c\n",
+ "\n",
+ "t4=(-b+(X**0.5))*(2*a)**-1 #s\n",
+ "#Sub value of t4 in equation of displacement and we get\n",
+ "s3=t4**2-3*t4**3*6**-1+47.5*t4+C2 \n",
+ "\n",
+ "#Result\n",
+ "print\"Acceleration from origin at start of observation is\",round(a,2),\"m/s**2\"\n",
+ "print\"Velocity from origin at start of observation is\",round(v,2),\"m/s**2\"\n",
+ "print\"distance from origin at start of observationis\",round(s2,2),\"m\"\n",
+ "print\"Time after start of observation is\",round(t4,2),\"s\"\n",
+ "print\"Distance from origin is\",round(s3,2),\"m\""
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "Acceleration from origin at start of observation is 3.0 m/s**2\n",
+ "Velocity from origin at start of observation is 47.5 m/s**2\n",
+ "distance from origin at start of observationis 10.0 m\n",
+ "Time after start of observation is 6.33 s\n",
+ "Distance from origin is 223.93 m\n"
+ ]
+ }
+ ],
+ "prompt_number": 57
+ }
+ ],
+ "metadata": {}
+ }
+ ]
+}
\ No newline at end of file diff --git a/Engineering_Mechanics/chapter_13.ipynb b/Engineering_Mechanics/chapter_13.ipynb new file mode 100644 index 00000000..3500af86 --- /dev/null +++ b/Engineering_Mechanics/chapter_13.ipynb @@ -0,0 +1,717 @@ +{
+ "metadata": {
+ "name": "chapter_13.ipynb"
+ },
+ "nbformat": 3,
+ "nbformat_minor": 0,
+ "worksheets": [
+ {
+ "cells": [
+ {
+ "cell_type": "heading",
+ "level": 1,
+ "metadata": {},
+ "source": [
+ "Chapter 13:Kinematics of Curvilinear Motion,Circular Motion,,Rotation And Translation"
+ ]
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 13.1,Page No.471"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "\n",
+ "#Initilization of Variables\n",
+ "\n",
+ "w_o=5 #Rad/s #Initial Angular Velocity\n",
+ "w=13 #rad/s #IFinal angular Velocity\n",
+ "t=4 #s #time\n",
+ "\n",
+ "#Calculation\n",
+ "\n",
+ "#Angular Acceleration of the body\n",
+ "alpha=(w-w_o)*t**-1 #rad/s**2\n",
+ "\n",
+ "#Result\n",
+ "print\"Angular Acceleration of the body is\",round(alpha,2),\"Rad/s**2\""
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "Angular Acceleration of the body is 2.0 Rad/s**2\n"
+ ]
+ }
+ ],
+ "prompt_number": 1
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 13.2,Page No.471"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "from math import sin, cos, tan, radians, pi\n",
+ "\n",
+ "#Initilization of Variables\n",
+ "\n",
+ "N_o=20 #Initial r.p.m of wheel\n",
+ "n=50 #No. of revolution\n",
+ "n2=100 \n",
+ "t=70 #s #time\n",
+ "\n",
+ "#Calculation\n",
+ "\n",
+ "#Angular Dispalcement\n",
+ "theta=2*pi*n\n",
+ "\n",
+ "#Initial Angular Velocity\n",
+ "w_o=2*pi*N_o*60**-1\n",
+ "\n",
+ "#Angular Velocity at the end of 70 s\n",
+ "alpha=(theta-w_o*t)*((t**2)*2**-1)**-1 #rad/s**2\n",
+ "w=w_o+alpha*t #rad/s\n",
+ "\n",
+ "#Time Required for the speed to reach 100 r.p.m\n",
+ "\n",
+ "#Final Angular Velocity\n",
+ "w2=2*pi*n2*60**-1 #rad/s\n",
+ "\n",
+ "#Time required for speed to reach 100 revolutions\n",
+ "t=(w2-w_o)*alpha**-1 #s\n",
+ "\n",
+ "#Result\n",
+ "print\"Angular Velocity at the end of 70 s is\",round(w,2),\"rad/s**2\"\n",
+ "print\"Time required for speed to reach 100 revolutions is\",round(t,2),\"s\""
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "Angular Velocity at the end of 70 s is 6.88 rad/s**2\n",
+ "Time required for speed to reach 100 revolutions is 122.5 s\n"
+ ]
+ }
+ ],
+ "prompt_number": 2
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 13.3,Page No.472"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "\n",
+ "#Initilization of Variables\n",
+ "\n",
+ "alpha=1 #rad/s**2 #Angular Acceleration\n",
+ "w_o=5.25 #rad/s**2 #Initial Angular velocity\n",
+ "w=10.50 #rad/s**2 #Final angular velocity\n",
+ "\n",
+ "#Calculation\n",
+ "\n",
+ "#Total angle turned\n",
+ "theta=(w**2-w_o**2)*2**-1 #rad\n",
+ "\n",
+ "#Result\n",
+ "print\"Total angle turned is\",round(theta,2),\"rad\""
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "Total angle turned is 41.34 rad\n"
+ ]
+ }
+ ],
+ "prompt_number": 3
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 13.4,Page No.472"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "from math import sin, cos, tan, radians, pi\n",
+ "\n",
+ "#Initilization of Variables\n",
+ "\n",
+ "#Part-1\n",
+ "w_o=0 #Initial angular velocity\n",
+ "alpha=1 #rad/s**2 #Angular accleration\n",
+ "t=90 #s #time\n",
+ "\n",
+ "#Part-2\n",
+ "\n",
+ "w_o2=90 #rad/s #Initial Angular velocity\n",
+ "w2=0 #final angular velocity\n",
+ "alpha2=-0.5 #rad/s**2 #Angular retardation\n",
+ "\n",
+ "\n",
+ "#Calculation\n",
+ "\n",
+ "#Part-1\n",
+ "\n",
+ "#Angular Velocity\n",
+ "w=w_o+alpha*t #rad/s\n",
+ "\n",
+ "#Speed in r.p.m\n",
+ "N=60*w*(2*pi)**-1 #r.p.m\n",
+ "\n",
+ "#Part-2\n",
+ "\n",
+ "#Time taken by flywheel in seconds to come to rest \n",
+ "t1=-w_o2*alpha2**-1 #s\n",
+ "\n",
+ "#Result\n",
+ "print\"Speed in r.p.m is\",round(N,2)\n",
+ "print\"Time taken by flywheel in seconds to come to rest is\",round(t1,2),\"s\""
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "Speed in r.p.m is 859.44\n",
+ "Time taken by flywheel in seconds to come to rest is 180.0 s\n"
+ ]
+ }
+ ],
+ "prompt_number": 1
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 13.5,Page No.473"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "from math import sin, cos, tan, radians, pi\n",
+ "\n",
+ "#Initilization of Variables\n",
+ "\n",
+ "N=200 #r.p.m #initial speed\n",
+ "f1=20.94 #rad/s #Frequency\n",
+ "N2=160 #r.p.m\n",
+ "t=10 #s #time\n",
+ "f2=16.75 #rad/s\n",
+ "f3=0 #Final angular velocity\n",
+ "\n",
+ "#Calculation\n",
+ "\n",
+ "#Uniform retardation\n",
+ "alpha=(f2-f1)*t**-1 #rad/s**2\n",
+ "\n",
+ "#total angular displacement\n",
+ "theta=(f3**2-f1**2)*(2*alpha)**-1 #rad\n",
+ "n=theta*(2*pi)**-1 #revolutions\n",
+ "\n",
+ "#Time taken by wheel before it comes to rest\n",
+ "t=-f1*alpha**-1\n",
+ "\n",
+ "\n",
+ "#Result\n",
+ "print\"Number of revolutions is\",round(n,2),\"revolution\"\n",
+ "print\"Time taken by wheel before it comes to rest is\",round(t,2),\"s\""
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "Number of revolutions is 83.28 revolution\n",
+ "Time taken by wheel before it comes to rest is 49.98 s\n"
+ ]
+ }
+ ],
+ "prompt_number": 2
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 13.6,Page No.474"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "\n",
+ "#Initilization of Variables\n",
+ "\n",
+ "#Angle of rotation\n",
+ "#theta=2*t**3-5*t**2+8*t+6\n",
+ "t=0 #s\n",
+ "t2=4 #s\n",
+ "\n",
+ "#Calculation\n",
+ "\n",
+ "#After deriving above equation we get\n",
+ "f1=6*t**2-10*t+8 #rad/s\n",
+ "\n",
+ "#Again differentiating above equation we get\n",
+ "alpha1=12*t-10 #rad/s**2\n",
+ "\n",
+ "#for t2=4\n",
+ "f2=6*t2**2-10*t2+8 #rad/s\n",
+ "alpha2=12*t2-10 #rad/s**2\n",
+ "\n",
+ "#Result\n",
+ "print\"Angular Velocity at t=0 is\",round(f1,2),\"rad/s\"\n",
+ "print\"Angular acceleration at t=4 is\",round(alpha1,2),\"rad/s**2\"\n",
+ "print\"Angular Velocity at t=0 is\",round(f2,2),\"rad/s\"\n",
+ "print\"Angular acceleration at t=4 is\",round(alpha2,2),\"rad/s**2\""
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "Angular Velocity at t=0 is 8.0 rad/s\n",
+ "Angular acceleration at t=4 is -10.0 rad/s**2\n",
+ "Angular Velocity at t=0 is 64.0 rad/s\n",
+ "Angular acceleration at t=4 is 38.0 rad/s**2\n"
+ ]
+ }
+ ],
+ "prompt_number": 6
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 13.6(A),Page No.474"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "\n",
+ "#Initilization of Variables\n",
+ "\n",
+ "#angular rotation\n",
+ "#theta=9*32**-1*t**3\n",
+ "t=1.6 #s\n",
+ "\n",
+ "#Calculation\n",
+ "\n",
+ "#after differentiating above equation twice we get\n",
+ "alpha=27*16**-1*t #rad/s**2\n",
+ "\n",
+ "#Result\n",
+ "print\"Angular accelerations is\",round(alpha,2),\"rad/s**2\""
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "Angular accelerations is 2.7 rad/s**2\n"
+ ]
+ }
+ ],
+ "prompt_number": 7
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 13.7,Page No.475"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "\n",
+ "#Initilization of Variables\n",
+ "\n",
+ "f1=2 #rad/s #initiaal angular velocity\n",
+ "alpha1=0 #Initial angular acceleration\n",
+ "\n",
+ "#Calculation\n",
+ "\n",
+ "#Integrating law of rotation we get\n",
+ "#f2=t**3-3*t+C .......1\n",
+ "#put t=0 weg et\n",
+ "C=2\n",
+ "\n",
+ "#now at t=5 #s\n",
+ "t=5 #s\n",
+ "f2=t**3-3*t+C\n",
+ "\n",
+ "#Integrting equation 1 we get\n",
+ "#theta=t**4*4**-1-3*t**2*2**-1+2*t\n",
+ "#Sub values and further simplifying we get\n",
+ "theta=t**4*4**-1-3*t**2*2**-1+2*t\n",
+ "\n",
+ "#Result\n",
+ "print\"Angular velocity when t=5s is\",round(f2,2),\"rad/s\"\n",
+ "print\"Angular displacement when t=5s is\",round(theta,2),\"radians\""
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "Angular velocity when t=5s is 112.0 rad/s\n",
+ "Angular displacement when t=5s is 128.75 radians\n"
+ ]
+ }
+ ],
+ "prompt_number": 8
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 13.8,Page No.476"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "from math import sin, cos, tan, radians, pi\n",
+ "\n",
+ "#Initilization of Variables\n",
+ "\n",
+ "#Angle of rotation of body \n",
+ "#theta=theta1+a*t+b*t**2\n",
+ "f=3*pi\n",
+ "f2=8*pi\n",
+ "t=0 #s\n",
+ "t2=2 #s\n",
+ "\n",
+ "#Calculations\n",
+ "\n",
+ "#differentiating above equation and further sub values and simplifuing we getweget\n",
+ "a=f\n",
+ "b=(f2-a)*4**-1\n",
+ "\n",
+ "#Result\n",
+ "print\"Constants a is\",round(a,2)\n",
+ "print\"Constants b is\",round(b,2)"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "Constants a is 9.42\n",
+ "Constants b is 3.93\n"
+ ]
+ }
+ ],
+ "prompt_number": 3
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 13.9,Page No.480"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "from math import sin, cos, tan, radians, pi\n",
+ "\n",
+ "#Initilization of Variables\n",
+ "\n",
+ "#Velocity\n",
+ "V_A=4 #m/s\n",
+ "theta=30 #Degrees\n",
+ "\n",
+ "#Calculation\n",
+ "\n",
+ "#Velocity\n",
+ "V_B=V_A*(tan(theta*pi*180**-1))**-1 #m/s\n",
+ "\n",
+ "#Result\n",
+ "print\"Velocity of point B is\",round(V_B,2),\"m/s\""
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "Velocity of point B is 6.93 m/s\n"
+ ]
+ }
+ ],
+ "prompt_number": 10
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 13.9(A),Page No.480"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "\n",
+ "#Initilization of Variables\n",
+ "\n",
+ "r=1 #m #radius\n",
+ "V_C=20 #m/s #Velocity\n",
+ "f=20 #rad/s #Angular velocity\n",
+ "\n",
+ "#Calculation\n",
+ "\n",
+ "#Length\n",
+ "L_DE=(r**2+r**2)**0.5 #m\n",
+ "L_DF=2 #m #Diameter\n",
+ "\n",
+ "#Velocity \n",
+ "V_E=L_DE*f #m/s\n",
+ "V_F=f*L_DF #m/s\n",
+ "\n",
+ "#Result\n",
+ "print\"Velocity of point E:V_E\",round(V_E,2),\"m/s\"\n",
+ "print\"Velocity of point E:V_F\",round(V_F,2),\"m/s\""
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "Velocity of point E:V_E 28.28 m/s\n",
+ "Velocity of point E:V_F 40.0 m/s\n"
+ ]
+ }
+ ],
+ "prompt_number": 11
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 13.9(B),Page No.481"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "\n",
+ "#Initilization of Variables\n",
+ "\n",
+ "D=50 #cm\n",
+ "r=0.25 #m #radius\n",
+ "V_A=L_AL=5 #m/s\n",
+ "V_B=L_BM=3 #m/s\n",
+ "\n",
+ "#Calculation\n",
+ "\n",
+ "#V_A=f*L_AO\n",
+ "#V_B=f*L_BO \n",
+ "\n",
+ "#After further simplifying and resolving we get\n",
+ "f=2*0.5**-1 #rad/s\n",
+ "x=L_BO=3*f**-1 \n",
+ "\n",
+ "#Linear Velocity\n",
+ "V_C=f*(r+x) #m/s\n",
+ "\n",
+ "#Result\n",
+ "print\"Linear Velocity of roller is\",round(V_C,2),\"m/s\"\n",
+ "print\"Angular velocity is\",round(f,2),\"rad/s\""
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "Linear Velocity of roller is 4.0 m/s\n",
+ "Angular velocity is 4.0 rad/s\n"
+ ]
+ }
+ ],
+ "prompt_number": 12
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 13.9(C),Page No.482"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "from math import sin, cos, tan, radians, pi\n",
+ "\n",
+ "#Initilization of Variables\n",
+ "\n",
+ "r=1 #m\n",
+ "u=20 #m/s\n",
+ "\n",
+ "#Calculation\n",
+ "\n",
+ "#Velocity component of point E\n",
+ "#u_E=u+u*sin(u*t)\n",
+ "#at t=0\n",
+ "t=0\n",
+ "u_E=u+u*sin(u*t*pi*180**-1)\n",
+ "v_E=u*cos(u*t)\n",
+ "V_E=(u_E**2+v_E**2)**0.5 #m/s\n",
+ "u_F=u+u*cos(u*t*pi*180**-1) #m/s\n",
+ "\n",
+ "#Result\n",
+ "print\"Velocity of point E is\",round(V_E,2),\"m/s\"\n",
+ "print\"Velocity of point F is\",round(u_F,2),\"m/s\""
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "Velocity of point E is 28.28 m/s\n",
+ "Velocity of point F is 40.0 m/s\n"
+ ]
+ }
+ ],
+ "prompt_number": 13
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 13.9(D),Page No.485"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "\n",
+ "#Initilization of Variables\n",
+ "\n",
+ "g=9.81 #Acceleration due to gravity\n",
+ "W1=W2=80*1000*g\n",
+ "D1=0.75*10**3 #mm\n",
+ "R1=0.75*500 #mm\n",
+ "a1=0.025 #m/s**2\n",
+ "D2=1.2*10**3 #mm\n",
+ "R2=1.2*500 #mm\n",
+ "a2=0.0625 #m/s**2\n",
+ "\n",
+ "#Calculation\n",
+ "\n",
+ "#Horizontal Forces\n",
+ "P1=W1*a1*R1**-1 #N\n",
+ "P2=W2*a2*R2**-1 #N\n",
+ "\n",
+ "#Result\n",
+ "print\"Horizontal Force required to maintain uniform speed is\",round(P1,2),\"N\"\n",
+ "print\"Horizontal Force for truck and trailer is\",round(P2,2),\"N\""
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "Horizontal Force required to maintain uniform speed is 52.32 N\n",
+ "Horizontal Force for truck and trailer is 81.75 N\n"
+ ]
+ }
+ ],
+ "prompt_number": 14
+ }
+ ],
+ "metadata": {}
+ }
+ ]
+}
\ No newline at end of file diff --git a/Engineering_Mechanics/chapter_14.ipynb b/Engineering_Mechanics/chapter_14.ipynb new file mode 100644 index 00000000..6cceab74 --- /dev/null +++ b/Engineering_Mechanics/chapter_14.ipynb @@ -0,0 +1,1114 @@ +{
+ "metadata": {
+ "name": "chapter_14.ipynb"
+ },
+ "nbformat": 3,
+ "nbformat_minor": 0,
+ "worksheets": [
+ {
+ "cells": [
+ {
+ "cell_type": "heading",
+ "level": 1,
+ "metadata": {},
+ "source": [
+ "Chapter 14:Projectiles"
+ ]
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 14.1,Page No.507 "
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "from math import sin, cos, tan, radians, pi\n",
+ "\n",
+ "#Initilization of Variables\n",
+ "alpha=60 #Degrees\n",
+ "R=5000 #m #Horizontal Range\n",
+ "g=9.81 #m/s**2 #Acceleration due to gravity\n",
+ "\n",
+ "#Calculation\n",
+ "\n",
+ "#By equation of Horizontal Range,we get\n",
+ "u=((R*g)*(sin(2*alpha*pi*180**-1))**-1)**0.5 #m/s\n",
+ "\n",
+ "#Max Height attained by projectile\n",
+ "h_max=u**2*(sin(alpha*pi*180**-1))**2*(2*g)**-1\n",
+ "\n",
+ "#Result\n",
+ "print\"Velocity of projection is\",round(u,2),\"m/s\"\n",
+ "print\"Max Height attained by projectile is\",round(h_max,2),\"m\""
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "Velocity of projection is 237.99 m/s\n",
+ "Max Height attained by projectile is 2165.06 m\n"
+ ]
+ }
+ ],
+ "prompt_number": 1
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 14.2,Page No.507"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "from math import sin, cos, tan, radians, pi\n",
+ "\n",
+ "#Initilization of Variables\n",
+ "u=100 #m/s #Velocity\n",
+ "alpha=30 #Degrees #Angle made by projectile with horizontal\n",
+ "g=9.81 #m/s #Acceleration due to gravity\n",
+ "\n",
+ "#Calculation\n",
+ "\n",
+ "#Horizontal Range\n",
+ "R=u**2*sin(2*alpha*pi*180**-1)*g**-1 #m\n",
+ "\n",
+ "#MAx height attained\n",
+ "h_max=u**2*sin(alpha*pi*180**-1)*g**-1 #m\n",
+ "\n",
+ "#Time of flight\n",
+ "T=2*u*sin(alpha*pi*180**-1)*g**-1 #s\n",
+ "\n",
+ "#Result\n",
+ "print\"Horizontal Range is\",round(R,2),\"m\"\n",
+ "print\"MAx Height attained is\",round(h_max,2),\"m\"\n",
+ "print\"Time of Flight is\",round(T,2),\"s\" "
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "Horizontal Range is 882.8 m\n",
+ "MAx Height attained is 509.68 m\n",
+ "Time of Flight is 10.19 s\n"
+ ]
+ }
+ ],
+ "prompt_number": 2
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 14.3,Page No.508"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "from math import sin, cos, tan, radians, pi\n",
+ "import numpy as np\n",
+ "\n",
+ "#Initilization of Variables\n",
+ "#R=4*h_max\n",
+ "\n",
+ "#Calculation\n",
+ "\n",
+ "#Equation ofhorizontal Range is\n",
+ "#R=u**2*sin(2*alpha)*g**-1 .........1\n",
+ "\n",
+ "#Equation of MAx height \n",
+ "#h_max=u**2*sin(alpha)**2*(2*g)**-1 .........2\n",
+ "\n",
+ "#After simplifying both equations,we get\n",
+ "alpha=np.arctan(1)*(pi**-1*180)\n",
+ "\n",
+ "#Result\n",
+ "print\"Angle of projections is\",round(alpha,2),\"degrees\""
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "Angle of projections is 45.0 degrees\n"
+ ]
+ }
+ ],
+ "prompt_number": 3
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 14.4,Page No.508"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "from math import sin, cos, tan, radians, pi\n",
+ "import numpy as np\n",
+ "\n",
+ "#Initilization of Variables\n",
+ "u=20 #m/s #Velocity\n",
+ "x=20 #m #X cordinate of trajectory\n",
+ "y=8 #m #Y cordinate of trajectory\n",
+ "\n",
+ "#Calculation\n",
+ "\n",
+ "#equation of trajectory\n",
+ "#y=x*tan(alpha)-g*x**2*(2*u**2*cos(alpha)**2)**-1\n",
+ "#After substituting values and further simplifying we get quadratic equation\n",
+ "#4.905*(tan(alpha))**2-20*tan(alpha)+12.905=0\n",
+ "a=4.905\n",
+ "b=-20\n",
+ "c=12.905\n",
+ "\n",
+ "X=b**2-4*a*c\n",
+ "\n",
+ "y1=(-b+X**0.5)*(2*a)**-1\n",
+ "y2=(-b-X**0.5)*(2*a)**-1\n",
+ "\n",
+ "alpha1=np.arctan(y1)*(pi**-1*180) #Degrees\n",
+ "alpha2=np.arctan(y2)*(pi**-1*180) #Degrees\n",
+ "\n",
+ "#Result\n",
+ "print\"Angle of projection of particle is:alpha1\",round(alpha1,2),\"Degrees\"\n",
+ "print\" :alpha2\",round(alpha2,2),\"Degrees\""
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "Angle of projection of particle is:alpha1 73.01 Degrees\n",
+ " :alpha2 38.79 Degrees\n"
+ ]
+ }
+ ],
+ "prompt_number": 2
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 14.5,Page No.509"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "from math import sin, cos, tan, radians, pi\n",
+ "\n",
+ "#Initilization of Variables\n",
+ "\n",
+ "x=4.8 #m #X-cord of projectile\n",
+ "y=3.6 #m #y-cord of projectile\n",
+ "alpha=60 #Degrees #Inclination of jet\n",
+ "g=9.81 #m/s**2\n",
+ "\n",
+ "#Calculation\n",
+ "\n",
+ "#Equation of trajectory\n",
+ "#y=x*tan(alpha)-g*x**2*(2*u**2*cos(alpha)**2)**-1\n",
+ "#After further simplifying we get\n",
+ "u=((g*x**2)*(2*(cos(alpha*pi*180**-1))**2*((x*tan(alpha*pi*180**-1))-y))**-1)**0.5 #m/s\n",
+ "\n",
+ "#Result\n",
+ "print\"required velocity of jet at nozzle exit is\",round(u,2),\"m/s\""
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "required velocity of jet at nozzle exit is 9.79 m/s\n"
+ ]
+ }
+ ],
+ "prompt_number": 5
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 14.6,Page No.510"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "from math import sin, cos, tan, radians, pi\n",
+ "import numpy as np\n",
+ "\n",
+ "#Initilization of Variables\n",
+ "\n",
+ "u=250 #m/s #Velocity\n",
+ "x=4000 #m #x-cord\n",
+ "y=700 #m #y-cord\n",
+ "\n",
+ "#Calculation\n",
+ "\n",
+ "#equation of trajectory\n",
+ "#y=x*tan(alpha)-g*x**2*(2*u**2*cos(alpha)**2)**-1\n",
+ "#After substituting values and further simplifying we get quadratic equation\n",
+ "#1255.68*tan(alpha)**2-4000*tan(alpha)+1955.68=0\n",
+ "a=1255.68\n",
+ "b=-4000\n",
+ "c=1955.68\n",
+ "\n",
+ "X=b**2-4*a*c\n",
+ "\n",
+ "y1=(-b+X**0.5)*(2*a)**-1\n",
+ "y2=(-b-X**0.5)*(2*a)**-1\n",
+ "\n",
+ "alpha1=np.arctan(y1)*(pi**-1*180) #Degrees\n",
+ "alpha2=np.arctan(y2)*(pi**-1*180) #Degrees\n",
+ "\n",
+ "#Result\n",
+ "print\"Firing angle to hit the target is:alpha1\",round(alpha1,2),\"Degrees\"\n",
+ "print\" :alpha2\",round(alpha2,2),\"Degrees\""
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "Firing angle to hit the target is:alpha1 68.83 Degrees\n",
+ " :alpha2 31.09 Degrees\n"
+ ]
+ }
+ ],
+ "prompt_number": 6
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 14.7,Page No.511"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "from math import sin, cos, tan, radians, pi\n",
+ "import numpy as np\n",
+ "\n",
+ "#Initilization of Variables\n",
+ "\n",
+ "alpha1=15 #Degrees #Angle of projectile 1\n",
+ "alpha2=45 #Degrees #Angle of projectile2\n",
+ "g=9.81 #m/s**2\n",
+ "#R1=R-12\n",
+ "#R2=R+24\n",
+ "\n",
+ "#Calculation\n",
+ "\n",
+ "#form Equation of horizontal Range we get,\n",
+ "#R-12=u**2*sin(2*alpha1)*g**-1 ..................1\n",
+ "\n",
+ "#R+24=u**2*sin(2*alpha2)*g**-1 ....................2\n",
+ "\n",
+ "#Dividing equation 1 by 2 and further simplifying we get\n",
+ "R=24+24 #m\n",
+ "\n",
+ "#Sub value of R in equation 2 we get\n",
+ "#u**2=g*72\n",
+ "\n",
+ "#Sub values of R and u**2 in equation of horizontal range we get\n",
+ "#sin(2*alpha)=R*g*(g*72)**-1\n",
+ "#LEt sin(2*alpha)=X\n",
+ "X=R*g*(g*72)**-1\n",
+ "alpha=(np.arcsin(X)*(180*pi**-1))*2**-1\n",
+ "\n",
+ "#Result\n",
+ "print\"Angle of projection to hit the mark is\",round(alpha,2)"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "Angle of projection to hit the mark is 20.91\n"
+ ]
+ }
+ ],
+ "prompt_number": 7
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 14.8,Page No.512"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "from math import sin, cos, tan, radians, pi\n",
+ "import numpy as np\n",
+ "\n",
+ "#Initilization of Variables\n",
+ "\n",
+ "u=100 #m/s #initial Velocity\n",
+ "alpha=30 #DEgrees #Angle of projection\n",
+ "g=9.81 #m/s**2\n",
+ "h=80 #m #Height below B\n",
+ "\n",
+ "#Calculation\n",
+ "\n",
+ "#Max Height \n",
+ "H=u**2*(sin(alpha*pi*180**-1))**2*(2*g)**-1 #m\n",
+ "\n",
+ "#Vertical Distance\n",
+ "S=H+h #m\n",
+ "\n",
+ "#Vertical Component of velocity striking the target\n",
+ "v2=(2*g*S)**0.5 #m/s\n",
+ "\n",
+ "#Horizontal component of velocity\n",
+ "v=u*cos(alpha*pi*180**-1)\n",
+ "\n",
+ "#Actual Velocity with which bullet strikes the target\n",
+ "V=(v2**2+v**2)**0.5\n",
+ "\n",
+ "#Angle made by actual velocity striking velocity\n",
+ "theta=np.arctan(v2*v**-1)*(pi**-1*180)\n",
+ "\n",
+ "#Result\n",
+ "print\"Max height attained by bullet\",round(H,2),\"m\"\n",
+ "print\"Actual Velocity with which it will strike the target\",round(theta,2),\"Degrees\""
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "Max height attained by bullet 127.42 m\n",
+ "Actual Velocity with which it will strike the target 36.38 Degrees\n"
+ ]
+ }
+ ],
+ "prompt_number": 8
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 14.9,Page No.514"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "from math import sin, cos, tan, radians, pi\n",
+ "import numpy as np\n",
+ "\n",
+ "#Initilization of Variables\n",
+ "h=150 #m #Height of cliff\n",
+ "u=180 #m/s #Initial Velocity\n",
+ "alpha=30 #ANgle of projection\n",
+ "g=9.81\n",
+ "\n",
+ "#Calculation\n",
+ "\n",
+ "#From equation of vertical Distance\n",
+ "#y=u*sin(Alpha)*t-0.5*g*t**2\n",
+ "#Sub values and further simplifying we get\n",
+ "#4.905t**2-90*t-150=0\n",
+ "a=4.905 \n",
+ "b=-90\n",
+ "c=-150\n",
+ "\n",
+ "X=(b**2-4*a*c)**0.5\n",
+ "\n",
+ "#Total time of flight\n",
+ "t=(-b+(X))*(2*a)**-1\n",
+ "\n",
+ "#Horizontal Distance \n",
+ "h1=u*cos(alpha*pi*180**-1)*t\n",
+ "\n",
+ "#MAx Height \n",
+ "H=u**2*sin(alpha*pi*180**-1)**2*(2*g)**-1 #m\n",
+ "\n",
+ "#ELEvation above the ground\n",
+ "H2=h+H #m\n",
+ "\n",
+ "#Result\n",
+ "print\"Horizontal Distance from gun is\",round(h1,2),\"m\"\n",
+ "print\"Elevation above the ground\",round(H2,2),\"m\""
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "Horizontal Distance from gun is 3099.98 m\n",
+ "Elevation above the ground 562.84 m\n"
+ ]
+ }
+ ],
+ "prompt_number": 3
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 14.10,Page No.515"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "from math import sin, cos, tan, radians, pi\n",
+ "import numpy as np\n",
+ "\n",
+ "#Initilization of Variables\n",
+ "\n",
+ "h=6 #m #Height of tunnel\n",
+ "u=50 #m/s #Initial Velocity\n",
+ "g=9.81\n",
+ "\n",
+ "#Calculation\n",
+ "\n",
+ "alpha=np.arcsin(((h*2*g)*((u**2)**-1))**0.5)*(pi**-1*180)\n",
+ "\n",
+ "#Horizontal Range \n",
+ "R=u**2*sin(2*alpha*pi*180**-1)*g**-1\n",
+ "\n",
+ "#Result\n",
+ "print\"Angle of projection is\",round(alpha,2),\"DEgrees\"\n",
+ "print\"Horizontal Range is\",round(R,2),\"m\""
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "Angle of projection is 12.53 DEgrees\n",
+ "Horizontal Range is 107.96 m\n"
+ ]
+ }
+ ],
+ "prompt_number": 10
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 14.11,Page No.516"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "from math import sin, cos, tan, radians, pi\n",
+ "\n",
+ "#Initilization of Variables\n",
+ "alpha1=30 #Degrees #Angle of projection1\n",
+ "alpha2=30 #Degrees #Angle of projection2\n",
+ "u1=350 #m/s #Velocity of projection at A\n",
+ "u2=300 #m/s #Velocity of projection at B\n",
+ "L_AB=30 #m #distance between A nd B\n",
+ "g=9.81 #m/s**2 \n",
+ "\n",
+ "#Calculation\n",
+ "\n",
+ "#Length AD\n",
+ "L_AD=L_AB*cos(alpha1*pi*180**-1)\n",
+ "\n",
+ "#Horizontal component of velocity at A\n",
+ "V_A=u1*cos(alpha1*pi*180) #m/s\n",
+ "\n",
+ "#Horizontal component of velocity at B\n",
+ "V_B=u2*cos(alpha2*pi*180) #m/s\n",
+ "\n",
+ "#Horizontal Distance covered by shot A\n",
+ "#x=(u1*cos(alpha1)*t ..........................1\n",
+ "\n",
+ "#Horizontal Distance covered by shot B\n",
+ "#15*(3)**0.5-x=(u2*cos(alpha2))*t ................2\n",
+ "\n",
+ "#Adding Equations 1 and 2 we get\n",
+ "t=15*(3)**0.5*((u1+u2)*cos(alpha1*pi*180**-1))**-1\n",
+ "\n",
+ "#sub values in equation 1 we get\n",
+ "x=(u1*cos(alpha1*pi*180**-1))*t\n",
+ "\n",
+ "#Intial velocity shot in vertical direction\n",
+ "V2=u1*sin(alpha1*pi*180**-1) #m/s\n",
+ "\n",
+ "#Distance in vertical direction\n",
+ "y=V2*t-g*t**2*2**-1\n",
+ "\n",
+ "#Result\n",
+ "print\"Time when these two shots meet\",round(t,2),\"s\"\n",
+ "print\"Vertical Distance at which they meet\",round(y,3),\"m\""
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "Time when these two shots meet 0.05 s\n",
+ "Vertical Distance at which they meet 8.066 m\n"
+ ]
+ }
+ ],
+ "prompt_number": 11
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 14.12,Page No.518"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "\n",
+ "#Initilization of Variables\n",
+ "v=720*10**3*3600**-1 #m/s #Speed of air craft\n",
+ "u=200 #m/s #Velocity of bomb\n",
+ "H=1000 #m #Height\n",
+ "g=9.81\n",
+ "\n",
+ "#Calculation\n",
+ "\n",
+ "#Time requaired by bomb\n",
+ "t=(H*2*g**-1)**0.5 #s\n",
+ "\n",
+ "#Horizontal distance of air craft\n",
+ "h=u*round(t,3) #m\n",
+ "\n",
+ "#Result\n",
+ "print\"Time requaired by bomb to reach the ground\",round(t,2),\"s\"\n",
+ "print\"Horizontal distance of air craft\",round(h,2),\"m\""
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "Time requaired by bomb to reach the ground 14.28 s\n",
+ "Horizontal distance of air craft 2855.6 m\n"
+ ]
+ }
+ ],
+ "prompt_number": 4
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 14.13,Page No.519"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "from math import sin, cos, tan, radians, pi\n",
+ "import numpy as np\n",
+ "\n",
+ "#Initilization of Variables\n",
+ "\n",
+ "v=108*10**3*3600**-1 #m/s #Spedd of air craft\n",
+ "u=30 #m/s #Horizontal Velocity\n",
+ "H=1000 #m #Height\n",
+ "g=9.81 #m/s**2\n",
+ "\n",
+ "#Calculation\n",
+ "\n",
+ "#Time taken by bomb\n",
+ "t=(H*2*g**-1)**0.5 #s\n",
+ "\n",
+ "#Horizontal Distance OB\n",
+ "h=u*t #m\n",
+ "\n",
+ "#Velocity of bomb hitting the ground\n",
+ "V=g*t #m/s**2\n",
+ "\n",
+ "#Resultant Velocity\n",
+ "V2=(u**2+V**2)**0.5 #m/s\n",
+ "\n",
+ "#Direction in which the bomb hits the ground\n",
+ "theta=np.arctan(V*u**-1)*(180*pi**-1)\n",
+ "\n",
+ "#Result\n",
+ "print\"HOrizontal Distance of air craft from target\",round(h,2),\"m\"\n",
+ "print\"Velocity of bomb\",round(V2,2),\"m/s\"\n",
+ "print\"Direction of bomb\",round(theta,2),\"Degrees\""
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "HOrizontal Distance of air craft from target 428.35 m\n",
+ "Velocity of bomb 143.25 m/s\n",
+ "Direction of bomb 77.91 Degrees\n"
+ ]
+ }
+ ],
+ "prompt_number": 13
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 14.14,Page No.520"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "\n",
+ "#Initilization of Variables\n",
+ "H=2000 #m #Height of aeroplane\n",
+ "u=10**6*3600**-1 #Velocity of plane #m/s\n",
+ "g=9.8 #m/s**2\n",
+ "\n",
+ "#Calculation\n",
+ "\n",
+ "#Time required by bomb\n",
+ "t=(2*H*g**-1)**0.5 #s\n",
+ "\n",
+ "#Horizontal Distance travelled by bomb\n",
+ "h=u*t #m\n",
+ "\n",
+ "#Result\n",
+ "print\"Time required by bomb to reach the ground\",round(t,2),\"s\"\n",
+ "print\"Horizontal Distance travelled by bomb\",round(h,2),\"m\""
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "Time required by bomb to reach the ground 20.2 s\n",
+ "Horizontal Distance travelled by bomb 5611.96 m\n"
+ ]
+ }
+ ],
+ "prompt_number": 14
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 14.16,Page No.521"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "from math import sin, cos, tan, radians, pi\n",
+ "import numpy as np\n",
+ "\n",
+ "#Initilization of Variables\n",
+ "L_AB1=4 #m #LEngth of AB in Horizontal Distance\n",
+ "L_AB2=2 #m #LEngth of AB in Vertical Distance\n",
+ "g=9.81 #m/s**2 \n",
+ "\n",
+ "#Calculation\n",
+ "\n",
+ "#time\n",
+ "t=((L_AB2*2)*(9.81)**-1)**0.5\n",
+ "\n",
+ "#Minimum veloacity of motorcyclye at A in Horizontal Direction\n",
+ "u=L_AB1*t**-1 #m/s\n",
+ "\n",
+ "#Vertical Component of velocity\n",
+ "v=g*t #m/s\n",
+ "\n",
+ "#Resultant velocity at B\n",
+ "V=(u**2+v**2)**0.5*3600*(10**3)**-1 #km/hr\n",
+ "\n",
+ "#Inclination\n",
+ "theta=np.arctan(v*u**-1)*(180*pi**-1)\n",
+ "\n",
+ "#Result\n",
+ "print\"Inclination of motorcycle clearing the ditch\",round(theta,2),\"Degrees\"\n",
+ "print\"MAgnitude of velocity of motorcycleafter clearing ditch\",round(V,2),\"km/hr\""
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "Inclination of motorcycle clearing the ditch 45.0 Degrees\n",
+ "MAgnitude of velocity of motorcycleafter clearing ditch 31.89 km/hr\n"
+ ]
+ }
+ ],
+ "prompt_number": 15
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 14.17,Page No.522"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "from math import sin, cos, tan, radians, pi\n",
+ "\n",
+ "#Initilization of Variables\n",
+ "alpha=25 #Degrees #Angle of ramp\n",
+ "L_BC1=4 #m #Horizontal Distance between B and C\n",
+ "L_BC2=2 #m #vertical Distance between B and C\n",
+ "g=9.81 #m/s**2\n",
+ "\n",
+ "#Calculation\n",
+ "\n",
+ "##From equation of path \n",
+ "X=(L_BC2+L_BC1*tan(alpha*pi*180**-1))\n",
+ "Y=(g*L_BC1**2)*(2*(cos(alpha*pi*180**-1))**2)**-1\n",
+ "u=(X**-1*Y)**0.5\n",
+ "\n",
+ "#Result\n",
+ "print\"Minimum speed of motorcycle is\",round(u,2),\"m/s\""
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "Minimum speed of motorcycle is 4.97 m/s\n"
+ ]
+ }
+ ],
+ "prompt_number": 5
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 14.18,Page No.526"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "from math import sin, cos, tan, radians, pi\n",
+ "\n",
+ "#Initilization of Variables\n",
+ "u=40 #m/s #Velocity of projection\n",
+ "alpha=50 #Degrees #Angle of projection\n",
+ "beta=20 #degrees #Ang;e if incline plane\n",
+ "g=9.81\n",
+ "\n",
+ "#Calculation\n",
+ "\n",
+ "#Time of flight\n",
+ "T=2*u*sin((alpha-beta)*pi*180**-1)*(g*cos(beta*pi*180**-1))**-1\n",
+ "\n",
+ "#Range \n",
+ "R=2*u**2*cos(alpha*pi*180**-1)*sin((alpha-beta)*pi*180**-1)*(g*(cos(beta*pi*180**-1))**2)**-1\n",
+ "\n",
+ "#Let alpha2 be the angle of projection for max range\n",
+ "alpha2=(90+beta)*2**-1\n",
+ "\n",
+ "#MAx range up the plane\n",
+ "R2=u**2*(g*(1+sin(beta*pi*180**-1)))**-1\n",
+ "\n",
+ "#Result\n",
+ "print\"Time of flight is\",round(T,2),\"s\"\n",
+ "print\"range up the plane is\",round(R,2),\"m\"\n",
+ "print\"Max range up the plane\",round(R2,2),\"m\""
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "Time of flight is 4.34 s\n",
+ "range up the plane is 118.73 m\n",
+ "Max range up the plane 121.53 m\n"
+ ]
+ }
+ ],
+ "prompt_number": 6
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 14.19,Page No.527"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "from math import sin, cos, tan, radians, pi\n",
+ "\n",
+ "#Initilization of Variables\n",
+ "\n",
+ "u=30 #m/s #velocity\n",
+ "alpha=55 #angle of projection\n",
+ "beta=20 #angle of plane\n",
+ "g=9.81\n",
+ "\n",
+ "#Calculation\n",
+ "#Maximum Range\n",
+ "R=u**2*(g*(1+sin(beta*pi*180**-1)))**-1 #m\n",
+ "\n",
+ "#Time of Flight\n",
+ "T=2*u*sin((alpha-beta)*pi*180**-1)*(g*cos(beta*pi*180**-1))**-1\n",
+ "\n",
+ "#Result\n",
+ "print\"Time of Fliight is\",round(T,2),\"s\"\n",
+ "print\"Maximum Range is \",round(R,2),\"m\""
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "Time of Fliight is 3.73 s\n",
+ "Maximum Range is 68.36 m\n"
+ ]
+ }
+ ],
+ "prompt_number": 7
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 14.20,Page No.527"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "from math import sin, cos, tan, radians, pi\n",
+ "\n",
+ "#Initilization of Variables\n",
+ "\n",
+ "u=3 #m/s #Velocity of projection\n",
+ "alpha=25 #Degrees #Angle of projection\n",
+ "beta=25 #degrees #Angle of plane with horizontal\n",
+ "g=9.81 #m/s**2\n",
+ "\n",
+ "#Calculation\n",
+ "\n",
+ "#Range\n",
+ "R=2*u**2*cos(alpha*pi*180**-1)*sin((alpha+beta)*pi*180**-1)*(g*(cos(beta*pi*180**-1))**2)**-1\n",
+ "\n",
+ "#L_BC=y\n",
+ "#L_AC=x\n",
+ "\n",
+ "#From tan(beta) we get\n",
+ "#y=0.466*x .................(1)\n",
+ "\n",
+ "#From Equation (L_AB)**2=(L_BC**2+L_AC)**2\n",
+ "#After sub values and further simplifying we get\n",
+ "x=(2.4*(1.217)**-1)**0.5 #m\n",
+ "\n",
+ "#Sub in equation 1 we get\n",
+ "y=0.466*x\n",
+ "\n",
+ "#Result\n",
+ "print\"Co-ordinates of point B are:x\",round(x,2),\"m\"\n",
+ "print\" :y\",round(y,2),\"m\""
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "Co-ordinates of point B are:x 1.4 m\n",
+ " :y 0.65 m\n"
+ ]
+ }
+ ],
+ "prompt_number": 12
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 14.21,Page No.528"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "from math import sin, cos, tan, radians, pi\n",
+ "import numpy as np\n",
+ "\n",
+ "#Initilization of Variables\n",
+ "\n",
+ "L_AB=75 #m #LEngth of AB\n",
+ "h=19.6 #m #Height of point of release\n",
+ "beta=26.564 #Degrees #angle of plane \n",
+ "\n",
+ "#Calculation\n",
+ "\n",
+ "#Length AC\n",
+ "L_AC=L_AB*cos(beta*pi*180**-1) #m\n",
+ "\n",
+ "#From horizontal Distance \n",
+ "#u*cos(alpha)=L_AC*t**-1 .............1\n",
+ "\n",
+ "#Vertical motion motion from point of release\n",
+ "#u*sin(alpha)=19.6 ....................2\n",
+ "\n",
+ "#vertical Distance\n",
+ "y=L_AB*sin(beta*pi*180**-1) #m\n",
+ "\n",
+ "#Vertical distance from point of release travelled by ball\n",
+ "#y=u*sin(alpha)*t-0.5*g*t**2\n",
+ "\n",
+ "#sub value of y in above equation and further simplifyin we get\n",
+ "#t**2-4t-6.84=0\n",
+ "a=1\n",
+ "b=-4\n",
+ "c=-6.84\n",
+ "\n",
+ "X=b**2-4*a*c\n",
+ "\n",
+ "t=(-b+X**0.5)*(2*a)**-1\n",
+ "\n",
+ "#sub value in equation 1 we get\n",
+ "#Let ucos(alpha)=X\n",
+ "X=67.08*t**-1 #..........................3\n",
+ "\n",
+ "#Dividing equation 1 by 3 we get\n",
+ "alpha=np.arctan(19.6*12.68**-1)*(180*pi**-1)\n",
+ "\n",
+ "#sub in equation 1 we get\n",
+ "u=12.68*cos(alpha*pi*180**-1)**-1\n",
+ "\n",
+ "#Result\n",
+ "print\"Initial Velocity\",round(u,2),\"m/s\"\n",
+ "print\"Inclination is\",round(alpha,4),\"Degrees\""
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "Initial Velocity 23.34 m/s\n",
+ "Inclination is 57.0996 Degrees\n"
+ ]
+ }
+ ],
+ "prompt_number": 9
+ }
+ ],
+ "metadata": {}
+ }
+ ]
+}
\ No newline at end of file diff --git a/Engineering_Mechanics/chapter_15.ipynb b/Engineering_Mechanics/chapter_15.ipynb new file mode 100644 index 00000000..e66c8bb8 --- /dev/null +++ b/Engineering_Mechanics/chapter_15.ipynb @@ -0,0 +1,2687 @@ +{
+ "metadata": {
+ "name": "chapter_15.ipynb"
+ },
+ "nbformat": 3,
+ "nbformat_minor": 0,
+ "worksheets": [
+ {
+ "cells": [
+ {
+ "cell_type": "heading",
+ "level": 1,
+ "metadata": {},
+ "source": [
+ "Chapter 15:Kinetics of Rigid Bodies And Laws of Motion"
+ ]
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 15.1,Page No.536"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "\n",
+ "#Initilization of Variables\n",
+ "\n",
+ "M=150 #kg #Mass of the Body\n",
+ "a=3 #m/s**2 #Acceleration \n",
+ "\n",
+ "\n",
+ "#Calculation\n",
+ "\n",
+ "#Force \n",
+ "F=M*a #N\n",
+ "\n",
+ "#Result\n",
+ "print\"FOrce is\",round(F,2),\"N\""
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "FOrce is 450.0 N\n"
+ ]
+ }
+ ],
+ "prompt_number": 2
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 15.2,Page No.537"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "\n",
+ "#Initilization of Variables\n",
+ "\n",
+ "F=100 #N #Force\n",
+ "m=4 #kg #mass\n",
+ "t=10 #seconds #time\n",
+ "u=5 #m/s #Initial Velocity\n",
+ "\n",
+ "#Calculation\n",
+ "\n",
+ "#Acceleration\n",
+ "a=F*m**-1 #m/s**2\n",
+ "\n",
+ "#Distance\n",
+ "s=u*t+a*t**2*2**-1 #m\n",
+ "\n",
+ "#Result\n",
+ "print\"Acceleration is\",round(a,2),\"m/s**2\"\n",
+ "print\"Distance moved is\",round(s,2),\"m\""
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "Acceleration is 25.0 m/s**2\n",
+ "Distance moved is 1300.0 m\n"
+ ]
+ }
+ ],
+ "prompt_number": 3
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 15.3,Page No.537"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "\n",
+ "#Initilization of Variables\n",
+ "\n",
+ "W=980 #N #Weight of body on the earth\n",
+ "g=9.80 #m/s**2 #Acceleration due to gravity\n",
+ "g2=1.6 #m/s**2 #Acceleration due to gravity on moon\n",
+ "g3=270 #m/s**2 #Acceleration due to gravity on sun\n",
+ "\n",
+ "#Calculation\n",
+ "\n",
+ "#Mass\n",
+ "m=W*g**-1 #Kg\n",
+ "\n",
+ "#Weight of body on moon\n",
+ "W1=m*g2 #N\n",
+ "\n",
+ "#Weight of body on sun\n",
+ "W2=m*g3 #N\n",
+ "\n",
+ "#Result\n",
+ "print\"Weight of body on moon\",round(W1,2),\"N\"\n",
+ "print\"Weight of body on sun\",round(W2,2),\"N\""
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "Weight of body on moon 160.0 N\n",
+ "Weight of body on sun 27000.0 N\n"
+ ]
+ }
+ ],
+ "prompt_number": 4
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 15.4,Page No.537"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "\n",
+ "#Initilization of Variables\n",
+ "\n",
+ "F=200 #N #Force \n",
+ "m=300 #kg #mass\n",
+ "t=90 #sec #time\n",
+ "u=20 #m/s #Initial velocity\n",
+ "\n",
+ "#Calculation\n",
+ "\n",
+ "#Acceleration\n",
+ "a=F*m**-1 #m/s**2 \n",
+ "\n",
+ "#Final Velocity in Direction of motion \n",
+ "v=u+a*t #m/s\n",
+ "\n",
+ "#Final Velocity in opposite direction of motion\n",
+ "v2=u-a*t #m/s\n",
+ "\n",
+ "#Result\n",
+ "print\"Final Velocity in Direction of motion\",round(v,2),\"m/s\"\n",
+ "print\"Final Velocity in opposite direction of motion\",round(v2,2),\"m/s\""
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "Final Velocity in Direction of motion 80.0 m/s\n",
+ "Final Velocity in opposite direction of motion -40.0 m/s\n"
+ ]
+ }
+ ],
+ "prompt_number": 5
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 15.5,Page No.538"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "\n",
+ "#Initilization of Variables\n",
+ "\n",
+ "m=15 #kg #Mass \n",
+ "h=19.6 #m #Height of body from ground\n",
+ "F=4900 #N #Force of resistance\n",
+ "g=9.80 #m/s**2 #Acceleration due to gravity\n",
+ "\n",
+ "#Calculation\n",
+ "\n",
+ "#Final Velocity of body\n",
+ "v=(2*g*h)**0.5 #m/s\n",
+ "\n",
+ "#Weight of body\n",
+ "W=m*g #N\n",
+ "\n",
+ "#Net Force acting in the upward direction\n",
+ "F2=F-W #N\n",
+ "\n",
+ "#Acceleration\n",
+ "a=F2*m**-1 #m/s**2 \n",
+ "\n",
+ "#Part-2\n",
+ "\n",
+ "v2=0 #Final Velocity after penetration into the ground\n",
+ "u=v #Initial Velocity on the ground\n",
+ "\n",
+ "#Distance penetrated into the ground\n",
+ "s=-(v2**2-u**2)*(2*a)**-1 #m \n",
+ "\n",
+ "#Result\n",
+ "print\"Distance penetrated into the ground\",round(s,3),\"m\""
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "Distance penetrated into the ground 0.606 m\n"
+ ]
+ }
+ ],
+ "prompt_number": 7
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 15.6,Page No.539"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "\n",
+ "#Initilization of Variables\n",
+ "\n",
+ "W=637 #N #Weight of man\n",
+ "h=19.6 #m #Height of Tower\n",
+ "u=0 #m/s #Initial Velocity of man when he reaches the water surface\n",
+ "g=9.8 #m/s**2 #acceleration due to gravity\n",
+ "s=2 #m #Distance travelled\n",
+ "\n",
+ "#Calculation\n",
+ "\n",
+ "#Final Velocity of man when he reaches the water surface\n",
+ "v=(2*g*h)**0.5 #m/s\n",
+ "\n",
+ "#acceleration\n",
+ "a=v**2*(2*s)**-1 #m/s**2 #m/s**2\n",
+ "\n",
+ "#Mass of man\n",
+ "m=W*g**-1 #Kg \n",
+ "\n",
+ "#Average resistance of water\n",
+ "F=m*a+W #N\n",
+ "\n",
+ "#Result\n",
+ "print\"Average Resistance of water\",round(F,2),\"N\""
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "Average Resistance of water 6879.6 N\n"
+ ]
+ }
+ ],
+ "prompt_number": 8
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 15.7,Page No.540"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "\n",
+ "#Initilization of Variables\n",
+ "\n",
+ "m=0.081 #kg\n",
+ "v=300 #m/s #velocity\n",
+ "s=0.1 #m #Depth\n",
+ "s2=0.05 #m #Distance travelled\n",
+ "\n",
+ "#Calculation\n",
+ "\n",
+ "#Acceleration \n",
+ "a=v**2*(2*s)**-1 #m/s**2 \n",
+ "\n",
+ "#Force offered by wood to the bullet\n",
+ "F=m*a #N\n",
+ "\n",
+ "#Velocity\n",
+ "v=-(u**2-(2*a*s2)) #m/s\n",
+ "v2=v**0.5 #m/s\n",
+ "\n",
+ "#Result\n",
+ "print\"Force of resistance\",round(v2,2),\"m/s\""
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "Force of resistance 212.13 m/s\n"
+ ]
+ }
+ ],
+ "prompt_number": 9
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 15.8,Page No.541"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "\n",
+ "#Initilization of Variables\n",
+ "\n",
+ "v=0 #Final Velocity\n",
+ "s=60 #m #Distance travelled\n",
+ "mu=0.4 #coefficient of friction\n",
+ "g=9.80\n",
+ "\n",
+ "\n",
+ "#Calculation\n",
+ "\n",
+ "#acceleration\n",
+ "a=mu*g #m/s**2\n",
+ "\n",
+ "#speed of car\n",
+ "u=(2*a*s)**0.5*1000**-1*3600 #m/s\n",
+ "\n",
+ "#Result\n",
+ "print\"Speed of car is\",round(u,2),\"Km/hr\""
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "Speed of car is 78.08 Km/hr\n"
+ ]
+ }
+ ],
+ "prompt_number": 1
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 15.9,Page No.542"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "\n",
+ "#Initilization of Variables\n",
+ "\n",
+ "F1=2000 #N #Tractive of force exerted by railway car\n",
+ "W=50 #KN #Weight of car\n",
+ "g=9.81 #m/s**2 #acceleration due to gravity \n",
+ "\n",
+ "#Calculation\n",
+ "\n",
+ "#mass of car\n",
+ "m=W*1000*g**-1 #N\n",
+ "\n",
+ "#Frictional resistance\n",
+ "F2=5*W\n",
+ "\n",
+ "#Net Force in Direction of motion\n",
+ "F=F1-F2 #N\n",
+ "\n",
+ "#Acceleration\n",
+ "a=F*m**-1\n",
+ "\n",
+ "#Result\n",
+ "print\"acceleration when the car is moving\",round(a,2),\"m/s**2\""
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "acceleration when the car is moving 0.34 m/s**2\n"
+ ]
+ }
+ ],
+ "prompt_number": 11
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 15.10,Page No.542"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "\n",
+ "#Initilization of Variables\n",
+ "\n",
+ "W=1960*1000 #N #Weight of train\n",
+ "g=9.80 #m/s**2 #Acceleration due to gravity\n",
+ "\n",
+ "#Calculation\n",
+ "\n",
+ "#mass of train \n",
+ "m=W*g**-1 #kg\n",
+ "\n",
+ "#final Velocity\n",
+ "v=100*3**-1 #m/s\n",
+ "t=5*60 #sec\n",
+ "\n",
+ "#Acceleration\n",
+ "a=v*t**-1 #m/s**2 \n",
+ "\n",
+ "#Average pull required\n",
+ "F2=m*a+19600\n",
+ "\n",
+ "\n",
+ "#Result\n",
+ "print\"Average pull required\",round(F2,2),\"N\""
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "Average pull required 41822.22 N\n"
+ ]
+ }
+ ],
+ "prompt_number": 12
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 15.11,Page No.544"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "from math import sin, cos, radians, pi\n",
+ "import numpy as np\n",
+ "\n",
+ "#Initilization of Variables\n",
+ "\n",
+ "W=200 #N #Weight of Body\n",
+ "g=9.81 #m/s**2 #aceleration due to gravity\n",
+ "theta=45 #Degrees #Angle of plane\n",
+ "u=0 #m/s #Initial Velocity\n",
+ "v=2 #m/s #Final velocity\n",
+ "mu=0.1 #coefficient of friction\n",
+ "\n",
+ "#Calculation\n",
+ "\n",
+ "#Acceleration of body\n",
+ "a=g*(sin(theta*pi*180**-1)-mu*cos(theta*pi*180**-1)) #m/s**2\n",
+ "\n",
+ "#Distance\n",
+ "s=(v**2-u**2)*(2*a)**-1 #m\n",
+ "\n",
+ "#Result\n",
+ "print\"Distance along inclined plane is\",round(s,2),\"m\""
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "Distance along inclined plane is 0.32 m\n"
+ ]
+ }
+ ],
+ "prompt_number": 2
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 15.12,Page No.544"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "from math import sin, cos, radians, pi\n",
+ "import numpy as np\n",
+ "\n",
+ "#Initilization of Variables\n",
+ "\n",
+ "u=0 #m/s #Initial Velocity\n",
+ "theta=20 #degree #Angle of inclination\n",
+ "mu1=0.08 #Coefficient of friction between the plane and lower body\n",
+ "mu2=0.08 #Coefficient of friction between the plane and upper body\n",
+ "d=10 #m #distance beween two body\n",
+ "g=9.81 #m/s**2 #Acceleration due to gravity\n",
+ "\n",
+ "#Calculation\n",
+ "\n",
+ "#Acceleration of lower body down the plane\n",
+ "a1=g*(sin(theta*pi*180**-1)-mu1*cos(theta*pi*180**-1)) #m/s**2\n",
+ "\n",
+ "#Acceleration of upper body \n",
+ "a2=g*(sin(theta*pi*180**-1)-mu2*cos(theta*pi*180**-1)) #m/s**2\n",
+ "\n",
+ "#Distance travelled by lower body\n",
+ "#s1=u*t+a1*t**2*2**-1\n",
+ "#After sub values and further simplifying we get\n",
+ "#s1=1.3805*t**2 ...................1\n",
+ "\n",
+ "#Distance travelled by upper body\n",
+ "#s1=u*t+a1*t**2*2**-1\n",
+ "#After sub values and further simplifying we get\n",
+ "#s1=1.447*t**2 .......................2\n",
+ "\n",
+ "#Further simplfying we get\n",
+ "t=(10*0.1385**-1)**0.5 #s\n",
+ "\n",
+ "#sub value of t in equation 1 and 2\n",
+ "s1=1.3805*round(t,2)**2 #m\n",
+ "s2=1.447*round(t,2)**2 #m\n",
+ "\n",
+ "#Result\n",
+ "print\"distance through which each body travels before they meet:s1\",round(s1,2),\"m\"\n",
+ "print\" :s2\",round(s2,2),\"m\"\n",
+ "\n",
+ "#Answer of s1 is incorrect in book"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "distance through which each body travels before they meet:s1 99.74 m\n",
+ " :s2 104.55 m\n"
+ ]
+ }
+ ],
+ "prompt_number": 3
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 15.13,Page No.546"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "from math import sin, cos, radians, pi\n",
+ "import numpy as np\n",
+ "\n",
+ "#Initilization of Variables\n",
+ "\n",
+ "W=6000 #N #Weight of truck\n",
+ "u=10 #m/s #speed of truck\n",
+ "#sin(theta)=1*40**-1\n",
+ "\n",
+ "#Calculation\n",
+ "\n",
+ "#Road Resistance\n",
+ "F1=W*1*40**-1 #N\n",
+ "\n",
+ "#Frictional Force\n",
+ "F2=F1*(W*10**-3)**-1\n",
+ "\n",
+ "#PArt-2\n",
+ "\n",
+ "#Speed of truck\n",
+ "u2=2*u #m/s\n",
+ "\n",
+ "#Force exerted by engine up theplane\n",
+ "P=W*1*40**-1+F1 #N\n",
+ "\n",
+ "#Power Exerted by engine\n",
+ "P2=P*u2*1000**-1 #KW\n",
+ "\n",
+ "#Result\n",
+ "print\"Frictional Force of truck is\",round(F2,2),\"N\"\n",
+ "print\"Power Exerted by engine is\",round(P2,2),\"KW\""
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "Frictional Force of truck is 25.0 N\n",
+ "Power Exerted by engine is 6.0 KW\n"
+ ]
+ }
+ ],
+ "prompt_number": 15
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 15.14,Page No.547"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "\n",
+ "#Initilization of Variables\n",
+ "\n",
+ "W=200*10**3 #N #Weight of train\n",
+ "#sin(theta)=1*150**-1 #Slope of track\n",
+ "u=5 #m/s #speed of train\n",
+ "p=3.5 #KW #Power developed by engine\n",
+ "\n",
+ "#Calculation\n",
+ "\n",
+ "#Case-1\n",
+ "\n",
+ "#power developed by engine\n",
+ "P=p*1000*u**-1 #N\n",
+ "\n",
+ "#Net Force \n",
+ "F=W*1*150**-1+P #N\n",
+ "\n",
+ "#Case-2\n",
+ "\n",
+ "#Force exerted by engine while moving up\n",
+ "P2=W*1*150**-1+F #N\n",
+ "\n",
+ "#Power developed by engine\n",
+ "P3=P2*u*1000**-1 #KW\n",
+ "\n",
+ "#Result\n",
+ "print\"Power Developed by Engine to pull up the train is\",round(P3,2),\"KW\"\n",
+ "\n",
+ "#Answer of Power developed by engine is incorrect i.e P so answer of Power Developed by Engine to pull up the train is also incorrect i.e P3"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "Power Developed by Engine to pull up the train is 16.83 KW\n"
+ ]
+ }
+ ],
+ "prompt_number": 16
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 15.15,Page No.549"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "\n",
+ "#Initilization of Variables\n",
+ "\n",
+ "L_BC=100 #m #Distance\n",
+ "V=20*3**-1 #m/s #Velocity\n",
+ "W=20000 #N #Weight\n",
+ "g=9.81 #m/s**2 #acceleration due to gravity\n",
+ "m=W*g**-1 #Mass of car\n",
+ "#sin(theta)=5*100**-1\n",
+ "\n",
+ "#Calculation\n",
+ "\n",
+ "#Frictional resistance due to track\n",
+ "F=8*20 #N\n",
+ "\n",
+ "#Final Velocity of car at D\n",
+ "v=0 \n",
+ "\n",
+ "#Component of weight of train\n",
+ "W2=W*5*100**-1 #N\n",
+ "\n",
+ "#Total Retarding Force against motion\n",
+ "F2=F+W2 #N\n",
+ "\n",
+ "#acceleration\n",
+ "a=F2*g*W**-1 #m/s**2\n",
+ "\n",
+ "#Distance\n",
+ "s=V**2*(2*round(a,3))**-1 #m\n",
+ "\n",
+ "#PArt-2\n",
+ "\n",
+ "#Dstance travelled by car From B to E\n",
+ "\n",
+ "#Distance BD\n",
+ "s_BD=s+L_BC #m\n",
+ "\n",
+ "F3=840 #N #Net Force down the grade\n",
+ "\n",
+ "#Acceleration \n",
+ "a2=F3*g*W**-1 #m/s**2\n",
+ "\n",
+ "#Velocity\n",
+ "v2=(2*a2*s_BD)**0.5 #m/s\n",
+ "\n",
+ "#PArt 3\n",
+ "\n",
+ "#Motion From B to E\n",
+ "\n",
+ "#acceleration\n",
+ "a3=F*g*W**-1 #m/s**2\n",
+ "\n",
+ "#Initial velocity at B\n",
+ "u_B=10.70 #m/s\n",
+ "\n",
+ "#Distance\n",
+ "s2=u_B**2*(2*round(a3,3))**-1 #m\n",
+ "\n",
+ "#Result\n",
+ "print\"Distance travelled by car before stopping is\",round(s,2),\"m\"\n",
+ "print\"Distance travelled by car beyond Bon level track before stopping at E\",round(s2,2),\"m\""
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "Distance travelled by car before stopping is 39.05 m\n",
+ "Distance travelled by car beyond Bon level track before stopping at E 733.91 m\n"
+ ]
+ }
+ ],
+ "prompt_number": 17
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 15.16,Page No.552"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "\n",
+ "#Initilization of Variables\n",
+ "\n",
+ "W=100 #N #Weight carried by lift\n",
+ "a=2.45 #m/s**2 #Acceleration\n",
+ "g=9.80 #m/s**2 #Acceleration due to gravity\n",
+ "\n",
+ "#Calculation\n",
+ "\n",
+ "#Tension in the cables supporting the lift\n",
+ "\n",
+ "#Lift moving upwards\n",
+ "T=W*(1+a*g**-1) #N\n",
+ "\n",
+ "#Lift moving downwards\n",
+ "T2=W*(1-a*g**-1) #N\n",
+ "\n",
+ "#Result\n",
+ "print\"Tension in the cables supporting the lift:when moving upwards\",round(T,2),\"N\"\n",
+ "print\"Tension in the cables supporting the lift:when moving downward\",round(T2,2),\"N\""
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "Tension in the cables supporting the lift:when moving upwards 125.0 N\n",
+ "Tension in the cables supporting the lift:when moving downward 75.0 N\n"
+ ]
+ }
+ ],
+ "prompt_number": 18
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 15.16(A),Page No.553"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "\n",
+ "#Initilization of Variables\n",
+ "\n",
+ "a=1 #m/s**2 #upward acceleration\n",
+ "W=600 #N #weight of man\n",
+ "g=9.81 #m/s**2 #Acceleration due to gravity\n",
+ "\n",
+ "#Calculation\n",
+ "\n",
+ "#NEt Force in upward direction\n",
+ "F=W*g**-1 #N\n",
+ "\n",
+ "#But net Force in upward direction\n",
+ "T=F+W #N\n",
+ "\n",
+ "#Result\n",
+ "print\"net Force in upward direction\",round(T,2),\"N\""
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "net Force in upward direction 661.16 N\n"
+ ]
+ }
+ ],
+ "prompt_number": 19
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 15.17,Page No.553"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "\n",
+ "#Initilization of Variables\n",
+ "\n",
+ "a=1.225 #m/s**2 #upward acceleration\n",
+ "W=500 #N #Weight of man\n",
+ "g=9.8 #m/s**2 #Acceleration due to gravity\n",
+ "\n",
+ "#Calculation\n",
+ "\n",
+ "#Tension in the cables supporting the lift\n",
+ "\n",
+ "#Lift moving upwards\n",
+ "T=W*(1+a*g**-1) #N\n",
+ "\n",
+ "#lift moving downwards\n",
+ "T2=W*(1-a*g**-1) #N\n",
+ "\n",
+ "#Lift moving upwards with unknown acceleration\n",
+ "T3=600 #N #Pressure exerted by man\n",
+ "a=(T3-W)*g*W**-1 #m/s**2\n",
+ "\n",
+ "#Result\n",
+ "print\"Acceleration upwards is\",round(a,2),\"m/s**2\""
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "Acceleration upwards is 1.96 m/s**2\n"
+ ]
+ }
+ ],
+ "prompt_number": 20
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 15.18,Page No.554"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "\n",
+ "#Initilization of Variables\n",
+ "\n",
+ "W=2500 #N #Weight of an elevator\n",
+ "u=0 #m/s #Initial Velocity\n",
+ "s=35 #m #Distance travelled\n",
+ "t=10 #sec #time\n",
+ "g=9.81 #m/s**2 #Acceleration due to gravity\n",
+ "\n",
+ "#Calculation\n",
+ "\n",
+ "#Tension in the cables\n",
+ "\n",
+ "#When acceleration is zero i.e a=0\n",
+ "a=0 #m/s**2\n",
+ "T=W*(1-a*g**-1) #N\n",
+ "\n",
+ "#When acceleration is zero i.e a=0\n",
+ "a2=9.81 #m/s**2\n",
+ "T2=W*(1-a2*g**-1) #N\n",
+ "\n",
+ "#Using equation of distance\n",
+ "a3=(s-u*t)*2*(t**2)**-1 #m/s**2\n",
+ "\n",
+ "#Tension in the cable at time t=10 sec\n",
+ "T3=W*(1-a3*g**-1) #N\n",
+ "\n",
+ "#Result\n",
+ "print\"Limits of table Tension is:when a=0\",round(T,2),\"N\"\n",
+ "print\" :when a=9.81 m/s**2\",round(T2,2),\"N\"\n",
+ "print\"Cable Tension at time t=10 sec\",round(T3,2),\"N\""
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "Limits of table Tension is:when a=0 2500.0 N\n",
+ " :when a=9.81 m/s**2 0.0 N\n",
+ "Cable Tension at time t=10 sec 2321.61 N\n"
+ ]
+ }
+ ],
+ "prompt_number": 21
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 15.19,Page No.555"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "\n",
+ "#Initilization of Variables\n",
+ "\n",
+ "g=9.80 #m/s**2 #Acceleration due to gravity\n",
+ "W=5000 #N #Weight of 10 men on the cage\n",
+ "u=0 #m/s #Initial Velocity of cage\n",
+ "v=12 #m/s #Final Velocity\n",
+ "s=20 #m #Distance travelled\n",
+ "\n",
+ "#Calculation\n",
+ "\n",
+ "#acceleration\n",
+ "a=(v**2-u**2)*(2*s)**-1 #m/s**2\n",
+ "\n",
+ "#Tension in cable while moving downwards\n",
+ "T=W*(1-a*g**-1) #N\n",
+ "\n",
+ "#Tension produced by one men\n",
+ "T2=T*10**-1 #N\n",
+ "\n",
+ "#Result\n",
+ "print\"Pressure Exerted by each man on the cage\",round(T2,2),\"N\""
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "Pressure Exerted by each man on the cage 316.33 N\n"
+ ]
+ }
+ ],
+ "prompt_number": 22
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 15.20,Page No.556"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "\n",
+ "#Initilization of Variables\n",
+ "\n",
+ "W=5000 #N #Weight of elevator\n",
+ "a=3 #m/s**2 #Acceleration\n",
+ "W2=700 #N #weight of perator \n",
+ "g=9.80\n",
+ "\n",
+ "#Calculation\n",
+ "\n",
+ "#Reaction offered by floor on operator\n",
+ "R=W*g**-1*a+W2 #N\n",
+ "\n",
+ "#Total Weight \n",
+ "W3=W+W2 #N\n",
+ "\n",
+ "#Total Tension in the cable\n",
+ "T=W3*g**-1*a+W3 #N\n",
+ "\n",
+ "#Result\n",
+ "print\"Total tension in the cable\",round(T,2),\"N\""
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "Total tension in the cable 7444.9 N\n"
+ ]
+ }
+ ],
+ "prompt_number": 4
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 15.21,Page No.558"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "\n",
+ "#Initilization of Variables\n",
+ "\n",
+ "W1=50 #N #Heavier Weight\n",
+ "W2=30 #N #lighter Weight\n",
+ "g=9.80 #m/s**2 #Acceleration due to gravity\n",
+ "\n",
+ "#Calculation\n",
+ "\n",
+ "#Acceleration of the system\n",
+ "a=g*(W1-W2)*(W1+W2)**-1 #m/s**2 \n",
+ "\n",
+ "#Tension in the string\n",
+ "T=2*W1*W2*(W1+W2)**-1 #N\n",
+ "\n",
+ "#Result\n",
+ "print\"Acceleration of the system\",round(a,2),\"m/s**2\"\n",
+ "print\"Tension in the string\",round(T,2),\"N\""
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "Acceleration of the system 2.45 m/s**2\n",
+ "Tension in the string 37.5 N\n"
+ ]
+ }
+ ],
+ "prompt_number": 24
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 15.22,Page No.558"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "\n",
+ "#Initilization of Variables\n",
+ "\n",
+ "g=9.80 #m/s**2 #Acceleration due to gravity\n",
+ "W1=60 #N #bigger weight\n",
+ "a=3 #m/s**2 #Acceleration of the system\n",
+ "\n",
+ "#Calculation\n",
+ "\n",
+ "#smaller Weight\n",
+ "W2=-(a*W1*g**-1-W1)*(a*g**-1+1)**-1 #N\n",
+ "\n",
+ "#Tension in the string\n",
+ "T=2*W1*W2*(W1+W2)**-1 #N\n",
+ "\n",
+ "#Result\n",
+ "print\"Smaller Weight is\",round(W2,2),\"N\"\n",
+ "print\"Tension in the string\",round(T,2),\"N\""
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "Smaller Weight is 31.88 N\n",
+ "Tension in the string 41.63 N\n"
+ ]
+ }
+ ],
+ "prompt_number": 25
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 15.23,Page No.559"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "\n",
+ "#Initilization of Variables\n",
+ "\n",
+ "W1=700 #N #Bigger Load\n",
+ "W2=500 #N #Smaller Load\n",
+ "\n",
+ "#Calculation\n",
+ "\n",
+ "#Weight of block A when acceleration is g/3\n",
+ "W1_1=((3*W2)+W2)*2**-1 #N\n",
+ "\n",
+ "#Weight added \n",
+ "W=W1_1-W1 #N\n",
+ "\n",
+ "#Result\n",
+ "print\"Weight added is\",round(W,2),\"N\""
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "Weight added is 300.0 N\n"
+ ]
+ }
+ ],
+ "prompt_number": 26
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 15.24,Page No.560"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "\n",
+ "#Initilization of Variables\n",
+ "\n",
+ "W_A=150 #N #Weight of block A\n",
+ "W_B=50 #N #Weight of block B\n",
+ "g=9.81 #m/s**2 #Acceleration due to gravity\n",
+ "\n",
+ "#Calculation\n",
+ "\n",
+ "#Acceleration\n",
+ "a=(W_A-W_B*2)*((W_B*2+(W_A*2**-1))*g**-1)**-1 #m/s**2\n",
+ "\n",
+ "#Acceleration of block B\n",
+ "a_B=a #m/s**2\n",
+ "\n",
+ "#Acceleration of block A\n",
+ "a_A=a*2**-1 #m/s**2 \n",
+ "\n",
+ "#Tensions in the string\n",
+ "T=W_B+W_B*g**-1*a #N\n",
+ "\n",
+ "#Result\n",
+ "print\"Tensions in the string is\",round(T,2),\"N\"\n",
+ "print\"Acceleration of block B is\",round(a_B,2),\"m/s**2\"\n",
+ "print\"Acceleration of block A is\",round(a_A,2),\"m/s**2\""
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "Tensions in the string is 64.29 N\n",
+ "Acceleration of block B is 2.8 m/s**2\n",
+ "Acceleration of block A is 1.4 m/s**2\n"
+ ]
+ }
+ ],
+ "prompt_number": 27
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 15.25,Page No.561"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "\n",
+ "#Initilization of Variables\n",
+ "\n",
+ "W1=15 #N #weight over pulley A\n",
+ "W2=10 #N #total weight over pulley B\n",
+ "w1=6 #N #weight over pulley B\n",
+ "w2=4 #N #weight over pulley B\n",
+ "g=9.80 #m/s**2 #acceleration due to gravity\n",
+ "\n",
+ "#Calculation\n",
+ "\n",
+ "#Consider motion of weight 15 N\n",
+ "#(W1-T1)=W1*g**-1*a ..........................(1)\n",
+ "\n",
+ "#Consider motion of weight 4 N\n",
+ "#(T2-w2)=w2*g**-1*(a1+a) ...................(2)\n",
+ "\n",
+ "#Consider motion of weight 6 N\n",
+ "#(w1-w2)=w1*g**-1*(a1-a) .........................(3)\n",
+ "\n",
+ "#Consider motion of pulley B\n",
+ "#T1=2*T2 ...............................(4)\n",
+ "\n",
+ "#Adding equations 2 and 3 we get\n",
+ "#g=5*a1-a .......................................(5)\n",
+ "\n",
+ "#Multiplying equation (2) by 2\n",
+ "#2*T2-8=8*g**-1*(a1+a)\n",
+ "\n",
+ "#But sub value 2*T2=T1 in equation above\n",
+ "#T1-8=8*g**-1*(a1+a) .......................................(6)\n",
+ "\n",
+ "#Adding equation 1 and 6\n",
+ "#7*g=23*a+8*a1 .......................................(7)\n",
+ "\n",
+ "#Multiplying equation (5) by 23\n",
+ "#23*g=-23*a+5*23*a1 .......................................(8)\n",
+ "\n",
+ "#Adding equation 7 and 8 we get\n",
+ "a1=30*g*123**-1 #m/s**2\n",
+ "\n",
+ "#sub value of equation 5 we get\n",
+ "a=5*a1-g #m/s**2\n",
+ "\n",
+ "#Acceleration of weight 15 N\n",
+ "a_15=a #m/s**2\n",
+ "\n",
+ "#Acceleration of weight 6 N\n",
+ "a_6=a1-a #m/s**2\n",
+ "\n",
+ "#Acceleration of weight 4 N\n",
+ "a_4=a1+a #m/s**2 \n",
+ "\n",
+ "#Result\n",
+ "print\"Acceleration of weight 15 N\",round(a_15,2),\"m/s**2\"\n",
+ "print\"Acceleration of weight 6 N\",round(a_6,2),\"m/s**2\"\n",
+ "print\"Acceleration of weight 4 N\",round(a_4,2),\"m/s**2\""
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "Acceleration of weight 15 N 2.15 m/s**2\n",
+ "Acceleration of weight 6 N 0.24 m/s**2\n",
+ "Acceleration of weight 4 N 4.54 m/s**2\n"
+ ]
+ }
+ ],
+ "prompt_number": 28
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 15.26,Page No.565"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "\n",
+ "#Initilization of Variables\n",
+ "\n",
+ "#Weight of bodies\n",
+ "W1=10 #N #Weight placed on Horizontal surface \n",
+ "W2=20 #N #Weight hanging free in air\n",
+ "g=9.81 #m/s**2 #Acceleration due to gravity\n",
+ "\n",
+ "#Calculation\n",
+ "\n",
+ "#Acceleration of the system\n",
+ "a=g*W1*(W1+W2)**-1 #m/s**2\n",
+ "\n",
+ "#tension in the string\n",
+ "T=W1*W2*(W1+W2)**-1 #N\n",
+ "\n",
+ "#Result\n",
+ "print\"Acceleration of the system\",round(a,2),\"m/s**2\"\n",
+ "print\"Tension in the string\",round(T,2),\"N\""
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "Acceleration of the system 3.27 m/s**2\n",
+ "Tension in the string 6.67 N\n"
+ ]
+ }
+ ],
+ "prompt_number": 29
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 15.27,Page No.565"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "\n",
+ "#Initilization of Variables\n",
+ "\n",
+ "W1=10 #N #Weight on horizontal surface\n",
+ "mu=0.3 #coefficient of friction\n",
+ "W2=20 #N #Weight hanging free in air\n",
+ "g=9.80\n",
+ "\n",
+ "#Calculation\n",
+ "\n",
+ "#Acceleration of the system\n",
+ "a=g*(W1-mu*W2)*(W1+W2)**-1 #m/s**2\n",
+ "\n",
+ "#tension in the string\n",
+ "T=W1*W2*(1+mu)*(W1+W2)**-1 #N\n",
+ "\n",
+ "\n",
+ "#Result\n",
+ "print\"Acceleration of the system\",round(a,2),\"m/s**2\"\n",
+ "print\"Tension in the string\",round(T,2),\"N\""
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "Acceleration of the system 1.31 m/s**2\n",
+ "Tension in the string 8.67 N\n"
+ ]
+ }
+ ],
+ "prompt_number": 1
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 15.28,Page No.566"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "\n",
+ "#Initilization of Variables\n",
+ "\n",
+ "W1=10 #N #Weight of block A\n",
+ "W2=20 #N #weight of block B\n",
+ "mu=0.25 #coefficient of friction\n",
+ "s=2 #m #Distance moved by block\n",
+ "u=0 #Initial velocity of block B\n",
+ "g=9.80\n",
+ "\n",
+ "#Calculation\n",
+ "\n",
+ "#Acceleration\n",
+ "a=g*(W1-mu*W2)*(W1+W2)**-1 #m/s**2\n",
+ "\n",
+ "#velocity of block B\n",
+ "v=u**2+2*a*s #m/s\n",
+ "\n",
+ "#Result\n",
+ "print\"velocity of block B\",round(v,2),\"m/s\""
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "velocity of block B 6.53 m/s\n"
+ ]
+ }
+ ],
+ "prompt_number": 2
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 15.29,Page No.566"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "\n",
+ "#Initilization of Variables\n",
+ "\n",
+ "W2=10 #Weight placed on rough horizontal surface\n",
+ "W1_1=1.5 #N #Weight hanging free in air\n",
+ "W1=0.5 #N #additional weight added \n",
+ "T=1.5 #N #Tension in the string\n",
+ "R=10 #N #Normal Reaction\n",
+ "g=9.80\n",
+ "\n",
+ "#Calculation\n",
+ "\n",
+ "#Total Weight hanging in air\n",
+ "W=W1_1+W1\n",
+ "\n",
+ "#Max Frictional Force \n",
+ "F=T=1.5 #N\n",
+ "\n",
+ "#Coefficient of friction \n",
+ "mu=F*R**-1\n",
+ "\n",
+ "#Acceleration of two weights\n",
+ "a=g*(W-mu*W2)*(W+W2)**-1 #m/s**2 \n",
+ "\n",
+ "#Tension in the string\n",
+ "T1=W*W2*(1+mu)*(W+W2)**-1 #N\n",
+ "\n",
+ "#Result\n",
+ "print\"Acceleration of two weights is\",round(a,3),\"m/s**2\"\n",
+ "print\"Tension in the string\",round(T1,3),\"N\""
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "Acceleration of two weights is 0.408 m/s**2\n",
+ "Tension in the string 1.917 N\n"
+ ]
+ }
+ ],
+ "prompt_number": 3
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 15.30,Page No.568"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "\n",
+ "#Initilization of Variables\n",
+ "\n",
+ "W2=1500 #N #weight of body A\n",
+ "W1=1000 #N #Weight of body B\n",
+ "g=9.80\n",
+ "\n",
+ "#Coefficient of friction\n",
+ "mu=mu1=mu2=0.2\n",
+ "\n",
+ "#T1=1.3691*T2\n",
+ "\n",
+ "#Calculation\n",
+ "\n",
+ "#Acceleration\n",
+ "a=(W1-1.3691*mu*W2)*((W1*g**-1)+1.3691*W2*g**-1)**-1 #m/s**2\n",
+ "\n",
+ "#Tension in the string to which weight 1500 N is attached\n",
+ "T2=W2*g**-1*round(a,2)+mu*W2 #N\n",
+ "\n",
+ "#Tension in the string to which weight 1000 N is attached\n",
+ "T1=1.3691*round(T2,3)\n",
+ "\n",
+ "#Result\n",
+ "print\"Acceleration of the systems is\",round(a,2),\"m/s**2\"\n",
+ "print\"Tension in the string:T1\",round(T1,2),\"N\"\n",
+ "print\" :T2\",round(T2,2),\"N\"\n",
+ "\n",
+ "#Answer for T2 is incorrect in the book"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "Acceleration of the systems is 1.89 m/s**2\n",
+ "Tension in the string:T1 806.79 N\n",
+ " :T2 589.29 N\n"
+ ]
+ }
+ ],
+ "prompt_number": 4
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 15.31,Page No.573"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "from math import sin, cos, tan, radians, pi\n",
+ "\n",
+ "#Initilization of Variables\n",
+ "\n",
+ "W1=15 #N #Weight of hanging free in air\n",
+ "W2=40 #N #weight placed on inclined plane\n",
+ "theta=15 #degree #Inclination\n",
+ "g=9.80 #m/s**2 #Acceleration due to gravity\n",
+ "\n",
+ "#Calculation\n",
+ "\n",
+ "#Acceleration\n",
+ "a=g*(W1-W2*sin(theta*pi*180**-1))*(W1+W2)**-1 #m/s**2\n",
+ " \n",
+ "#Tension in string\n",
+ "T=W1*W2*(1+sin(theta*pi*180**-1))*(W1+W2)**-1 #N\n",
+ "\n",
+ "#Result\n",
+ "print\"Acceleration is\",round(a,2),\"m/s**2\"\n",
+ "print\"Tension in the string is\",round(T,2),\"N\""
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "Acceleration is 0.83 m/s**2\n",
+ "Tension in the string is 13.73 N\n"
+ ]
+ }
+ ],
+ "prompt_number": 5
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 15.32,Page No.573"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "from math import sin, cos, tan, radians, pi\n",
+ "\n",
+ "#Initilization of Variables\n",
+ "\n",
+ "W1=25 #N #Weight of hanging free in air\n",
+ "W2=40 #N #weight placed on inclined plane\n",
+ "theta=15 #degree #Inclination\n",
+ "g=9.80 #m/s**2 #Acceleration due to gravity\n",
+ "mu=0.2 #coefficient of friction\n",
+ "\n",
+ "#Calculation\n",
+ "\n",
+ "#Acceleration\n",
+ "a=g*(W1-W2*sin(theta*pi*180**-1)-mu*W2*cos(theta*pi*180**-1))*(W1+W2)**-1 #m/s**2\n",
+ "\n",
+ "#Tension\n",
+ "T=W1*W2*(1+sin(theta*pi*180**-1)+mu*cos(theta*pi*180**-1))*(W1+W2)**-1\n",
+ "\n",
+ "#Distance\n",
+ "u=0 #m/s\n",
+ "t=3 #sec\n",
+ "s=u*t+a*t**2*2**-1 #m\n",
+ "\n",
+ "#Result\n",
+ "print\"Acceleration is\",round(a,2),\"m/s**2\"\n",
+ "print\"Tension is\",round(T,2),\"N\"\n",
+ "print\"Distance moved by 25 N is\",round(s,2),\"m\""
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "Acceleration is 1.04 m/s**2\n",
+ "Tension is 22.34 N\n",
+ "Distance moved by 25 N is 4.69 m\n"
+ ]
+ }
+ ],
+ "prompt_number": 6
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 15.33,Page No.578"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "from math import sin, cos, tan, radians, pi\n",
+ "\n",
+ "#Initilization of Variables\n",
+ "\n",
+ "#For Circular Lamina\n",
+ "D=60 #cm\n",
+ "m=0.001 #kg/cm**2 #mass per unit area\n",
+ "\n",
+ "#For circular cyclinder\n",
+ "D2=80 #cm\n",
+ "h=15 #cm #height\n",
+ "m2=0.002 #kg/cm**3\n",
+ "\n",
+ "#For solid sphere\n",
+ "D3=40 #cm\n",
+ "m3=0.0015 #kg/cm**3\n",
+ "\n",
+ "#Calculation\n",
+ "\n",
+ "#For Circular Lamina\n",
+ "\n",
+ "#Radius\n",
+ "R=D*2**-1 #cm\n",
+ "\n",
+ "#Total Mass\n",
+ "M=m*pi*R**2 #kg\n",
+ "\n",
+ "#Moment of Inertia of circular section\n",
+ "I_zz=M*R**2*2**-1 #Kg/cm**2\n",
+ "\n",
+ "#Radius of Gyration For circular section\n",
+ "k=R*((2)**0.5)**-1 #cm\n",
+ "\n",
+ "#For circular cyclinder\n",
+ "\n",
+ "#Radius\n",
+ "R2=D2*2**-1 #cm\n",
+ "\n",
+ "#Total Mass\n",
+ "M2=m2*pi*R2**2*h #kg\n",
+ "\n",
+ "#Moment of Inertia of circular section\n",
+ "I_zz2=M2*R2**2*2**-1 #Kg/cm**2\n",
+ "\n",
+ "#Radius of Gyration For circular section\n",
+ "k2=R2*((2)**0.5)**-1 #cm\n",
+ "\n",
+ "#For solid sphere\n",
+ "\n",
+ "#Radius\n",
+ "R3=D3*2**-1 #cm\n",
+ "\n",
+ "#Total Mass\n",
+ "M3=m3*4*pi*R3**3*3**-1 #kg\n",
+ "\n",
+ "#Moment of Inertia of circular section\n",
+ "I_zz3=2*5**-1*M3*R3**2 #Kg/cm**2\n",
+ "\n",
+ "#Radius of Gyration For circular section\n",
+ "k3=R3*0.6324 #cm\n",
+ "\n",
+ "#Result\n",
+ "print\"M.I of Circular Lamina is\",round(I_zz,2),\"Kg/cm**2\"\n",
+ "print\"Radius of gyration of Circular Lamina is\",round(k,2),\"cm\"\n",
+ "\n",
+ "print\"M.I of circular cyclinder is\",round(I_zz2,2),\"Kg/cm**2\"\n",
+ "print\"Radius of gyration of circular cyclinder is\",round(k2,2),\"cm\"\n",
+ "\n",
+ "\n",
+ "print\"M.I of solid sphere is\",round(I_zz3,2),\"Kg/cm**2\"\n",
+ "print\"Radius of gyration of solid sphere is\",round(k3,2),\"cm\"\n"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "M.I of Circular Lamina is 1272.35 Kg/cm**2\n",
+ "Radius of gyration of Circular Lamina is 21.21 cm\n",
+ "M.I of circular cyclinder is 120637.16 Kg/cm**2\n",
+ "Radius of gyration of circular cyclinder is 28.28 cm\n",
+ "M.I of solid sphere is 8042.48 Kg/cm**2\n",
+ "Radius of gyration of solid sphere is 12.65 cm\n"
+ ]
+ }
+ ],
+ "prompt_number": 36
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 15.34,Page No.579"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "from math import sin, cos, tan, radians, pi\n",
+ "\n",
+ "#Initilization of Variables\n",
+ "\n",
+ "D=90 #cm #Diameter of grindstone\n",
+ "t=10 #cm #Thickness\n",
+ "m=0.0026 #kg/cm**3 #Mass per unit volume\n",
+ "\n",
+ "#Calculation\n",
+ "\n",
+ "#Radius\n",
+ "R=D*2**-1 #cm\n",
+ "\n",
+ "#Total Mass\n",
+ "M=m*pi*R**2*t #kg\n",
+ "\n",
+ "#M.I of of grindstone\n",
+ "I_zz=M*R**2*2**-1 #Kg/cm**2\n",
+ "\n",
+ "#Radius of gyration\n",
+ "k=R*((2)**0.5)**-1 #cm\n",
+ "\n",
+ "#Result\n",
+ "print\"M.I of Grindstone is\",round(I_zz,2),\"Kg/cm**2\"\n",
+ "print\"Radius of gyration is\",round(k,2),\"cm\""
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "M.I of Grindstone is 167472.41 Kg/cm**2\n",
+ "Radius of gyration is 31.82 cm\n"
+ ]
+ }
+ ],
+ "prompt_number": 7
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 15.35,Page No.581"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "from math import sin, cos, tan, radians, pi\n",
+ "\n",
+ "#Initilization of Variables\n",
+ "\n",
+ "W=1000 #N #Weight of flying wheel\n",
+ "k=0.5 #m\n",
+ "T=1200 #N*m #Torque\n",
+ "g=9.80 #m/s**2\n",
+ "\n",
+ "#Calculation\n",
+ "\n",
+ "#MAss of flywheel\n",
+ "M=W*g**-1 #Kg\n",
+ "\n",
+ "#Moment of Inertia\n",
+ "I=M*k**2 #Kg/m**2\n",
+ "\n",
+ "#Angular Acceleration\n",
+ "alpha=T*I**-1 #radians/s**2\n",
+ "\n",
+ "#Result\n",
+ "print\"Angular Acceleration of flywheel is\",round(alpha,2),\"radians/s**2\""
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "Angular Acceleration of flywheel is 47.04 radians/s**2\n"
+ ]
+ }
+ ],
+ "prompt_number": 38
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 15.35(A),Page No.582"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "\n",
+ "#Initilization of Variables\n",
+ "\n",
+ "I=12 #Kg*m**2 #M.I of circular disc\n",
+ "t=3 #s #Time\n",
+ "T=800 #N*m #Torque\n",
+ "w_o=0 #m/s #Angular velocity initially\n",
+ "\n",
+ "#Calculation\n",
+ "\n",
+ "alpha=T*I**-1 #radians/s**2\n",
+ "\n",
+ "#Angular velocity after 3 seconds\n",
+ "w=w_o+alpha*t #rad/s\n",
+ "\n",
+ "#Result\n",
+ "print\"angular Velocity after 3 seconds\",round(w,2),\"rad/s\""
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "angular Velocity after 3 seconds 200.0 rad/s\n"
+ ]
+ }
+ ],
+ "prompt_number": 39
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 15.36,Page No.582"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "from math import sin, cos, tan, radians, pi\n",
+ "\n",
+ "#Initilization of Variables\n",
+ "\n",
+ "M=5000 #kg #Mass of flywheel\n",
+ "k=1 #m #radius of gyration \n",
+ "N_o=400 #r.p.m #Initial Velocity\n",
+ "N=280 #r.p.m #Final speed\n",
+ "t=120 #seconds #Time\n",
+ "\n",
+ "#Calculation\n",
+ "\n",
+ "#Initial Angular velocity\n",
+ "w_o=2*pi*N_o*60**-1 #rad/s\n",
+ "\n",
+ "#Final Angular velocity\n",
+ "w=2*pi*N*60**-1 #rad/s \n",
+ "\n",
+ "#M.I\n",
+ "I=M*k**2 #kg/m**2\n",
+ "\n",
+ "#Angular acceleration\n",
+ "alpha=(w-w_o)*t**-1 #rad/s**2\n",
+ "\n",
+ "#Torque\n",
+ "T=-M*alpha #N*m\n",
+ "\n",
+ "#Final K.E\n",
+ "E2=round(w,2)**2*I*2**-1 #N*m\n",
+ "\n",
+ "#Initial K.E\n",
+ "E1=41.88**2*I*2**-1 #N*m\n",
+ "\n",
+ "#Change in K.E\n",
+ "E=E2-E1 #N*m\n",
+ "\n",
+ "#Initial Momentum\n",
+ "p1=I*round(w,2) #N*m/s\n",
+ "\n",
+ "#Final Momentum\n",
+ "p2=I*41.88 #N*m/s\n",
+ "\n",
+ "#Change in angular Momentum\n",
+ "p=p2-p1 #N*m/s\n",
+ "\n",
+ "#Result\n",
+ "print p1\n",
+ "print\"Retading Torque acting is\",round(T,2),\"N*m\"\n",
+ "print\"Change in K.E is\",round(E,2),\"N*m\"\n",
+ "print\"Change in Angular Momentum is\",round(p,2),\"N*m/s\""
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "146600.0\n",
+ "Retading Torque acting is 523.6 N*m\n",
+ "Change in K.E is -2235680.0 N*m\n",
+ "Change in Angular Momentum is 62800.0 N*m/s\n"
+ ]
+ }
+ ],
+ "prompt_number": 8
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 15.37,Page No.583"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "\n",
+ "#Initilization of Variables\n",
+ "\n",
+ "V=0.2 #m/s #Linear Velocity\n",
+ "W=0.1 #N #Weight of cyclinder\n",
+ "R=0.1 #m #Radius\n",
+ "g=9.81 #m/s**2 #Acceleration due to gravity\n",
+ "\n",
+ "#Calculation\n",
+ "\n",
+ "#Mass \n",
+ "M=W*g**-1 #Mass\n",
+ "\n",
+ "#M.I\n",
+ "I=M*R**2*2**-1 \n",
+ "\n",
+ "#Angular Velocity\n",
+ "w=V*R**-1 #rad/s\n",
+ "\n",
+ "#Total K.E\n",
+ "E=(I*w**2+M*V**2)*2**-1 #N*m\n",
+ "\n",
+ "#Result\n",
+ "print\"Total Kinetic Energy is\",round(E,6),\"N*m\""
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "Total Kinetic Energy is 0.000306 N*m\n"
+ ]
+ }
+ ],
+ "prompt_number": 41
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 15.38,Page No.584"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "from math import sin, cos, tan, radians, pi\n",
+ "\n",
+ "#Initilization of Variables\n",
+ "\n",
+ "k=0.5 #m #Radius of Gyration\n",
+ "W=6000 #N #Weight of flywheel\n",
+ "N_o=0 #Initial r.p.m\n",
+ "N=200 #Final r.p.m \n",
+ "t=120 #seconds\n",
+ "g=9.80 #m/s**2\n",
+ "\n",
+ "#Calculation\n",
+ "\n",
+ "#MAss\n",
+ "M=W*g**-1 #Kg\n",
+ "\n",
+ "#Initial Angular Velocity\n",
+ "w_o=2*pi*N_o*60**-1 \n",
+ "\n",
+ "#Final Angular Velocity\n",
+ "w=2*pi*N*60**-1 #rad/s\n",
+ "\n",
+ "#M.I\n",
+ "I=M*k**2 \n",
+ "\n",
+ "#Angular acceleration\n",
+ "alpha=(w-w_o)*t**-1 #rad/s**2\n",
+ "\n",
+ "#Torque Exerted\n",
+ "T=I*alpha #N*m\n",
+ "\n",
+ "#Result\n",
+ "print\"Average Torque exerted is\",round(T,2),\"N*m\"\n",
+ "\n",
+ "#Answer for M.I is incorrect so value of Torque in book is incorrect"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "Average Torque exerted is 26.71 N*m\n"
+ ]
+ }
+ ],
+ "prompt_number": 9
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 15.38(A),Page No.585"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "from math import sin, cos, tan, radians, pi\n",
+ "\n",
+ "#Initilization of Variables\n",
+ "\n",
+ "#weights\n",
+ "W_A=100 #N\n",
+ "W_B=180 #N\n",
+ "\n",
+ "#Radii\n",
+ "r_A=0.1 #m \n",
+ "r_B=0.15 #m\n",
+ "\n",
+ "#RAdius of gyration\n",
+ "k_A=0.08 #m \n",
+ "k_B=0.13 #m\n",
+ "\n",
+ "theta=30 #degree #Inclination of plane\n",
+ "g=9.81 #m/s**2 #Acceleration due to gravity\n",
+ "\n",
+ "#Calculation\n",
+ "\n",
+ "#Wheel A\n",
+ "\n",
+ "#Angular acceleration \n",
+ "alpha_A=(W_A*sin(theta*pi*180**-1)*r_A)*(W_A*g**-1*(k_A**2+r_A**2))**-1 #rad/s\n",
+ "\n",
+ "#Linear acc. of wheel \n",
+ "alpha_A_a=alpha_A*r_A #m/s**2\n",
+ "\n",
+ "#Wheel B\n",
+ "\n",
+ "#Angular acceleration\n",
+ "alpha_B=W_B*sin(theta*pi*180**-1)*r_B*((W_B*g**-1*(k_B**2+r_B**2)))**-1\n",
+ "\n",
+ "#Linear acc. of wheel \n",
+ "alpha_B_b=alpha_B*r_B #m/s**2\n",
+ "\n",
+ "#Acceleration of A with respect to B\n",
+ "a_A_B=-(round(alpha_B_b,2)-round(alpha_A_a,2))\n",
+ "\n",
+ "#Result\n",
+ "print\"Acceleration of A with respect to B\",a_A_B,\"m/s**2\""
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "Acceleration of A with respect to B 0.19 m/s**2\n"
+ ]
+ }
+ ],
+ "prompt_number": 10
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 15.39,Page No.589"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "\n",
+ "#Initilization of Variables\n",
+ "\n",
+ "W=5 #N #Weight suspended by arope\n",
+ "W_o=50 #N #Weight of pulley\n",
+ "R=0.3 #m #Radius of pulley\n",
+ "g=9.81 #m/s**2\n",
+ "\n",
+ "#Calculation\n",
+ "\n",
+ "#Acceleration\n",
+ "a=g*W*(W+W_o*2**-1)**-1 #m/s**2\n",
+ "\n",
+ "#Tension in the string\n",
+ "T=W*W_o*(2*W+W_o)**-1 #N\n",
+ "\n",
+ "#Result\n",
+ "print\"Acceleration is\",round(a,2),\"m/s**2\"\n",
+ "print\"Tension in the string is\",round(T,2),\"N\""
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "Acceleration is 1.64 m/s**2\n",
+ "Tension in the string is 4.17 N\n"
+ ]
+ }
+ ],
+ "prompt_number": 44
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 15.40,Page No.590"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "\n",
+ "#Initilization of Variables\n",
+ "\n",
+ "W1=100 #N #bigger Weight\n",
+ "W2=40 #N #Smaller Weight\n",
+ "W_o=50 #N #Weight of pulley\n",
+ "g=9.80\n",
+ "\n",
+ "#Calculation\n",
+ "\n",
+ "#Acceleration \n",
+ "a=g*(W1-W2)*(W1+W2+W_o*2**-1)**-1 #m/s**2\n",
+ "\n",
+ "#TEnsion T1\n",
+ "T1=W1*(2*W2+W_o*2**-1)*(W1+W2+W_o*2**-1)**-1 #N\n",
+ "\n",
+ "#Tension T2\n",
+ "T2=W2*(2*W1+W_o*2**-1)*(W1+W2+W_o*2**-1)**-1 #N\n",
+ "\n",
+ "#Result\n",
+ "print\"Acceleration of block is\",round(a,2),\"m/s**2\"\n",
+ "print\"Tension T1\",round(T1,2),\"N\"\n",
+ "print\"Tension T2\",round(T2,2),\"N\""
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "Acceleration of block is 3.56 m/s**2\n",
+ "Tension T1 63.64 N\n",
+ "Tension T2 54.55 N\n"
+ ]
+ }
+ ],
+ "prompt_number": 11
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 15.41,Page No.591"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "\n",
+ "#Initilization of Variables\n",
+ "\n",
+ "W=2940 #N #Weight of cage\n",
+ "D=1.20 #m #Diameter of drum\n",
+ "R=0.6 #m #Radius of drum\n",
+ "W_o=735 #N #Weight of drum\n",
+ "k=0.55 #m #Radius of gyration\n",
+ "T1=4000 #N*m #Constant Torque Exerted by motor\n",
+ "g=9.8 #m/s**2 #Acceleration due to gravity\n",
+ "\n",
+ "#Calculation\n",
+ "\n",
+ "\n",
+ "#Mass of the cage\n",
+ "M=W*g**-1 #Kg\n",
+ "\n",
+ "#Net Force\n",
+ "#(P-W)=M*a ........................1\n",
+ "\n",
+ "#M.I of Drum\n",
+ "I=W_o*g**-1*k**2 \n",
+ "\n",
+ "#Torque on Drum\n",
+ "#(T1-R*P)=I*alpha ..................(2)\n",
+ "\n",
+ "#Angular Acceleration\n",
+ "#alpha=(a*R**-1)\n",
+ "\n",
+ "#Sub value of I and alpha in equation 2 we get\n",
+ "#(4000-0.6*P)=37.8125*a ...................3\n",
+ "\n",
+ "#After multipliying equation 1 by R we get\n",
+ "#(R*P-R*W)=R*M*a .............................4\n",
+ "\n",
+ "#Adding equations 3 and 4 we get equation as\n",
+ "#(4000-0.6*2940)=37.8125*a+0.6*300*a\n",
+ "#AFter further simplifying we get\n",
+ "a=2236*(217.8125)**-1 #m/s**2 #Acceleration\n",
+ "\n",
+ "#Sub value of a in equation 1 \n",
+ "P=M*a+W #N\n",
+ "\n",
+ "#PArt-2\n",
+ "#Time Required to raise the cage 20 m from ground\n",
+ "\n",
+ "u=0 #m/s #Initial Velocity\n",
+ "a=10.265 #m/s**2 #acceleraation\n",
+ "s=20 #m #Height from ground\n",
+ "\n",
+ "#time required\n",
+ "t=((2*s)*a**-1)**0.5 #s\n",
+ "\n",
+ "#Result\n",
+ "print\"Acceleration of the cage is\",round(a,2),\"m/s**2\"\n",
+ "print\"Tension in the cage is\",round(P,2),\"N\"\n",
+ "print\"Time required to raise the cage 20 m from ground\",round(t,2),\"s\""
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "Acceleration of the cage is 10.27 m/s**2\n",
+ "Tension in the cage is 6019.71 N\n",
+ "Time required to raise the cage 20 m from ground 1.97 s\n"
+ ]
+ }
+ ],
+ "prompt_number": 46
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 15.42,Page No.593"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "\n",
+ "#Initilization of Variables\n",
+ "\n",
+ "W_o=100 #N #Weight of cyclinder\n",
+ "W=10 #N #Weight of block\n",
+ "D=1 #m #diameter of cyclinder\n",
+ "R=0.5 #m #Radius of cyclinder\n",
+ "g=9.80 #m/s**2 #Acceleration due to gravity\n",
+ "\n",
+ "#Calculation\n",
+ "\n",
+ "#Mass of block\n",
+ "M=W*g**-1 #Kg\n",
+ "\n",
+ "#Net Force\n",
+ "#(W-P)=W1*g**-1*alpha .........................1\n",
+ "\n",
+ "#M.I\n",
+ "I=M*R**2*2**-1 #kgm**2\n",
+ "\n",
+ "#Torque equation\n",
+ "#T=I*alpha \n",
+ "\n",
+ "#Multiplying equation of net force with 2 we get\n",
+ "#P=25*g**-1*alpha ..............................2\n",
+ "\n",
+ "#Adding equations 1 and 2 we get\n",
+ "alpha=W*3.06**-1 #rad/s**2\n",
+ "\n",
+ "#Initial velocity\n",
+ "u=0 #m/s\n",
+ "t=2 #sec #time\n",
+ "\n",
+ "#Angular acceleration \n",
+ "alpha=3.268 #rad/s**2\n",
+ "\n",
+ "#Angular Velocity\n",
+ "u_o=u+alpha*t\n",
+ "\n",
+ "#Result\n",
+ "print\"Angular Velocity after 2 seconds is\",round(u_o,2),\"m/s**2\""
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "Angular Velocity after 2 seconds is 6.54 m/s**2\n"
+ ]
+ }
+ ],
+ "prompt_number": 47
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 15.43,Page No.595"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "\n",
+ "#Initilization of Variables\n",
+ "\n",
+ "W1=100 #N #Weight of Block\n",
+ "W2=300 #N #weight of pulley\n",
+ "k=0.25 #m #Radius of gyration\n",
+ "r_A=0.2 #m #Radius of pulley A\n",
+ "r_B=0.3 #m #Radius of pulley B\n",
+ "g=9.81 #m/s**2 #Acceleration due to gravity\n",
+ "\n",
+ "#Calculation\n",
+ "\n",
+ "#Motion of block B\n",
+ "#(W1-T_B)=W1*g**-1*r_B*alpha ..................1\n",
+ "\n",
+ "#Motion of block A\n",
+ "#(T_A-W1)=W1*g**-1*r_A*alpha ..................2\n",
+ "\n",
+ "#M.I of pulley\n",
+ "I=W2*g**-1*k**2\n",
+ "\n",
+ "#Rotation of pulley\n",
+ "#T_B*r_B-T_A*r_A=I*alpha .....................3\n",
+ "\n",
+ "#After multiplying equation 1 by r_B we get\n",
+ "#30-r_B*T_B=W1*g**-1*r_B*alpha ..................4 \n",
+ "\n",
+ "#After multiplying equation 2 by r_A we get\n",
+ "#0.2*T_A-20=W1*g**-1*r_A*alpha ..................5\n",
+ "\n",
+ "#Adding equations 3,4,5 and further simplifying we get\n",
+ "alpha=10*g*31.75**-1 #Rad/s**2\n",
+ "\n",
+ "#Linear acceleration of pulley\n",
+ "alpha_B=0.3*alpha #m/s**2\n",
+ "alpha_A=0.2*alpha #m/s**2 \n",
+ "\n",
+ "#Tension in strings\n",
+ "T_A=W1+W1*g**-1*alpha_A #N\n",
+ "T_B=W1-W1*g**-1*alpha_B #N\n",
+ "\n",
+ "\n",
+ "#Result\n",
+ "print\"Angular Acceleration of pulley\",round(alpha,2),\"rad/s**2\"\n",
+ "print\"Linear acceleration of blocks A and B:alpha_A\",round(alpha_A,2),\"rad/s**2\"\n",
+ "print\" :alpha_B\",round(alpha_B,2),\"rad/s**2\"\n",
+ "print\"Tension in the strings\",round(T_A,2),\"N\"\n",
+ "print\" \",round(T_B,2),\"N\""
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "Angular Acceleration of pulley 3.09 rad/s**2\n",
+ "Linear acceleration of blocks A and B:alpha_A 0.62 rad/s**2\n",
+ " :alpha_B 0.93 rad/s**2\n",
+ "Tension in the strings 106.3 N\n",
+ " 90.55 N\n"
+ ]
+ }
+ ],
+ "prompt_number": 10
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 15.44,Page No.598"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "\n",
+ "#Initilization of Variables\n",
+ "\n",
+ "#Weights\n",
+ "W1=200 #N\n",
+ "W2=800 #N\n",
+ "\n",
+ "F=400 #N #Force applied\n",
+ "mu=0.3 #Coefficient of friction\n",
+ "g=9.80 #m/s**2 #Acceleration due to gravity\n",
+ "\n",
+ "#Calculation\n",
+ "\n",
+ "#Total Weights\n",
+ "W=W1+W2 #N\n",
+ "\n",
+ "#Total Mass \n",
+ "M=W*g**-1 #Kg\n",
+ "\n",
+ "#Force of friction\n",
+ "F2=mu*W #N\n",
+ "\n",
+ "#acceleration\n",
+ "a=-((-F+F2)*g)*W**-1 #m/s**2 \n",
+ "\n",
+ "#PArt-2\n",
+ "\n",
+ "#Force of Friction\n",
+ "F3=mu*W1 #N\n",
+ "\n",
+ "#Reverse Effective Force on it\n",
+ "F4=W1*g**-1*a #N\n",
+ "\n",
+ "#Tension in thread\n",
+ "T=F3+F4 #N\n",
+ "\n",
+ "#Result\n",
+ "print\"acceleration of the weights is\",round(a,2),\"m/s**2\"\n",
+ "print\"Tension in the string is\",round(T,2),\"N\""
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "acceleration of the weights is 0.98 m/s**2\n",
+ "Tension in the string is 80.0 N\n"
+ ]
+ }
+ ],
+ "prompt_number": 48
+ }
+ ],
+ "metadata": {}
+ }
+ ]
+}
\ No newline at end of file diff --git a/Engineering_Mechanics/chapter_16.ipynb b/Engineering_Mechanics/chapter_16.ipynb new file mode 100644 index 00000000..0dce522c --- /dev/null +++ b/Engineering_Mechanics/chapter_16.ipynb @@ -0,0 +1,1312 @@ +{
+ "metadata": {
+ "name": "chapter_16.ipynb"
+ },
+ "nbformat": 3,
+ "nbformat_minor": 0,
+ "worksheets": [
+ {
+ "cells": [
+ {
+ "cell_type": "heading",
+ "level": 1,
+ "metadata": {},
+ "source": [
+ "Chapter 16:Simple Harmonic Motion And Mechanical Vibrations"
+ ]
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 16.1,Page No.615"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "from math import sin, cos, radians, pi\n",
+ "import numpy as np\n",
+ "\n",
+ "\n",
+ "#Declaration Of Variables\n",
+ "\n",
+ "t=0.3 #s #Time\n",
+ "r=0.8 #m #Amplitude\n",
+ "T=1.6 #s #Period of oscillations\n",
+ "\n",
+ "#Calculations\n",
+ "\n",
+ "#frequency\n",
+ "f=2*pi*T**-1 #rad/s\n",
+ "\n",
+ "#Velocity\n",
+ "v=round(f,3)*r*sin(round(f,3)*t) #m/s\n",
+ "\n",
+ "#Accleration\n",
+ "a=f**2*r*cos(f*t) #m/s**2\n",
+ "\n",
+ "#Value for acceleration in textbook is incorrect\n",
+ "\n",
+ "#Result\n",
+ "print\"Velocity is\",round(v,2),\"m/s\"\n",
+ "print\"Acceleration is\",round(a,2),\"m/s**2\""
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "Velocity is 2.9 m/s\n",
+ "Acceleration is 4.72 m/s**2\n"
+ ]
+ }
+ ],
+ "prompt_number": 1
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 16.2,Page No.615"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "from math import sin, cos, radians, pi\n",
+ "import numpy as np\n",
+ "\n",
+ "#Declaration Of Variables\n",
+ "\n",
+ "r=1 #m #Amplitude\n",
+ "T=2 #s #Period of oscillations\n",
+ "\n",
+ "#Calculations\n",
+ "\n",
+ "#Time taken by body from mid pos\n",
+ "t=T*5**-1 #s\n",
+ "\n",
+ "#Time taken by body from extreme position to mid position\n",
+ "t2=T*4**-1 #s\n",
+ "\n",
+ "#time taken by body fom extreme position\n",
+ "t3=t2-t #s\n",
+ "\n",
+ "#Angular velocity\n",
+ "f=2*pi*T**-1 #rad/s\n",
+ "\n",
+ "#Velocity\n",
+ "v=-f*r*sin(f*t3) #m/s\n",
+ "\n",
+ "#Value of velocity in book is incorrect in textbook i.e 0.09831\n",
+ "\n",
+ "#Acceleration\n",
+ "a=-f**2*r*cos(pi*t3) #m/s**2\n",
+ "\n",
+ "#Result\n",
+ "print\"Velocity is\",round(v,2),\"m/s\"\n",
+ "print\"Acceleration is\",round(a,2),\"m/s**2\""
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "Velocity is -0.97 m/s\n",
+ "Acceleration is -9.39 m/s**2\n"
+ ]
+ }
+ ],
+ "prompt_number": 1
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 16.3,Page No.616"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "from math import sin, cos, radians, pi\n",
+ "import numpy as np\n",
+ "\n",
+ "\n",
+ "#Declaration Of Variables\n",
+ "\n",
+ "t=0.4 #s #Time\n",
+ "r=1 #m #Amplitude\n",
+ "T=2 #s #Period of oscillations\n",
+ "\n",
+ "#Calculations\n",
+ "\n",
+ "#frequency\n",
+ "f=2*pi*T**-1 #rad/s\n",
+ "\n",
+ "#Velocity\n",
+ "v=round(f,3)*r*sin(round(f,3)*t) #m/s\n",
+ "\n",
+ "#Accleration\n",
+ "a=f**2*r*cos(f*t) #m/s**2\n",
+ "\n",
+ "#Value for acceleration in textbook is incorrect\n",
+ "\n",
+ "#Result\n",
+ "print\"Velocity is\",round(v,2),\"m/s\"\n",
+ "print\"Acceleration is\",round(a,2),\"m/s**2\""
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "Velocity is 2.99 m/s\n",
+ "Acceleration is 3.05 m/s**2\n"
+ ]
+ }
+ ],
+ "prompt_number": 2
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 16.4,Page No.617"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "\n",
+ "#Declaration Of Variables\n",
+ "\n",
+ "N=100 #r.p.m #Speed of crank\n",
+ "\n",
+ "#Calculations\n",
+ "\n",
+ "#Angular velocity\n",
+ "f=2*pi*N*60**-1 #rad/s \n",
+ "\n",
+ "#Stroke of piston\n",
+ "n=1.8 #cm\n",
+ "\n",
+ "#Ampiltude\n",
+ "r=n*2**-1 #m\n",
+ "\n",
+ "#Displacement of piston from centre\n",
+ "x=0.6 #m\n",
+ "\n",
+ "\n",
+ "#Let f*t=y\n",
+ "#Displacement\n",
+ "y=arccos(x*r**-1)*(180*pi**-1)\n",
+ "\n",
+ "#Velocity of piston\n",
+ "v=-f*r*sin(y*180**-1*pi)\n",
+ "\n",
+ "#Acceleration of piston\n",
+ "a=-f**2*r*cos(y*180**-1*pi) #m/s**2\n",
+ "\n",
+ "#Result\n",
+ "print\"Velocity is\",round(v,2),\"m/s\"\n",
+ "print\"Acceleration is\",round(a,2),\"m/s**2\""
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "Velocity is -7.02 m/s\n",
+ "Acceleration is -65.8 m/s**2\n"
+ ]
+ }
+ ],
+ "prompt_number": 9
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 16.5,Page No.617"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "from math import sin, cos, radians, pi\n",
+ "import numpy as np\n",
+ "\n",
+ "#Declaration Of Variables\n",
+ "\n",
+ "#Velocities of Body\n",
+ "v1=8 #m/s\n",
+ "v2=3 #m/s\n",
+ "\n",
+ "#Distance of Body\n",
+ "x1=1.5 #m #When v1=8 #m/s\n",
+ "x2=2.5 #m #When v2=3 #m/s\n",
+ "\n",
+ "#Calculations\n",
+ "\n",
+ "#For 1st velocity\n",
+ "#v1=-f*((r**2-x1**2))**2\n",
+ "#After Substituting values and further simplifying we get\n",
+ "#8=-f*((r**2-1.5**2))**2 ..........................................1\n",
+ "\n",
+ "#For 2nd velocity\n",
+ "#v2=-f*((r**2-x2**2))**2\n",
+ "#After Substituting values and further simplifying we get\n",
+ "#3=-f*((r**2-2.5**2))**2 ..........................................2\n",
+ "\n",
+ "#Dividing equations 1 and 2 and further simplifying we get\n",
+ "#Amplitude\n",
+ "r=(42.19*6.111**-1)**0.5 #m \n",
+ "\n",
+ "#Sub value of r in equation 2 we get\n",
+ "f=v2*(((r**2-x2**2))**0.5)**-1 #rad/s\n",
+ "\n",
+ "#Period\n",
+ "T=2*pi*f**-1 #s\n",
+ "\n",
+ "#Result\n",
+ "print\"Amplitude of Body is\",round(r,2),\"m\"\n",
+ "print\"Period of Body is\",round(T,2),\"s\""
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "Amplitude of Body is 2.63 m\n",
+ "Period of Body is 1.69 s\n"
+ ]
+ }
+ ],
+ "prompt_number": 3
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 16.6,Page No.618"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "from math import sin, cos, radians, pi\n",
+ "import numpy as np\n",
+ "\n",
+ "#Declaration Of Variables\n",
+ "\n",
+ "#Velocities of Body\n",
+ "v1=12 #m/s\n",
+ "v2=3 #m/s\n",
+ "\n",
+ "#Distance of Body\n",
+ "x1=0.05 #m #When v1=8 #m/s\n",
+ "x2=0.1 #m #When v2=3 #m/s\n",
+ "x=0.075 #m\n",
+ "\n",
+ "#Calculations\n",
+ "\n",
+ "#For 1st velocity\n",
+ "#v1=-f*((r**2-x1**2))**2\n",
+ "#After Substituting values and further simplifying we get\n",
+ "#12=-f*((r**2-0.05**2))**2 ..........................................1\n",
+ "\n",
+ "#For 2nd velocity\n",
+ "#v2=-f*((r**2-x2**2))**2\n",
+ "#After Substituting values and further simplifying we get\n",
+ "#3=-f*((r**2-0.1**2))**2 ..........................................2\n",
+ "\n",
+ "#Dividing equations 1 and 2 and further simplifying we get\n",
+ "#Amplitude\n",
+ "r=(0.1575*15**-1)**0.5 #m \n",
+ "\n",
+ "#Sub value of r in equation 2 we get\n",
+ "f=v2*(((r**2-x2**2))**0.5)**-1 #rad/s\n",
+ "\n",
+ "#Frequency\n",
+ "n=f*(2*pi)**-1 #cycles/s\n",
+ "\n",
+ "#Acceleration\n",
+ "a=f**2*x\n",
+ "\n",
+ "#Result\n",
+ "print\"Frequency of motion is\",round(f,2),\"rad/s\"\n",
+ "print\"Amplitude of motion is\",round(r,4),\"m\"\n",
+ "print\"Acceleration when the displacement is 75 mm is\",round(a,2),\"m/s**2\""
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "Frequency of motion is 134.16 rad/s\n",
+ "Amplitude of motion is 0.1025 m\n",
+ "Acceleration when the displacement is 75 mm is 1350.0 m/s**2\n"
+ ]
+ }
+ ],
+ "prompt_number": 4
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 16.7,Page No.619"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "from math import sin, cos, radians, pi\n",
+ "import numpy as np\n",
+ "\n",
+ "#Declaration Of Variables\n",
+ "\n",
+ "r=4.5 #m #amplitude\n",
+ "T=3.5 #s #Period\n",
+ "x1=3.5 #m #Distance of 1st point from centre\n",
+ "x2=1.5 #m #Distsnce of 2nd point from centre\n",
+ "\n",
+ "#Calculations\n",
+ "\n",
+ "#Angular velocity\n",
+ "f=2*pi*T**-1 #rad/s\n",
+ "\n",
+ "#For 1st point\n",
+ "#x1=r*cos(f*t1)\n",
+ "#After substituting and further simplifying \n",
+ "t1=0.6796*1.795**-1\n",
+ "\n",
+ "#For second point\n",
+ "#x2=r*cos(f*t2)\n",
+ "#After substituting and further simplifying \n",
+ "t2=1.231*1.795**-1\n",
+ "\n",
+ "#Time required by body in passing between two points\n",
+ "t=t2-t1 #s\n",
+ "\n",
+ "#Result\n",
+ "print\"Time required by body in passing between two points is\",round(t,2),\"s\""
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "Time required by body in passing between two points is 0.31 s\n"
+ ]
+ }
+ ],
+ "prompt_number": 5
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 16.8,Page No.620"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "from math import sin, cos, radians, pi\n",
+ "import numpy as np\n",
+ "\n",
+ "#Declaration Of Variables\n",
+ "\n",
+ "#Velocities of Body\n",
+ "v1=6 #m/s\n",
+ "v2=3 #m/s\n",
+ "\n",
+ "#Distance of Body\n",
+ "x1=0.125 #m #When v1=6 #m/s\n",
+ "x2=0.200 #m #When v2=3 #m/s\n",
+ "\n",
+ "W=0.2 #kg #Weight of cross head\n",
+ "g=9.81 #Acceleration due to gravity\n",
+ "\n",
+ "\n",
+ "#Calculations\n",
+ "\n",
+ "#For 1st velocity\n",
+ "#v1=-f*((r**2-x1**2))**2\n",
+ "#After Substituting values and further simplifying we get\n",
+ "#6=-f*((r**2-0.125**2))**2 ..........................................1\n",
+ "\n",
+ "#For 2nd velocity\n",
+ "#v2=-f*((r**2-x2**2))**2\n",
+ "#After Substituting values and further simplifying we get\n",
+ "#3=-f*((r**2-0.200**2))**2 ..........................................2\n",
+ "\n",
+ "#Dividing equations 1 and 2 and further simplifying we get\n",
+ "#Amplitude\n",
+ "r=(0.1444*3**-1)**0.5 #m \n",
+ "\n",
+ "#Sub value of r in equation 2 we get\n",
+ "f=v2*(((round(r,4)**2-x2**2))**0.5)**-1 #rad/s\n",
+ "\n",
+ "#Period\n",
+ "T=2*pi*f**-1 #s\n",
+ "\n",
+ "#Max Velocity\n",
+ "V_max=f*r #m/s\n",
+ "\n",
+ "#mass of cross head\n",
+ "m=W*g**-1 #N\n",
+ "\n",
+ "#Max acceleration\n",
+ "a_max=round(f,2)**2*round(r,4) #m/s**2\n",
+ "\n",
+ "#Max Force\n",
+ "F_max=m*a_max\n",
+ "\n",
+ "#Result\n",
+ "print\"Amplitude of vibration is\",round(r,2),\"m\"\n",
+ "print\"Max Velocity is\",round(V_max,2),\"m/s\"\n",
+ "print\"period of Vibration is\",round(T,2),\"s\"\n",
+ "print\"MAx Force in direction of motion\",round(F_max,2),\"Kg*f\""
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "Amplitude of vibration is 0.22 m\n",
+ "Max Velocity is 7.3 m/s\n",
+ "period of Vibration is 0.19 s\n",
+ "MAx Force in direction of motion 4.95 Kg*f\n"
+ ]
+ }
+ ],
+ "prompt_number": 6
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 16.9,Page No.621"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "from math import sin, cos, radians, pi\n",
+ "import numpy as np\n",
+ "\n",
+ "\n",
+ "#Declaration Of Variables\n",
+ "\n",
+ "#Distance of Body\n",
+ "x1=0.07 #m #When v1=0.6*V_max #m/s\n",
+ "x2=0.05 #m #When v2 #m/s\n",
+ "T=7.5 #s #Time to perform oscillation\n",
+ "\n",
+ "#Calculations\n",
+ "\n",
+ "#Equation of velocity\n",
+ "#v=-f*((r**2-x**2)**0.5) ..................1\n",
+ "\n",
+ "#Velocity\n",
+ "#v=0.6*V_max ........2\n",
+ "#x=x1 ................3\n",
+ "\n",
+ "#Frequency\n",
+ "f=2*pi*T**-1 #rad/s\n",
+ "\n",
+ "#MAx Velocity\n",
+ "#V_max=-f*r ............4\n",
+ "\n",
+ "#Sub all values in equation 1 and further simplifying we get\n",
+ "r=(0.0049*0.64**-1)**0.5\n",
+ "\n",
+ "#Velocity \n",
+ "v=f*((r**2-x2**2)**0.5)\n",
+ "\n",
+ "#Max Acceleration\n",
+ "a_max=f**2*r\n",
+ "\n",
+ "#Result\n",
+ "print\"Amplitude of motion is\",round(r,4),\"m\"\n",
+ "print\"Velocity of particle is\",round(v,2),\"m/s\"\n",
+ "print\"MAx Acceleration is\",round(a_max,4),\"m/s**2\""
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "Amplitude of motion is 0.0875 m\n",
+ "Velocity of particle is 0.06 m/s\n",
+ "MAx Acceleration is 0.0614 m/s**2\n"
+ ]
+ }
+ ],
+ "prompt_number": 7
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 16.10,Page No.625"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "from math import sin, cos, radians, pi\n",
+ "import numpy as np\n",
+ "\n",
+ "#Declaration Of Variables\n",
+ "\n",
+ "W=50 #N #Weight attached\n",
+ "n=4 #No. of oscillation\n",
+ "T=0.25 #s #Period of oscillation\n",
+ "\n",
+ "#Calculations\n",
+ "\n",
+ "#Static Extension\n",
+ "P=(T*(2*pi)**-1)**2*9.81*100 #cm\n",
+ "\n",
+ "#Stiffness of spring\n",
+ "k=W*round(P,2)**-1 #N/cm\n",
+ "\n",
+ "#Result\n",
+ "print\"Stiffness of spring is\",round(k,2),\"N/cm\""
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "Stiffness of spring is 32.26 N/cm\n"
+ ]
+ }
+ ],
+ "prompt_number": 8
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 16.11,Page No.625"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "from math import sin, cos, radians, pi\n",
+ "import numpy as np\n",
+ "\n",
+ "#Declaration Of Variables\n",
+ "\n",
+ "C=150 #N/m #Stiffness\n",
+ "T=1.5 #s #PEriod time\n",
+ "\n",
+ "#Calculations\n",
+ "\n",
+ "#Static Extension\n",
+ "P=(T*(2*pi)**-1)**2*9.81\n",
+ "\n",
+ "#Weight Attached\n",
+ "W=C*P #N\n",
+ "\n",
+ "#Result\n",
+ "print\"Weight attached to spring\",round(W,2),\"N\""
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "Weight attached to spring 83.87 N\n"
+ ]
+ }
+ ],
+ "prompt_number": 16
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 16.12,Page No.626"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "from math import sin, cos, radians, pi\n",
+ "import numpy as np\n",
+ "\n",
+ "#Declaration Of Variables\n",
+ "\n",
+ "#Frequency\n",
+ "n1=12 #cycles/s #when Weight W1=W\n",
+ "n2=10 #cycles/s #when Weight W2=(W+20)\n",
+ "g=9.81 #m/s**2 #Acceleration due to gravity\n",
+ "\n",
+ "#Calculations\n",
+ "\n",
+ "#frequency equation\n",
+ "#f=1*(2*pi)**-1*((k*g)*W**-1)**0.5\n",
+ "\n",
+ "#For First case f=12 \n",
+ "#12=1*(2*pi)**-1*((k*g)*W**-1)**0.5 ...............1\n",
+ "\n",
+ "#For Second case f=10\n",
+ "#10=1*(2*pi)**-1*((k*g)*W**-1)**0.5 .............2\n",
+ "\n",
+ "#Dividing equation 1 by 2 we get\n",
+ "#12*10**-1=((W+20)*W**-1)**0.5 \n",
+ "\n",
+ "#Squaring above equation and further simplifying we get \n",
+ "W=2000*44**-1\n",
+ "\n",
+ "#Sub value of W in equation 1 we get\n",
+ "k=(n1*2*pi)**2*W*g**-1*10**-3 #KN/m\n",
+ "\n",
+ "#Result\n",
+ "print\"Weight of spring is\",round(W,2),\"N\"\n",
+ "print\"Stiffness of the spring is\",round(k,2),\"KN/m\""
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "Weight of spring is 45.45 N\n",
+ "Stiffness of the spring is 26.34 KN/m\n"
+ ]
+ }
+ ],
+ "prompt_number": 17
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 16.15,Page No.629"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "from math import sin, cos, radians, pi\n",
+ "import numpy as np\n",
+ "\n",
+ "#Declaration Of Variables\n",
+ "\n",
+ "M=50 #kg #Mass of block\n",
+ "g=9.81 #Acceleration due to gravity\n",
+ "C1=4000 #N/m #Stiffness of 1st spring\n",
+ "C2=6000 #N/m #Stiffness of 2nd spring\n",
+ "r=0.04 #m #MAx amplitude\n",
+ "\n",
+ "#Calculations\n",
+ "\n",
+ "#Static Extension of 1st spring\n",
+ "x1=M*g*C1**-1 #m\n",
+ "\n",
+ "\n",
+ "#Static Extension of 2nd spring\n",
+ "x2=M*g*C2**-1 #m\n",
+ "\n",
+ "#Total Extension \n",
+ "x=x1+x2 #m\n",
+ "\n",
+ "#Period of vibration \n",
+ "T=2*pi*(x*g**-1)**0.5 #s\n",
+ "\n",
+ "#Angular velocity\n",
+ "f=2*pi*T**-1 #rad/s\n",
+ "\n",
+ "#MAx velocity\n",
+ "V_max=f*r #m/s\n",
+ "\n",
+ "#Max Acceleration\n",
+ "A_max=f**2*r #m/s**2\n",
+ "\n",
+ "#2nd case\n",
+ "\n",
+ "#Let\n",
+ "#W1=Weight supported by first spring\n",
+ "#W2=Weight suppoerted by second spring\n",
+ "\n",
+ "#W=W1+W2 #Total Weight ......................1\n",
+ "\n",
+ "#Extension of first spring\n",
+ "#X1=W1*C1**-1 ...........................2\n",
+ "\n",
+ "#Extension of second spring\n",
+ "#X2=W2*C2**-1 .........................3\n",
+ "\n",
+ "#As Extension of 1st spring is equal to 2nd spring\n",
+ "#W1*C1**-1=W2*C2**-1 \n",
+ "\n",
+ "#sub value in equation 1 and further simplifying we get\n",
+ "W2=50*g*3*5**-1 #N\n",
+ "\n",
+ "#Static extension of block\n",
+ "X3=W2*C2**-1 #m\n",
+ "\n",
+ "#Period of vibration \n",
+ "T2=2*pi*(X3*g**-1)**0.5 #s\n",
+ "\n",
+ "#Angular velocity\n",
+ "f2=2*pi*T2**-1 #rad/s\n",
+ "\n",
+ "#MAx velocity\n",
+ "V_max2=f2*r #m/s\n",
+ "\n",
+ "#Acceleration\n",
+ "A_max2=f2**2*r #m/s**2\n",
+ "\n",
+ "\n",
+ "#result\n",
+ "print\"Period of vibrations\",round(T,4),\"s\"\n",
+ "print\"MAx velocity\",round(V_max,2),\"m/s\"\n",
+ "print\"Max Acceleration\" ,round(A_max,2),\"m/s**2\"\n",
+ "\n",
+ "#When Block is suppoetred with spring\n",
+ "print\"Period of vibrations\",round(T2,2),\"s\"\n",
+ "print\"MAx velocity\",round(V_max2,2),\"m/s\"\n",
+ "print\"Max Acceleration\" ,round(A_max2,2),\"m/s**2\""
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "Period of vibrations 0.9069 s\n",
+ "MAx velocity 0.28 m/s\n",
+ "Max Acceleration 1.92 m/s**2\n",
+ "Period of vibrations 0.44 s\n",
+ "MAx velocity 0.57 m/s\n",
+ "Max Acceleration 8.0 m/s**2\n"
+ ]
+ }
+ ],
+ "prompt_number": 18
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 16.16,Page No.631"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "from math import sin, cos, radians, pi\n",
+ "import numpy as np\n",
+ "\n",
+ "#Declaration Of Variables\n",
+ "\n",
+ "x=0.3 #mm #Extension of spring\n",
+ "W1=20 #N #Weight \n",
+ "W2=700 #N #Weight supported\n",
+ "e=1.05 #cm #Static Extension\n",
+ "r=0.90 #cm #Amplitude\n",
+ "g=980 #m/s**2 #Acceleration due to gravity\n",
+ "x3=0.4 #cm #Displacement of weight from equilibrium position\n",
+ "\n",
+ "#Calculations\n",
+ "\n",
+ "#Stiffness of spring\n",
+ "C=W1*x**-1 #N/mm\n",
+ "\n",
+ "#Extension of spring\n",
+ "x2=W2*C**-1 #cm\n",
+ "\n",
+ "#Period of vibration\n",
+ "T=2*pi*((e*g**-1)**0.5) #s\n",
+ "\n",
+ "#Frequency\n",
+ "n=1*T**-1 #vib/s\n",
+ "\n",
+ "#Angular velocioty\n",
+ "f=(g*e**-1)**0.5 #rad/s\n",
+ "\n",
+ "#Velocity\n",
+ "v=-f*((r**2-x3**2)**0.5)\n",
+ "\n",
+ "#Result\n",
+ "print\"Frequency of vibration is\",round(n,2),\"vib/s\"\n",
+ "print\"Period of vibration is\",round(T,2),\"s\"\n",
+ "print\"Velocity of weight is\",round(v,2),\"m/s\""
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "Frequency of vibration is 4.86 vib/s\n",
+ "Period of vibration is 0.21 s\n",
+ "Velocity of weight is -24.63 m/s\n"
+ ]
+ }
+ ],
+ "prompt_number": 19
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 16.17,Page No.632"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "from math import sin, cos, radians, pi\n",
+ "import numpy as np\n",
+ "\n",
+ "\n",
+ "#Declaration Of Variables\n",
+ "\n",
+ "W_o=24 #tf #Weight of empty wagon\n",
+ "W1=32 #tf #Weight of goods\n",
+ "W=W_o+W1 #Total Weight\n",
+ "e1=8 #cm #Total Compression of spring\n",
+ "g=981 #Acceleration due to gravity\n",
+ "r=10 #cm #Amplitude\n",
+ "x=4 #cm #displacement\n",
+ "\n",
+ "#Calculations\n",
+ "\n",
+ "#Stiffness of spring\n",
+ "c=W*e1**-1 #tf/cm\n",
+ "\n",
+ "#Compression of spring due to weight of wagon\n",
+ "e_o=W_o*c**-1 #cm\n",
+ "\n",
+ "#When Wagon is empty \n",
+ "T_o=2*pi*((e_o*g**-1)**0.5)\n",
+ "\n",
+ "#When Wagon is Loaded \n",
+ "T1=2*pi*((e1*g**-1)**0.5)\n",
+ "\n",
+ "#Angular velocity\n",
+ "f=2*pi*T_o**-1 #rad/s\n",
+ "\n",
+ "#Velocity \n",
+ "v=f*((r**2-x**2)**0.5)*10**-2\n",
+ "\n",
+ "#Result\n",
+ "print\"Natural period of Vibrations is:When wagon is empty\",round(T_o,2),\"s\"\n",
+ "print\" :When wagon is loaded\",round(T1,2),\"s\"\n",
+ "print\"Velocity when displacement is\",round(v,2),\"m/s\""
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "Natural period of Vibrations is:When wagon is empty 0.37 s\n",
+ " :When wagon is loaded 0.57 s\n",
+ "Velocity when displacement is 1.55 m/s\n"
+ ]
+ }
+ ],
+ "prompt_number": 20
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 16.18,Page No.634"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "from math import sin, cos, radians, pi\n",
+ "import numpy as np\n",
+ "\n",
+ "\n",
+ "#Declaration Of Variables\n",
+ "\n",
+ "T=2 #s #time\n",
+ "g2=981 #Acceleration due to gravity\n",
+ "g=980 #Acceleration due to gravity\n",
+ "\n",
+ "#Calculations\n",
+ "\n",
+ "#Length of seconds pendulum with g=980\n",
+ "L1=(T*(2*pi)**-1)**2*g\n",
+ "\n",
+ "#Length of seconds pendulum with g=981\n",
+ "L2=(T*(2*pi)**-1)**2*g2\n",
+ "\n",
+ "#Result\n",
+ "print\"Length of seconds pendulum with g=980 is\",round(L1,2),\"cm\"\n",
+ "print\"Length of seconds pendulum with g=981 is\",round(L2,3),\"cm\""
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "Length of seconds pendulum with g=980 is 99.29 cm\n",
+ "Length of seconds pendulum with g=981 is 99.396 cm\n"
+ ]
+ }
+ ],
+ "prompt_number": 21
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 16.19,Page No.634"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "from math import sin, cos, radians, pi\n",
+ "import numpy as np\n",
+ "\n",
+ "#Declaration Of Variables\n",
+ "\n",
+ "l=0.6 #m #Length of string\n",
+ "W=80 #g\n",
+ "g=9.81 \n",
+ "\n",
+ "#Calculations\n",
+ "\n",
+ "#Time\n",
+ "T=2*pi*((l*g**-1)**0.5) #s\n",
+ "\n",
+ "#Result\n",
+ "print\"Time period of pendulum is\",round(T,2),\"s\""
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "Time period of pendulum is 1.55 s\n"
+ ]
+ }
+ ],
+ "prompt_number": 22
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 16.20,Page No.635"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "from math import sin, cos, radians, pi\n",
+ "import numpy as np\n",
+ "\n",
+ "#Declaration Of Variables\n",
+ "\n",
+ "l=99.93 #cm #LEngth of pendulum\n",
+ "dn=-5 #s #Number of beats clock loses\n",
+ "n=39.155\n",
+ "\n",
+ "#Calculations\n",
+ "\n",
+ "#Number of seconds in days \n",
+ "dl=-dn*2*l*n**-1\n",
+ "\n",
+ "#Result\n",
+ "print\"Length of pendulum for correct time is\",round(dl,5),\"cm\""
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "Length of pendulum for correct time is 25.52164 cm\n"
+ ]
+ }
+ ],
+ "prompt_number": 13
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 16.21,Page No.635"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "from math import sin, cos, radians, pi\n",
+ "import numpy as np\n",
+ "\n",
+ "#Declaration Of Variables\n",
+ "\n",
+ "T=2 #s #Time\n",
+ "g=981 #cm/s**2\n",
+ "\n",
+ "#Calculations\n",
+ "\n",
+ "#Length of pendulum\n",
+ "L=(T*(2*pi)**-1)**2*g #cm\n",
+ "\n",
+ "#Part-2\n",
+ "\n",
+ "#Decrease in gravity\n",
+ "dg=g-981 #cm/s**2\n",
+ "\n",
+ "#Number of beats in day\n",
+ "n=24*60*60\n",
+ "\n",
+ "# number of beats clock will lose\n",
+ "dn=n*(2*g)**-1 #s\n",
+ "\n",
+ "#Result\n",
+ "print\"Length of Pendulum\",round(L,2),\"cm\"\n",
+ "print\"Number of beats clock will lose is\",round(dn,2),\"s\""
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "Length of Pendulum 99.4 cm\n",
+ "Number of beats clock will lose is 44.04 s\n"
+ ]
+ }
+ ],
+ "prompt_number": 14
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 16.24,Page No.640"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "from math import sin, cos, radians, pi\n",
+ "import numpy as np\n",
+ "\n",
+ "#Declaration Of Variables\n",
+ "\n",
+ "d=100 #mm #Diameter of shaft\n",
+ "L=1000 #mm #Length of shaft\n",
+ "W=5000 #N #Weight attached\n",
+ "C=8.16*10**4 #N/mm**2 #Modulus of rigidity\n",
+ "g=9.81 #m/s**2\n",
+ "E=2*10**5 #N/mm**2 #Modulus of Elasticity\n",
+ "k=250 #mm #Radius of gyration\n",
+ "\n",
+ "#Calculations\n",
+ "\n",
+ "#Stress\n",
+ "F=W*(pi*4**-1*d**2)**-1 #N/mm**2\n",
+ "\n",
+ "#static deflection\n",
+ "dell=F*L*E**-1*10**-3 #m\n",
+ "\n",
+ "#Frequency of longitudinal vibrations\n",
+ "f=1*(2*pi)**-1*((g*dell**-1))**0.5\n",
+ "\n",
+ "#Part-2\n",
+ "\n",
+ "#Torsional stiffness\n",
+ "q=C*pi*32**-1*d**4*L**-1\n",
+ "\n",
+ "#M.I\n",
+ "I=W*(g*1000)**-1*k**2\n",
+ "\n",
+ "#Frequency of torsional vibrations\n",
+ "f2=1*(2*pi)**-1*((q*I**-1))**0.5\n",
+ "\n",
+ "#Result\n",
+ "print\"Frequencies for free longitudinal vibrations is\",round(f,2),\"m\"\n",
+ "print\"Frequencies for free torsional vibrations is\",round(f2,2),\"cycles/s\""
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "Frequencies for free longitudinal vibrations is 279.4 m\n",
+ "Frequencies for free torsional vibrations is 25.24 cycles/s\n"
+ ]
+ }
+ ],
+ "prompt_number": 17
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 16.25,Page No.641"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "from math import sin, cos, radians, pi\n",
+ "import numpy as np\n",
+ "\n",
+ "#Declaration Of Variables\n",
+ "\n",
+ "d=5 #mm #Diameter of shaft\n",
+ "L=1000 #mm #Length of shaft\n",
+ "W=20 #N #Weight of rotor\n",
+ "D=200 #mm #Diameter of rotor\n",
+ "C=0.85*10**5 #N/mm**2 #Modulus of rigidity\n",
+ "g=9.81*1000 #mm/s**2\n",
+ "\n",
+ "#Calculations\n",
+ "\n",
+ "#Radius of rotor\n",
+ "R=D*2**-1 #mm\n",
+ "\n",
+ "#Polar Modulus \n",
+ "J=pi*32**-1*d**4 #mm**4\n",
+ "\n",
+ "#Torsional Stiffness\n",
+ "q=C*J*L**-1 #N*mm\n",
+ "\n",
+ "#M.I\n",
+ "I=W*g**-1*R**2*2**-1 #N*mm-s**2\n",
+ "\n",
+ "#Frequency of torsional vibrations\n",
+ "f=1*(2*pi)**-1*((q*I**-1))**0.5\n",
+ "\n",
+ "#Result\n",
+ "print\"Torsional Vibrations of the system is\",round(f,2),\"cycles/s\""
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "Torsional Vibrations of the system is 3.6 cycles/s\n"
+ ]
+ }
+ ],
+ "prompt_number": 18
+ }
+ ],
+ "metadata": {}
+ }
+ ]
+}
\ No newline at end of file diff --git a/Engineering_Mechanics/chapter_17.ipynb b/Engineering_Mechanics/chapter_17.ipynb new file mode 100644 index 00000000..9ec115f2 --- /dev/null +++ b/Engineering_Mechanics/chapter_17.ipynb @@ -0,0 +1,879 @@ +{
+ "metadata": {
+ "name": "chapter_17.ipynb"
+ },
+ "nbformat": 3,
+ "nbformat_minor": 0,
+ "worksheets": [
+ {
+ "cells": [
+ {
+ "cell_type": "heading",
+ "level": 1,
+ "metadata": {},
+ "source": [
+ "Chapter 17:Collision of Elastic Bodies"
+ ]
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 17.1,Page No.650"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "\n",
+ "#Initilization of Variables\n",
+ "\n",
+ "m1=1 #Kg #MAss of ball A\n",
+ "u1=2 #m/s #Initial velocity of ball A\n",
+ "v1=0 #Final velocity of ball A\n",
+ "\n",
+ "#Ball-2\n",
+ "m2=2 #kg #mass\n",
+ "u2=0 #m/s #Initial velocity\n",
+ "\n",
+ "#Calculation\n",
+ "\n",
+ "#Total Initial momentum\n",
+ "V1=m1*u1+m2*u2 #kg*m/s\n",
+ "\n",
+ "#Total Initial momentum\n",
+ "#V2=m1*v1+m2*u2 #kg*m/s\n",
+ "\n",
+ "#Final velocity of ball B\n",
+ "v2=V1*2**-1 #m/s\n",
+ "\n",
+ "#Coefficient of restitution\n",
+ "e=(v2-v1)*(u1-u2)**-1 \n",
+ "\n",
+ "#Result\n",
+ "print\"Final velocity of ball B is\",round(v2,2),\"m/s\"\n",
+ "print\"Coefficient of restitution is\",round(e,2)"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "Final velocity of ball B is 1.0 m/s\n",
+ "Coefficient of restitution is 0.5\n"
+ ]
+ }
+ ],
+ "prompt_number": 1
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 17.2,Page No.650"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "\n",
+ "#Initilization of Variables\n",
+ "\n",
+ "#first body\n",
+ "m1=50 #kg #mass\n",
+ "u1=6 #m/s #Initial velocity\n",
+ "\n",
+ "#second body\n",
+ "m2=30 #kg #mass\n",
+ "u2=0 #m/s #Initial velocity\n",
+ "\n",
+ "#Calculation\n",
+ "\n",
+ "#MAss of two bodies\n",
+ "M=m1+m2 #kg\n",
+ "\n",
+ "#Total momentum before impact\n",
+ "M2=m1*u1+m2*u2 #kg*m/s\n",
+ "\n",
+ "#Total momentum after impact\n",
+ "#M3=(m1+m2)*V #kg*m/s\n",
+ "\n",
+ "#Velocitites of two bodies\n",
+ "V=M2*80**-1 #m/s\n",
+ "\n",
+ "#Result\n",
+ "print\"Common Velocity is\",round(V,2),\"m/s\""
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "Common Velocity is 3.75 m/s\n"
+ ]
+ }
+ ],
+ "prompt_number": 2
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 17.3,Page No.651"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "\n",
+ "#Initilization of Variables\n",
+ "\n",
+ "#Bullet\n",
+ "m1=0.05 #Kg #mass\n",
+ "\n",
+ "#Target\n",
+ "m2=5 #kg #mass\n",
+ "u2=0 #m/s #Initital Velocity\n",
+ "v=7 #m/s #Final Velocity\n",
+ "\n",
+ "#Calculation\n",
+ "\n",
+ "m=m1+m2 #kg #total mass\n",
+ "\n",
+ "#total Initial momentum\n",
+ "#v1=m1*u1+m2*u2\n",
+ "#After sub values and further simplifying we get\n",
+ "#v1=0.05*u1\n",
+ "\n",
+ "#Total Final momentum\n",
+ "v2=m*v #kg*m/s\n",
+ "\n",
+ "#Velocity of bullet\n",
+ "u1=v2*0.05**-1 #m/s\n",
+ "\n",
+ "#Result\n",
+ "print\"Velocity of bullet is\",round(u1,2),\"m/s\""
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "Velocity of bullet is 707.0 m/s\n"
+ ]
+ }
+ ],
+ "prompt_number": 3
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 17.4,Page No.651"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "\n",
+ "#Initilization of Variables\n",
+ "\n",
+ "m1=20 #kg #MAss of first ball\n",
+ "u1=5 #m/s #Initital velocity of first ball\n",
+ "\n",
+ "#second ball\n",
+ "m2=10 #kg #mass \n",
+ "u2=-10 #m/s #Velocity\n",
+ "e=5*6**-1 #coefficient of restitution\n",
+ "\n",
+ "#Calculation\n",
+ "\n",
+ "#Total momentum before impact\n",
+ "v1=m1*u1+m2*u2 #m/s\n",
+ "\n",
+ "\n",
+ "#Total momentum after impact\n",
+ "#v2=m1*v1+m2*v2\n",
+ "\n",
+ "#Velocity of second ball after impact\n",
+ "V2=25*3**-1 #m/s \n",
+ "\n",
+ "#Velocity of first ball after impact\n",
+ "V1=-V2*2**-1 #m/s\n",
+ "\n",
+ "#Result\n",
+ "print\"Velocity of first ball after impact is\",round(V1,2),\"m/s\"\n",
+ "print\"Velocity of second ball after impact is\",round(V2,2),\"m/s\""
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "Velocity of first ball after impact is -4.17 m/s\n",
+ "Velocity of second ball after impact is 8.33 m/s\n"
+ ]
+ }
+ ],
+ "prompt_number": 4
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 17.6,Page No.654"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "from math import sin, cos, tan, radians, pi\n",
+ "import numpy as np\n",
+ "\n",
+ "#Initilization of Variables\n",
+ "\n",
+ "m1=1 #kg #mass of first ball\n",
+ "m2=2 #kg #mass of second ball\n",
+ "u1=6 #m/s #Initial velocity of first ball\n",
+ "u2=2 #m/s #Initial velocity of second ball\n",
+ "theta1=30 #degrees #angle made by first ball\n",
+ "theta2=30 #degrees #angle made by second ball\n",
+ "e=0.5 #coefficient of restitutiion\n",
+ "\n",
+ "#Calculation\n",
+ "\n",
+ "#for ball A\n",
+ "#v1*sin(phi1)=3 .............1\n",
+ "\n",
+ "#for ball B\n",
+ "#v2*sin(phi)=1 .............2\n",
+ "\n",
+ "#according to lwa of conservation of momentum\n",
+ "#v1*cos(ph11)+2*v2*cos(phi2)=8.66 ..............3\n",
+ "\n",
+ "#coefficient of restitution for this case\n",
+ "#v2*cos(ph12)-v1*cos(phi1)=1.732 .........4\n",
+ "\n",
+ "#Adding equation 3 and 4 we get\n",
+ "#v2*cos(ph2)=3.464 ....................5\n",
+ " \n",
+ "#sub values in equation 3 we get\n",
+ "#v1*cos(ph1)=1.732 .................6\n",
+ "\n",
+ "#dividing equation 1 by equation6\n",
+ "phi1=np.arctan(3*1.732**-1)*(180*pi**-1)\n",
+ "\n",
+ "#dividing equation 2 by 5 we get\n",
+ "phi2=np.arctan(1*3.464**-1)*(pi**-1*180)\n",
+ "\n",
+ "#sub value of phi2 in equation 5\n",
+ "v2=3.464*(cos(phi2*pi*180**-1))**-1\n",
+ "\n",
+ "#sub value in equation 1\n",
+ "v1=1.732*(cos(phi1*pi*180**-1))**-1\n",
+ "\n",
+ "#Result\n",
+ "print\"velocity of 1Kg ball is\",round(v1,2),\"m/s\"\n",
+ "print\"velocity of 2nd ball is\",round(v2,2),\"m/s\"\n",
+ "print\"Direction of 1Kg ball is\",round(phi1,2),\"degrees\"\n",
+ "print\"Direction of 2nd ball is\",round(phi2,2),\"Degrees\""
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "velocity of 1Kg ball is 3.46 m/s\n",
+ "velocity of 2nd ball is 3.61 m/s\n",
+ "Direction of 1Kg ball is 60.0 degrees\n",
+ "Direction of 2nd ball is 16.1 Degrees\n"
+ ]
+ }
+ ],
+ "prompt_number": 1
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 17.7,Page No.656"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "from math import sin, cos, radians, pi\n",
+ "import numpy as np\n",
+ "\n",
+ "#Initilization of Variables\n",
+ "\n",
+ "m1=2 #kg #mass of first ball\n",
+ "m2=2 #kg #mass of second ball\n",
+ "u1=20 #m/s #Initial velocity of first ball\n",
+ "u2=30 #m/s #Initial velocity of second ball\n",
+ "theta1=30 #degrees #angle made by first ball\n",
+ "theta2=60 #degrees #angle made by second ball\n",
+ "e=0.9 #coefficient of restitutiion\n",
+ "\n",
+ "#Calculation\n",
+ "\n",
+ "#for ball A\n",
+ "#v1*sin(phi1)=10 .............1\n",
+ "\n",
+ "#for ball B\n",
+ "#v2*sin(phi)=25.98 .............2\n",
+ "\n",
+ "#according to lwa of conservation of momentum\n",
+ "#v1*cos(ph11)+2*v2*cos(phi2)=2.32 ..............3\n",
+ "\n",
+ "#coefficient of restitution for this case\n",
+ "#v2*cos(ph12)-v1*cos(phi1)=29.08 .........4\n",
+ "\n",
+ "#Adding equation 3 and 4 we get\n",
+ "#v2*cos(ph2)=15.7 ....................5\n",
+ " \n",
+ "#sub values in equation 3 we get\n",
+ "#v1*cos(ph1)=13.38 .................6\n",
+ "\n",
+ "#dividing equation 1 by equation6\n",
+ "phi1=np.arctan(10*13.38**-1)*(180*pi**-1)\n",
+ "\n",
+ "#dividing equation 2 by 5 we get\n",
+ "phi2=np.arctan(25.98*15.7**-1)*(pi**-1*180)\n",
+ "\n",
+ "#sub value of phi2 in equation 5\n",
+ "v2=25.98*(sin(phi2*pi*180**-1))**-1\n",
+ "\n",
+ "#sub value in equation 1\n",
+ "v1=13.38*(cos(phi1*pi*180**-1))**-1\n",
+ "\n",
+ "#Result\n",
+ "print\"velocity of 1Kg ball is\",round(v1,2),\"m/s\"\n",
+ "print\"velocity of 2nd ball is\",round(v2,2),\"m/s\"\n",
+ "print\"Direction of 1Kg ball is\",round(phi1,2),\"degrees\"\n",
+ "print\"Direction of 2nd ball is\",round(phi2,2),\"Degrees\""
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "velocity of 1Kg ball is 16.7 m/s\n",
+ "velocity of 2nd ball is 30.36 m/s\n",
+ "Direction of 1Kg ball is 36.77 degrees\n",
+ "Direction of 2nd ball is 58.85 Degrees\n"
+ ]
+ }
+ ],
+ "prompt_number": 2
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 17.8,Page No.658"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "\n",
+ "#Initilization of Variables\n",
+ "\n",
+ "#First vechile\n",
+ "m1=600 #kg #mass\n",
+ "u1=12 #m/s #Initial velocity\n",
+ "\n",
+ "#Second vechile\n",
+ "m2=400 #kg #mass\n",
+ "u2=9 #m/s #initial velocity\n",
+ "\n",
+ "#Calculation\n",
+ "\n",
+ "#Total mass\n",
+ "M=m1+m2 #kg\n",
+ "\n",
+ "#Total Momentum before impact\n",
+ "v1=m1*u1+m2*u2\n",
+ "\n",
+ "#Total momentum\n",
+ "#v=M*V\n",
+ "\n",
+ "#By law of conservation of momentum\n",
+ "V=v1*1000**-1 #m/s\n",
+ "\n",
+ "#Kinetic Energy before impact\n",
+ "KE1=(m1*u1**2+m2*u2**2)*2**-1 #N*m\n",
+ "\n",
+ "#Total KE after impact\n",
+ "KE2=M*V**2*2**-1 #N*m\n",
+ "\n",
+ "#Loss of KE\n",
+ "KE3=KE1-KE2 #N*m\n",
+ "\n",
+ "#Result\n",
+ "print\"Loss of Kinetic Energy due to impact is\",round(KE3,2),\"N*m\""
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "Loss of Kinetic Energy due to impact is 1080.0 N*m\n"
+ ]
+ }
+ ],
+ "prompt_number": 7
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 17.9,Page No.659"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "\n",
+ "#Initilization of Variables\n",
+ "\n",
+ "m1=0.1 #kg #MAss of bullet\n",
+ "m2=10 #kg #mass of target\n",
+ "u2=0 #Initial velocity of target\n",
+ "v=7 #m/s #common velocity\n",
+ "\n",
+ "#Calculation\n",
+ "\n",
+ "#Total momentum before impact\n",
+ "#v1=0.1*u1\n",
+ "\n",
+ "#Total momentum after impact\n",
+ "v2=(m1+m2)*v\n",
+ "\n",
+ "#Initial velocity of bullet\n",
+ "u1=v2*0.1**-1 #m/s\n",
+ "\n",
+ "#Total KE before impact\n",
+ "KE=(m1*u1**2+m2*u2**2)*2**-1\n",
+ "\n",
+ "#Total KE after impact\n",
+ "KE2=(m1+m2)*v**2*2**-1 #m/s\n",
+ "\n",
+ "#Loss of KE\n",
+ "KE3=KE-KE2 #N*m\n",
+ "\n",
+ "#Result\n",
+ "print\"Loss of Kinetic Energy is\",round(KE3,2),\"N*m\""
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "Loss of Kinetic Energy is 24745.0 N*m\n"
+ ]
+ }
+ ],
+ "prompt_number": 8
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 17.12,Page No.662"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "\n",
+ "#Initilization of Variables\n",
+ "\n",
+ "e=0.75 #coefficient of restitution\n",
+ "m1=1 #kg #MAss of first sphere\n",
+ "m2=5 #kg #mass of second sphere\n",
+ "u1=3 #m/s #Initial velocity of 1st sphere\n",
+ "u2=0.6 #m/s #Initial velocity of 2nd sphere\n",
+ "\n",
+ "#Calculation\n",
+ "\n",
+ "#From law of conservation of momentum equation we get\n",
+ "#v1+5*v2=6 ..................1\n",
+ "\n",
+ "#Form coefficient of restitution formula we get\n",
+ "#v2-v1=1.8 ........................2\n",
+ "\n",
+ "#Adding equations 1 and 2 we get\n",
+ "v2=7.8*6**-1 #m/s\n",
+ "\n",
+ "#sub in equation 2 we get\n",
+ "v1=1.8-v2 #m/s\n",
+ "\n",
+ "#Loss of KE during impact\n",
+ "KE=((m1*u1**2+m2*u2**2)-(m1*v1**2+m2*v2**2))*2**-1\n",
+ "\n",
+ "#Result\n",
+ "print\"Loss of Kinetic Energy during impact is\",round(KE,2),\"N*m\""
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "Loss of Kinetic Energy during impact is 1.05 N*m\n"
+ ]
+ }
+ ],
+ "prompt_number": 9
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 17.13,Page No.664"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "\n",
+ "#Initilization of Variables\n",
+ "\n",
+ "m=0.5 #kg #mass of ball\n",
+ "H=18 #m #Height from which the ball is dropped\n",
+ "h=8 # #Height to which ball rebounds\n",
+ "g=9.81 #m/s**2 \n",
+ "\n",
+ "\n",
+ "#Calculation\n",
+ "\n",
+ "#Velocity with which ball strikes the floor\n",
+ "u=(2*g*H)**0.5 #m/s\n",
+ "\n",
+ "#Velocty of ball after impact\n",
+ "v=(2*g*h)**0.5 #m/s\n",
+ "\n",
+ "#Coefficient of restitution\n",
+ "e=v*u**-1\n",
+ "\n",
+ "#Result\n",
+ "print\"coefficient of restitution between floor and ball\",round(e,2)"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "coefficient of restitution between floor and ball 0.67\n"
+ ]
+ }
+ ],
+ "prompt_number": 10
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 17.13(A),Page No.664"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "\n",
+ "#Initilization of Variables\n",
+ "\n",
+ "H1=1.6 #m #Initial Height\n",
+ "H2=0.9 #m #Height after rebound\n",
+ "g=9.81 #m/s**2\n",
+ "\n",
+ "#Calculation\n",
+ "\n",
+ "#Consider motion of ball from height H1, wwe get\n",
+ "v1=(2*g*H1)**0.5 #m/s ................................1\n",
+ "\n",
+ "#Consider motion of ball from floor to a height H2\n",
+ "u2=(2*g*H2)**0.5 #m/s .........................2\n",
+ "\n",
+ "#Dividing equation 2 by 1 we get\n",
+ "e=u2*v1**-1 \n",
+ "\n",
+ "#Result\n",
+ "print\"Coefficient of restitution is\",round(e,2)"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "Coefficient of restitution is 0.75\n"
+ ]
+ }
+ ],
+ "prompt_number": 11
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 17.14,Page No.665"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "\n",
+ "#Initilization of Variables\n",
+ "\n",
+ "h=16 #m #Height after impact\n",
+ "e=0.8 #coeficient of restitution\n",
+ "g=9.81 #m/s**2\n",
+ "\n",
+ "#Calculation\n",
+ "\n",
+ "#Velocity with which ball strikes the floor\n",
+ "u=(2*g*h)**0.5 #m/s \n",
+ "\n",
+ "#Height from which ball is dropped\n",
+ "H=2*g*h*(e**2*2*g)**-1 #m\n",
+ "\n",
+ "#Result\n",
+ "print\"Height from which the ball is dropped is\",round(H,2),\"m\""
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "Height from which the ball is dropped is 25.0 m\n"
+ ]
+ }
+ ],
+ "prompt_number": 12
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 17.15,Page No.665"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "\n",
+ "#Initilization of Variables\n",
+ "\n",
+ "H=13.5 #Height from which ball is dropped\n",
+ "h=9 #m #Height to which ball rebounds\n",
+ "g=9.81 #m/s**2\n",
+ "\n",
+ "#Calculation\n",
+ "\n",
+ "#velocity with which ball stirkes the floor\n",
+ "u=(2*g*H)**0.5 #m/s\n",
+ "\n",
+ "#velocity of ball after impact\n",
+ "v=(2*g*h)**0.5 #m/s\n",
+ "\n",
+ "#Coefficient of restitution \n",
+ "e=(v*u**-1)\n",
+ "\n",
+ "#Height of second rebound\n",
+ "\n",
+ "#velocity with which ball stirkes the floor second time\n",
+ "u1=(2*g*h) #m/s ..............1\n",
+ "\n",
+ "#velocity of ball after impact rebounds second time\n",
+ "#v1=(2*g*h2) ....................2\n",
+ " \n",
+ "#After simplifying equation 1 and 2 we get\n",
+ "h2=e**2*u1*(2*g)**-1 #m\n",
+ "\n",
+ "#Result\n",
+ "print\"Height of second rebound is\",round(h2,2),\"m\""
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "Height of second rebound is 6.0 m\n"
+ ]
+ }
+ ],
+ "prompt_number": 13
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 17.16,Page No.667"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "from math import sin, cos, radians, pi\n",
+ "import numpy as np\n",
+ "\n",
+ "#Initilization of Variables\n",
+ "\n",
+ "u=10 #m/s #Initial velocity of ball\n",
+ "alpha=30 #degrees #angle made by intial velocity\n",
+ "theta=60 #degrees\n",
+ "e=0.5 #coefficient of restitution\n",
+ "\n",
+ "#Calculation\n",
+ "\n",
+ "#As components of intial velocity and final velocity with line of impact is same at right angles\n",
+ "#v*sin(phi)=8.66 ........1\n",
+ "\n",
+ "#v*cos(phi)=2.5 ................2\n",
+ "\n",
+ "#Dividing equation 1 by 2\n",
+ "phi=np.arctan(8.66*2.5**-1)*(180*pi**-1)\n",
+ "\n",
+ "#Sub value in equation 1 we get\n",
+ "v=8.66*(sin(phi*pi*180**-1))**-1 #m/s\n",
+ "\n",
+ "#Result\n",
+ "print\"Direction of ball after impact is\",round(phi,2),\"Degrees\"\n",
+ "print\"Velocity of ball after impact\",round(v,2),\"m/s\""
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "Direction of ball after impact is 73.9 Degrees\n",
+ "Velocity of ball after impact 9.01 m/s\n"
+ ]
+ }
+ ],
+ "prompt_number": 3
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 17.17,Page No.667"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "\n",
+ "#Initilization of Variables\n",
+ "\n",
+ "u=5 #m/s #Initial velocity of body\n",
+ "alpha=30 #Degrees #Angle made by initial velocity with fixed plane\n",
+ "theta=60 #degrees\n",
+ "phi=45 #degrees #angle made by final velocity\n",
+ "beta=45 #degrees #Angle made by final velocity with line of impact\n",
+ "\n",
+ "#Calculation\n",
+ "\n",
+ "#Components of final velocity and initial velocity at right angles to line of impact\n",
+ "v=u*sin(alpha*pi*180**-1)*(sin(phi*pi*180**-1))**-1 #m/s\n",
+ "\n",
+ "#For indirect impacton a fixed plane\n",
+ "e=v*cos(phi*pi*180**-1)*(u*cos(theta*pi*180**-1))**-1\n",
+ "\n",
+ "#Result\n",
+ "print\"coefficient of restitution between ball and fixed plane is\",round(e,2)\n",
+ "print\"velocity of body after impact is\",round(v,2),\"m/s\""
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "coefficient of restitution between ball and fixed plane is 1.0\n",
+ "velocity of body after impact is 3.54 m/s\n"
+ ]
+ }
+ ],
+ "prompt_number": 15
+ }
+ ],
+ "metadata": {}
+ }
+ ]
+}
\ No newline at end of file diff --git a/Engineering_Mechanics/chapter_18.ipynb b/Engineering_Mechanics/chapter_18.ipynb new file mode 100644 index 00000000..a56de6ea --- /dev/null +++ b/Engineering_Mechanics/chapter_18.ipynb @@ -0,0 +1,1586 @@ +{
+ "metadata": {
+ "name": "chapter_18.ipynb"
+ },
+ "nbformat": 3,
+ "nbformat_minor": 0,
+ "worksheets": [
+ {
+ "cells": [
+ {
+ "cell_type": "heading",
+ "level": 1,
+ "metadata": {},
+ "source": [
+ "Chapter 18:Work,Power And Energy "
+ ]
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 18.1,Page No.673"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "from math import sin, cos, radians, pi\n",
+ "\n",
+ "#Initilization of Variables\n",
+ "\n",
+ "W=500 #N #Weight of Body\n",
+ "S=5 #m #Distance\n",
+ "P=250 #N #Force\n",
+ "P2=200 #N #Force 2\n",
+ "theta=30 #Degrees #Angle made by Force with Horizontal\n",
+ "\n",
+ "#Calculation\n",
+ "\n",
+ "#Part-1\n",
+ "\n",
+ "#Work Done\n",
+ "w=P*S #N*m\n",
+ "\n",
+ "#Work Done\n",
+ "w2=P2*cos(theta*pi*180**-1)*S #N*m\n",
+ "\n",
+ "#Result\n",
+ "print\"Work Done when Force 250 N is applied\",round(w,2),\"N*m\"\n",
+ "print\"Work Done when Force 200 N is applied\",round(w2,2),\"N*m\""
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "Work Done when Force 250 N is applied 1250.0 N*m\n",
+ "Work Done when Force 200 N is applied 866.03 N*m\n"
+ ]
+ }
+ ],
+ "prompt_number": 1
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 18.2,Page No.673"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "\n",
+ "#Initilization of Variables\n",
+ "\n",
+ "W=1500 #N #Weight of Body\n",
+ "S=500 #m #Distance\n",
+ "P=15 #N #Force\n",
+ "\n",
+ "#Calculation\n",
+ "\n",
+ "#Work Done by Resistance \n",
+ "w=P*S #N*m\n",
+ "\n",
+ "#Result\n",
+ "print\"Work Done on body by Resistance is\",round(w,2),\"N*m\""
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "Work Done on body by Resistance is 7500.0 N*m\n"
+ ]
+ }
+ ],
+ "prompt_number": 2
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 18.3,Page No.673"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "from math import sin, cos, radians, pi\n",
+ "\n",
+ "#Initilization of Variables\n",
+ "\n",
+ "W=800 #N #Weight of Body\n",
+ "theta=30 #Degrees #angle made by Force\n",
+ "S=5 #Distance\n",
+ "\n",
+ "#Calculation\n",
+ "\n",
+ "#Force apllied on Block\n",
+ "P=W*sin(theta*pi*180**-1) #N\n",
+ "\n",
+ "#Work done on body\n",
+ "w=P*S #N*m\n",
+ "\n",
+ "#Result\n",
+ "print\"Work Done in Pulling up the Body is\",round(w,2),\"N*m\""
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "Work Done in Pulling up the Body is 2000.0 N*m\n"
+ ]
+ }
+ ],
+ "prompt_number": 2
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 18.4,Page No.674"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "from math import sin, cos, radians, pi\n",
+ "\n",
+ "#Initilization of Variables\n",
+ "\n",
+ "mu=0.3 #coefficient of Friction\n",
+ "S=5 #m #Distance\n",
+ "W=800 #N #weight of Body\n",
+ "theta=30 #Degrees #Angle made by Weight\n",
+ "\n",
+ "#Calculation\n",
+ "\n",
+ "#reaction Force \n",
+ "R=W*cos(theta*pi*180**-1) #N\n",
+ "\n",
+ "#Force of friction\n",
+ "F=mu*R\n",
+ "\n",
+ "#Forces along plane\n",
+ "P=W*sin(theta*pi*180**-1)+F #N*m\n",
+ "\n",
+ "#Work done\n",
+ "w=P*S #N*m\n",
+ "\n",
+ "#Result\n",
+ "print\"Work done in pullint the Body\",round(w,2),\"N*m\""
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "Work done in pullint the Body 3039.23 N*m\n"
+ ]
+ }
+ ],
+ "prompt_number": 4
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 18.5,Page No.674"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "from math import sin, cos, radians, pi\n",
+ "\n",
+ "#Initilization of Variables\n",
+ "\n",
+ "L=50.5 #m #Total Length of chain\n",
+ "R=0.16 #m #Radius of pulley\n",
+ "L_AC=40 #m #Length of chain between A and C\n",
+ "W=505 #N #Weight of chain\n",
+ "w=10 #N #weight of chain per metre length\n",
+ "\n",
+ "#Calculation\n",
+ "\n",
+ "#Length of BD\n",
+ "L_BD=L-2*pi*R*2**-1-L_AC #m\n",
+ "\n",
+ "#Weight of chain \n",
+ "W_AC=w*L_AC #N\n",
+ "\n",
+ "#Weight of chain BD\n",
+ "W_BD=w*L_BD #N\n",
+ "\n",
+ "#Force applied at D\n",
+ "P=W_AC-W_BD #N\n",
+ "\n",
+ "#Length of chain\n",
+ "l=(L_AC-w)*2**-1\n",
+ "\n",
+ "#Work Done\n",
+ "W=P*l*2**-1 #N\n",
+ "\n",
+ "#Result\n",
+ "print\"Work Done by the man\",round(W,2),\"N\""
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "Work Done by the man 2250.2 N\n"
+ ]
+ }
+ ],
+ "prompt_number": 5
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 18.6,Page No.675"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "\n",
+ "#Initilization of Variables\n",
+ "\n",
+ "W=2000 #N #Weight of Body\n",
+ "P_o=750 #N #Initial Force\n",
+ "x_o=0 #Initial Force,distance moved is zero\n",
+ "S=25 #m #Distance Moved\n",
+ "\n",
+ "#Calculation\n",
+ "\n",
+ "#Force after a distance of 25 m\n",
+ "P=P_o+10*S #N\n",
+ "\n",
+ "#Work Done\n",
+ "w=(P_o+P)*2**-1*S #N*m\n",
+ "\n",
+ "#Result\n",
+ "print\"Work Done by applied Force\",round(w,2),\"N*m\""
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "Work Done by applied Force 21875.0 N*m\n"
+ ]
+ }
+ ],
+ "prompt_number": 6
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 18.7,Page No.676"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "from scipy.integrate import * \n",
+ "\n",
+ "#Initilization of Variables\n",
+ "\n",
+ "L=10 #m #Length of free cable\n",
+ "W=50 #N #weight of cable per m length\n",
+ "\n",
+ "#Calculation\n",
+ "\n",
+ "#Weight of element \n",
+ "#X=50*dx\n",
+ "\n",
+ "#work done on the elemnt\n",
+ "#dw=500-50*x*dx\n",
+ "\n",
+ "def f(x) :\n",
+ " return 500-50*x\n",
+ "\n",
+ "I,err = quad(f,0,10)\n",
+ "\n",
+ "#Result\n",
+ "print\"Work done by Electric Motor is\",round(I,2),\"N*m\""
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "Work done by Electric Motor is 2500.0 N*m\n"
+ ]
+ }
+ ],
+ "prompt_number": 7
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 18.8,Page No.677"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "\n",
+ "#Initilization of Variables\n",
+ "\n",
+ "W=2000 #KN #Weight of train\n",
+ "v=10 #m/s #speed of train\n",
+ "F=20000 #N #Resistance due to friction\n",
+ "p=F #Net Force in Direction of motion\n",
+ "\n",
+ "#Calculation\n",
+ "\n",
+ "#Power\n",
+ "P=p*v*10**-3 #KW\n",
+ "\n",
+ "#Result\n",
+ "print\"Power of the Engine\",P,\"KW\""
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "Power of the Engine 200.0 KW\n"
+ ]
+ }
+ ],
+ "prompt_number": 8
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 18.9,Page No.677"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "\n",
+ "#Initilization of Variables\n",
+ "\n",
+ "W=2000 #KN #Weight of train\n",
+ "F=20000 #N #Resistance Force\n",
+ "v=10 #m/s #Velocity\n",
+ "a=0.5 #m/s**2 #Acceleration\n",
+ "g=9.81 #m/s**2 #acceleration due to gravity\n",
+ "\n",
+ "#Calculation\n",
+ "\n",
+ "#Mass of train\n",
+ "m=W*10**3*g**-1 #Kg\n",
+ "\n",
+ "#Net Force\n",
+ "F=m*a+F #N\n",
+ "\n",
+ "#Power of the engine \n",
+ "P=F*v*10**-3 #KW\n",
+ "\n",
+ "#Result\n",
+ "print\"Power of the Engine is\",round(P,2),\"KW\""
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "Power of the Engine is 1219.37 KW\n"
+ ]
+ }
+ ],
+ "prompt_number": 9
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 18.10,Page No.678"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "\n",
+ "#Initilization of Variables\n",
+ "\n",
+ "W=1500*1000 #N #Weight of train \n",
+ "v=10 #m/s #speed\n",
+ "F=7500 #N #Force exerted by engine\n",
+ "#sin(theta)=1*100**-1 \n",
+ "\n",
+ "#Calculation\n",
+ "\n",
+ "#from equation of Net Force\n",
+ "#p=W*sin(theta*pi*180**-1)+F\n",
+ "#After sub values and further simplifying we get\n",
+ "p=15000+7500 #N\n",
+ "\n",
+ "#Power Exerted by Engine\n",
+ "P=p*v*10**-3 #KW\n",
+ "\n",
+ "\n",
+ "#Result\n",
+ "print\"Power Exerted by the Engine is\",round(P,2),\"KW\""
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "Power Exerted by the Engine is 225.0 KW\n"
+ ]
+ }
+ ],
+ "prompt_number": 10
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 18.11,Page No.678"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "\n",
+ "#Initilization of Variables\n",
+ "\n",
+ "W=2*10**6 #N\n",
+ "v=5 #m/s velocity\n",
+ "P=35*10**3 #W\n",
+ "\n",
+ "#Calculation\n",
+ "\n",
+ "#After simplifying Net Force acting on engine in direction of motion, we get\n",
+ "#F=13333.3-F+P ................1\n",
+ "\n",
+ "#Power\n",
+ "P2=P*v**-1\n",
+ "\n",
+ "#Sub value in equation 1 we get\n",
+ "F=13333.3+P2 #N\n",
+ "\n",
+ "#case-2\n",
+ "\n",
+ "#frpm Net force in direction of motion after simplifying we get,value of \n",
+ "F2=W*150**-1+F #N\n",
+ "\n",
+ "#Power developed by engine \n",
+ "P3=F2*v*10**-3 #KW\n",
+ "\n",
+ "\n",
+ "#Result\n",
+ "print\"Power required to pull the train is\",round(P3,2),\"KW\""
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "Power required to pull the train is 168.33 KW\n"
+ ]
+ }
+ ],
+ "prompt_number": 13
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 18.12,Page No.680"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "from math import pi\n",
+ "\n",
+ "#Initilization of Variables\n",
+ "\n",
+ "P=1800 #N #Force\n",
+ "D=0.01 #m #Diameter\n",
+ "R=0.005 #m #Radius\n",
+ "theta=2*pi #Radians\n",
+ "\n",
+ "#Calculation\n",
+ "\n",
+ "#Torque\n",
+ "T=P*R #N*m\n",
+ "\n",
+ "#Work done\n",
+ "W=T*theta #N*m\n",
+ "\n",
+ "#Result\n",
+ "print\"Work Done is\",round(W,2),\"N*m\""
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "Work Done is 56.55 N*m\n"
+ ]
+ }
+ ],
+ "prompt_number": 1
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 18.13,Page No.681"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "from math import pi\n",
+ "\n",
+ "#Initilization of Variables\n",
+ "\n",
+ "F=1800 #N #Force\n",
+ "R=0.005 #m #Radius\n",
+ "T=9 #N*m #Torque\n",
+ "N=200 #r.p.m\n",
+ "\n",
+ "#Calculation\n",
+ "\n",
+ "#Power of the shaft\n",
+ "P=2*pi*N*T*60**-1 #W\n",
+ "\n",
+ "#Result\n",
+ "print\"Power of the shaft is\",round(P,2),\"N*m\""
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "Power of the shaft is 188.5 N*m\n"
+ ]
+ }
+ ],
+ "prompt_number": 2
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 18.14,Page No.683"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "\n",
+ "#Initilization of Variables\n",
+ "\n",
+ "M=2 #Kg #Mass\n",
+ "v=50 #m/s**2 #Velocity\n",
+ "\n",
+ "#Calculation\n",
+ "\n",
+ "#Let K.E be E\n",
+ "E=1*2**-1*M*v**2 #N*m\n",
+ "\n",
+ "#Result\n",
+ "print\"Kinetic Energy is\",round(E,2),\"N*m\""
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "Kinetic Energy is 2500.0 N*m\n"
+ ]
+ }
+ ],
+ "prompt_number": 16
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 18.15,Page No.683"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "\n",
+ "#Initilization of Variables\n",
+ "\n",
+ "m=0.081 #Kg\n",
+ "u=300 #m/s #Initial Velocity of bullet\n",
+ "\n",
+ "#Calculation\n",
+ "\n",
+ "#Part-1\n",
+ "\n",
+ "S=0.1 #m #Penetration of bullet\n",
+ "v=0 #Final Velocity of bullet\n",
+ "\n",
+ "#Kinetic Energy of bullet\n",
+ "KE=(m*v**2-m*u**2)*2**-1 #N*m\n",
+ "\n",
+ "#Force of Resistance\n",
+ "P=-KE*S**-1 #N\n",
+ "\n",
+ "#Part-2\n",
+ "\n",
+ "#Depth of penetration\n",
+ "S2=0.05 #m\n",
+ "\n",
+ "#work Done by force of Resistance\n",
+ "W2=-P*S2 #N*m\n",
+ "\n",
+ "#velocity of bullet after 5cm penetration\n",
+ "v1=((W2+(m*u**2*2**-1))*2*m**-1)**0.5\n",
+ "\n",
+ "#Result\n",
+ "print\"Force of Resistance is\",round(P,2),\"N\"\n",
+ "print\"Velocity with which bullet will emerge is\",round(v1,2),\"m/s\""
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "Force of Resistance is 36450.0 N\n",
+ "Velocity with which bullet will emerge is 212.13 m/s\n"
+ ]
+ }
+ ],
+ "prompt_number": 17
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 18.15(A),Page No.684"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "\n",
+ "#Initilization of Variables\n",
+ "\n",
+ "m=0.01 #Kg \n",
+ "u=1000 #m/s #Velocity\n",
+ "t=0.002 #s #time taken b bullet to travel\n",
+ "v=0 #Final Velocity\n",
+ "g=9.81 #acceleration due to gravity\n",
+ "\n",
+ "#Calculation\n",
+ "\n",
+ "#Kinetic energy of bullet\n",
+ "KE=m*u**2*2**-1 #N*m\n",
+ "\n",
+ "#acceleration\n",
+ "a=-(v-u)*t**-1 #m/s**2\n",
+ "\n",
+ "#Frictional Force\n",
+ "F=m*a #N\n",
+ "\n",
+ "#Distance travelled by bullet\n",
+ "S=F*KE**-1 #m\n",
+ "\n",
+ "#Part-2\n",
+ "\n",
+ "#Probable speed of the car just before brakes are applied \n",
+ "V=(30*2*g)**0.5*1000**-1*3600 #m/s\n",
+ "\n",
+ "#Result\n",
+ "print\"Average Force acted on the bullet is\",round(F,2),\"N\"\n",
+ "print\"Distance penetrated by it\",round(S,2),\"m\" \n",
+ "print\"Probable speed of the car just before brakes are applied\",round(V,2),\"km/hr\""
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "Average Force acted on the bullet is 5000.0 N\n",
+ "Distance penetrated by it 1.0 m\n",
+ "Probable speed of the car just before brakes are applied 87.34 km/hr\n"
+ ]
+ }
+ ],
+ "prompt_number": 18
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 18.16,Page No.686"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "\n",
+ "#Initilization of Variables\n",
+ "\n",
+ "W=20*10**3 #N #Weight of Truck\n",
+ "u=45*10**3*(3600)**-1 #speed of truck #m/s\n",
+ "v=0 #Final Velocity of truck\n",
+ "g=9.81 #Acceleration due to gravity\n",
+ "m=W*g**-1 #mass of truck\n",
+ "S=20 #m #DIstance\n",
+ "\n",
+ "#Calculation\n",
+ "\n",
+ "#Kinetic energy of Truck\n",
+ "KE=-m*(v**2-u**2)*2**-1 #N*m\n",
+ "\n",
+ "#Average Force of Resisting acting on the truck\n",
+ "P=KE*S**-1 #N\n",
+ "\n",
+ "#Result\n",
+ "print\"Average Force of Resisting acting on the truck\",round(P,2),\"N\""
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "Average Force of Resisting acting on the truck 7963.81 N\n"
+ ]
+ }
+ ],
+ "prompt_number": 19
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 18.17,Page No.687"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "\n",
+ "#Initilization of Variables\n",
+ "\n",
+ "W=9810 #N #Weight of train\n",
+ "m=1000 #Kg #Mass of car\n",
+ "u=0 #m/s #Intial Velocity\n",
+ "v=12.5 #m/s #Final by car\n",
+ "S=50 #m #Distance\n",
+ "P=100 #N #Resistance\n",
+ "\n",
+ "#Calculation\n",
+ "\n",
+ "#Change in Kinetic Energy\n",
+ "KE=m*(v**2-u**2)*2**-1 #N*m\n",
+ "\n",
+ "#Average driving Force exerted by engine\n",
+ "P2=KE*S**-1+P #N\n",
+ "\n",
+ "#Power Developed by Engine\n",
+ "P3=P2*v*10**-3 #KW\n",
+ "\n",
+ "#Result\n",
+ "print\"Average driving Force exerted by engine\",round(P2,2),\"N\"\n",
+ "print\"Power Developed by Engine\",round(P3,2),\"N\""
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "Average driving Force exerted by engine 1662.5 N\n",
+ "Power Developed by Engine 20.78 N\n"
+ ]
+ }
+ ],
+ "prompt_number": 20
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 18.18,Page No.688"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "from math import cos, pi,sin, radians\n",
+ "\n",
+ "#Initilization of Variables\n",
+ "\n",
+ "W=196.2 #N #Weight of train\n",
+ "m=20 #Kg #Mass\n",
+ "P=300 #N #force\n",
+ "theta=30 #Degrees #Angle of inclination\n",
+ "mu=0.2 #Coefficient of friction\n",
+ "u=0 #initial Velocity\n",
+ "t=4 #seconds\n",
+ "\n",
+ "#Calculation\n",
+ "\n",
+ "R=W*cos(theta*pi*180**-1) #N\n",
+ "\n",
+ "#Net Force in Direction of motion\n",
+ "F=P-W*sin(theta*pi*180**-1)-mu*R #N\n",
+ "\n",
+ "#Acceleration\n",
+ "a=F*m**-1 #m/s**2\n",
+ "\n",
+ "#Distance travelled in four seconds\n",
+ "s=u*t+a*t**2*2**-1\n",
+ "\n",
+ "#Velocity after 4 seconds\n",
+ "v=u+a*t #m/s\n",
+ "\n",
+ "#Kinetic Energy after 4 seconds\n",
+ "KE=m*v**2*2**-1 #N*m\n",
+ "\n",
+ "#Work Done on Body\n",
+ "W2=F*s #N*m\n",
+ "\n",
+ "#Momentum of the body after four seconds\n",
+ "e=m*v #Kg*m/s\n",
+ "\n",
+ "#Impulse applied in four seconds\n",
+ "I=F*t #N*s\n",
+ "\n",
+ "#Result\n",
+ "print\"Acceleration of Body\",round(a,2),\"m/s**2\"\n",
+ "print\"Distance travelled in four seconds\",round(s,2),\"m\"\n",
+ "print\"Velocity after 4 seconds\",round(v,2),\"m/s\"\n",
+ "print\"Kinetic Energy after 4 seconds\",round(KE,2),\"N*m\"\n",
+ "print\"Work Done on Body\",round(W2,2),\"N*m\"\n",
+ "print\"Momentum of the body after four seconds\",round(e,2),\"Kg*m/s\"\n",
+ "print\"Impulse applied in four seconds\",round(I,2),\"N*s\""
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "Acceleration of Body 8.4 m/s**2\n",
+ "Distance travelled in four seconds 67.17 m\n",
+ "Velocity after 4 seconds 33.58 m/s\n",
+ "Kinetic Energy after 4 seconds 11278.47 N*m\n",
+ "Work Done on Body 11278.47 N*m\n",
+ "Momentum of the body after four seconds 671.67 Kg*m/s\n",
+ "Impulse applied in four seconds 671.67 N*s\n"
+ ]
+ }
+ ],
+ "prompt_number": 3
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 18.19,Page No.689"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "from math import cos, pi,sin, radians\n",
+ "\n",
+ "#Initilization of Variables\n",
+ "\n",
+ "W=20 #N #Weight \n",
+ "theta=20 #Degrees #Angle\n",
+ "u=12 #m/s #Initial Velocity\n",
+ "mu=0.15 #Coefficient of friction\n",
+ "g=9.81 #acceleration due to gravity\n",
+ "m=W*g**-1 #Kg\n",
+ "\n",
+ "#Calculation\n",
+ "\n",
+ "#PArt-1\n",
+ "\n",
+ "v=0 #Final Velocity\n",
+ "R=W*cos(theta*pi*180**-1)\n",
+ "F=mu*R\n",
+ "\n",
+ "#Net Force\n",
+ "F2=W*sin(theta*pi*180**-1)+mu*R #N\n",
+ "\n",
+ "#Change in Kinetic Energy\n",
+ "KE=m*(v**2-u**2)*2**-1 #N*m\n",
+ "\n",
+ "S=KE*F2**-1 #Max Distance\n",
+ "\n",
+ "#PArt-2\n",
+ "\n",
+ "#Net Force in direction of motion is\n",
+ "F3=W*sin(theta*pi*180**-1)-mu*R #N\n",
+ "\n",
+ "#Work Done on the body \n",
+ "W2=F3*S #N*m\n",
+ "\n",
+ "#Velocity of the body\n",
+ "V1=(-W2*2*g*W**-1)**0.5\n",
+ "\n",
+ "#Result\n",
+ "print\"MAx Distance that the bodt will move up the inclined plane\",round(S,2),\"m\"\n",
+ "print\"Velocity of the body\",round(V1,2),\"m/s\""
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "MAx Distance that the bodt will move up the inclined plane -15.2 m\n",
+ "Velocity of the body 7.74 m/s\n"
+ ]
+ }
+ ],
+ "prompt_number": 4
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 18.20,Page No.691"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "\n",
+ "#Initilization of Variables\n",
+ "\n",
+ "m1=0.025 #Kg #Mass of bullet\n",
+ "u1=600 #m/s #Initial Veloctiy of Bullet\n",
+ "m2=5 #Kg #Mass of Wooden Block\n",
+ "u2=0 #m/s #Final Velocity of bullet\n",
+ "S=0.9 #m #Distance travelled by block and bullet\n",
+ "g=9.81 #Acceleration due to gravity\n",
+ "\n",
+ "#Calculation\n",
+ "\n",
+ "#Total mass of bullet\n",
+ "M=m1+m2 #Kg\n",
+ "\n",
+ "#common Velocityof bullet and block after impact\n",
+ "V=(m1*u1+m2*u2)*M**-1 #m/s\n",
+ "\n",
+ "#Average resistance between block and horizontal surface\n",
+ "\n",
+ "#Initial Velocity of Block And Bullet\n",
+ "Vi=V #m/s\n",
+ "\n",
+ "#Final Velocity\n",
+ "Vf=0 #m/s\n",
+ "\n",
+ "#Change of KE of bullet and Block\n",
+ "KE=M*(Vf**2-Vi**2)*2**-1 #N*m\n",
+ "\n",
+ "#Frictional resistance \n",
+ "P=-KE*S**-1 #N\n",
+ "\n",
+ "#Coefficient of Friction \n",
+ "\n",
+ "W=M*g #N\n",
+ "R=W #N \n",
+ "\n",
+ "mu=P*R**-1 \n",
+ "\n",
+ "#Result\n",
+ "print\"Average Resistance between Block and horizontal surface\",round(P,2),\"N\"\n",
+ "print\"Coefficient of friction is\",round(mu,2)"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "Average Resistance between Block and horizontal surface 24.88 N\n",
+ "Coefficient of friction is 0.5\n"
+ ]
+ }
+ ],
+ "prompt_number": 23
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 18.21,Page No.692"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "\n",
+ "#Initilization of Variables\n",
+ "\n",
+ "m1=0.01 #Kg #mass of bullet\n",
+ "m2=1 #Kg #Mass of Block\n",
+ "S=1 #m #Distance travelled by block and bullet\n",
+ "mu=0.2 #coefficient of friction\n",
+ "g=9.81 #Acceleration due to gravity\n",
+ "\n",
+ "#Calculation\n",
+ "\n",
+ "#total mass of buulet and wooden block\n",
+ "M=m1+m2 #Kg\n",
+ "\n",
+ "#Friction Force\n",
+ "F=mu*M*g #N\n",
+ "\n",
+ "#Work Done by force of friction\n",
+ "W=F*S #N\n",
+ "\n",
+ "#Velocity of bullet\n",
+ "u1=(W*2*M**-1)**0.5*M*m1**-1 #m/s\n",
+ "\n",
+ "#Result\n",
+ "print\"Velocity of bullet is\",round(u1,2),\"m/s\""
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "Velocity of bullet is 200.07 m/s\n"
+ ]
+ }
+ ],
+ "prompt_number": 24
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 18.22,Page No.694"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "\n",
+ "#Initilization of Variables\n",
+ "\n",
+ "M=1500 #Kg #Mass of Hammer\n",
+ "h=0.6 #m #Height from which hammer drops\n",
+ "m=750 #kg #Mass of pile\n",
+ "S=0.05 #m #Depth of penetration\n",
+ "g=9.81 #Acceleration due to gravity\n",
+ "\n",
+ "#Calculation\n",
+ "\n",
+ "#Velocity of hammer after falling through height of 0.6 m from rest\n",
+ "v=(2*g*h)**0.5 #m/s\n",
+ "\n",
+ "#Total momentum of hammer and pile just before impact\n",
+ "p=M*v #Kg*m/s\n",
+ "\n",
+ "#Common Velocity\n",
+ "V=p*(M+m)**-1 #m/s\n",
+ "\n",
+ "#Part-2\n",
+ "\n",
+ "#K.E of system\n",
+ "KE=(M+m)*round(V,2)**2*2**-1 #N*m\n",
+ "\n",
+ "#Loss of P.E of system\n",
+ "PE=(M+m)*g*S #N*m\n",
+ "\n",
+ "#Total Energy loss\n",
+ "E=KE+PE #N*m\n",
+ "\n",
+ "#Resistance of ground\n",
+ "R=E*S**-1 #N\n",
+ "\n",
+ "#Result\n",
+ "print\"Common Velocity after impact\",round(V,2),\"m/s\"\n",
+ "print\"Average Resistance of the ground\",round(R,2),\"N\""
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "Common Velocity after impact 2.29 m/s\n",
+ "Average Resistance of the ground 140064.75 N\n"
+ ]
+ }
+ ],
+ "prompt_number": 25
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 18.23,Page No.695"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "\n",
+ "#Initilization of Variables\n",
+ "\n",
+ "M=750 #Kg #MAss of hammer\n",
+ "h=1.2 #m #Height through which hammer drops\n",
+ "m=200 #kg #mass of pile\n",
+ "R=79*10**3 #N #Average resistance of ground\n",
+ "g=9.81 #Acceleration due to gravity\n",
+ "\n",
+ "#Calculation\n",
+ "\n",
+ "#Velocity of hammer after falling through height of 0.6 m from rest\n",
+ "v=(2*g*h)**0.5 #m/s\n",
+ "\n",
+ "#Total momentum of hammer and pile just before impact\n",
+ "p=M*v #Kg*m/s\n",
+ "\n",
+ "#Common Velocity\n",
+ "V=p*(M+m)**-1 #m/s\n",
+ "\n",
+ "#Part-2\n",
+ "\n",
+ "#K.E of system\n",
+ "KE=(M+m)*round(V,2)**2*2**-1 #N*m\n",
+ "\n",
+ "#Depth of penetration into the ground\n",
+ "S=KE*(R-(M+m)*g)**-1\n",
+ "\n",
+ "#Result\n",
+ "print\"Depth of penetration into the ground\",round(S,2),\"m\""
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "Depth of penetration into the ground 0.1 m\n"
+ ]
+ }
+ ],
+ "prompt_number": 26
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 18.24,Page No.696"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "\n",
+ "#Initilization of Variables\n",
+ "\n",
+ "M=400 #Kg #Mass of Hammer\n",
+ "h=3 #m #Height from which hammer drops\n",
+ "m=0 #kg #Mass of pile\n",
+ "S=1 #m #Depth of penetration\n",
+ "g=9.81 #Acceleration due to gravity\n",
+ "\n",
+ "\n",
+ "#Calculation\n",
+ "\n",
+ "#Velocity of hammer after falling through height of 0.6 m from rest\n",
+ "v=(2*g*h)**0.5 #m/s\n",
+ "\n",
+ "#Total momentum of hammer and pile just before impact\n",
+ "p=M*v #Kg*m/s\n",
+ "\n",
+ "#Common Velocity\n",
+ "V=p*(M+m)**-1 #m/s\n",
+ "\n",
+ "#Part-2\n",
+ "\n",
+ "#K.E of system\n",
+ "KE=(M+m)*V**2*2**-1 #N*m\n",
+ "\n",
+ "#Loss of P.E of system\n",
+ "PE=(M+m)*g*S #N*m\n",
+ "\n",
+ "#Total Energy loss\n",
+ "E=KE+PE #N*m\n",
+ "\n",
+ "#Resistance of ground\n",
+ "R=E*S**-1 #N\n",
+ "\n",
+ "\n",
+ "#Result\n",
+ "print\"Resistance of ground for penetration is\",round(R,2),\"N\""
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "Resistance of ground for penetration is 15696.0 N\n"
+ ]
+ }
+ ],
+ "prompt_number": 27
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 18.25,Page No.697"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "\n",
+ "#Initilization of Variables\n",
+ "\n",
+ "M=10 #Kg #Mass of Body\n",
+ "k=100 #N/cm #stiffnes\n",
+ "h=2 #cm #Height through which mass 10 kg is dropped \n",
+ " \n",
+ "#Calculation\n",
+ "\n",
+ "#For Position 1\n",
+ "#PE+KE=M*g*(x+h) ............1\n",
+ "\n",
+ "#For Position 2\n",
+ "#PE of spring=50*x**2 .............2\n",
+ "\n",
+ "#Equating equations 1 and 2 we get\n",
+ "#5x**2-9.81*x-19.62=0\n",
+ "\n",
+ "a=5\n",
+ "b=-9.81\n",
+ "c=-19.62\n",
+ "\n",
+ "X=b**2-4*a*c\n",
+ "\n",
+ "#Max Displacement of spring\n",
+ "x1=(-b+X**0.5)*(2*a)**-1\n",
+ "x2=(-b-X**0.5)*(2*a)**-1\n",
+ "\n",
+ "#Result\n",
+ "print\"Max Displacement of spring\",round(x1,2),\"m\""
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "Max Displacement of spring 3.19 m\n"
+ ]
+ }
+ ],
+ "prompt_number": 28
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 18.26,Page No.698"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "from math import sin, cos, radians, pi\n",
+ "\n",
+ "#Initilization of Variables\n",
+ "\n",
+ "m=0.01 #kg #Mass of bullet\n",
+ "M=1 #kg #Mass of body\n",
+ "L=1 #m #Length of string\n",
+ "theta=18.2 #degrees\n",
+ "g=9.81 #acceleration due to gravity\n",
+ "L_OA=1 #m #Length of OA\n",
+ "L_OB=1 #m #Length of OB\n",
+ "\n",
+ "#Calculation\n",
+ "\n",
+ "#From Geometry of figure\n",
+ "h=L_OA-L_OB*cos(theta*pi*180**-1) #m\n",
+ "\n",
+ "#Potential Energy of body and bullet at B\n",
+ "PE=(M+m)*g*h\n",
+ "\n",
+ "#from Kinetic Energy of body and bullet after impact\n",
+ "V=(PE*2*(M+m)**-1)**0.5 #m/s #Velocity of body and bullet\n",
+ "\n",
+ "#Velocity of bullet\n",
+ "u=(M+m)*V*m**-1\n",
+ "\n",
+ "#Result\n",
+ "print\"Velocity of Bullet is\",round(u,2),\"m/s\""
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "Velocity of Bullet is 100.06 m/s\n"
+ ]
+ }
+ ],
+ "prompt_number": 5
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 18.27,Page No.700"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "from math import sin, cos, radians, pi\n",
+ "import numpy as np\n",
+ "\n",
+ "#Initilization of Variables\n",
+ "\n",
+ "m=0.03 #kg #Mass of bullet\n",
+ "u=483 #m/s #Velocity of bullet\n",
+ "M=10 #kg #MAss of body\n",
+ "L=0.8 #m #Length of string\n",
+ "g=9.81\n",
+ "\n",
+ "#Calculation\n",
+ "\n",
+ "#Momentum of bullet and body before impact\n",
+ "p=m*u #Kg*m/s\n",
+ "\n",
+ "#from Momentum of bullet and body after impact\n",
+ "V=p*(M+m)**-1 #m/s\n",
+ "\n",
+ "#K.E of the bullet and body after impact\n",
+ "KE=(M+m)*V**2*2**-1 #N*m\n",
+ "\n",
+ "#Angle through which body swings\n",
+ "theta=np.arccos(-((KE*((M+m)*g)**-1)-L)*L**-1)*(pi**-1*180) #Degrees\n",
+ "\n",
+ "#Result\n",
+ "print\"Angle through which body swings is\",round(theta,2),\"Degrees\""
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "Angle through which body swings is 29.88 Degrees\n"
+ ]
+ }
+ ],
+ "prompt_number": 2
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 18.28,Page No.701"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "from math import sin, cos, radians, pi\n",
+ "import numpy as np\n",
+ "\n",
+ "#Initilization of Variables\n",
+ "\n",
+ "m=0.03 #kg #mass of bullet\n",
+ "u=483 #m/s #velocity of bullet\n",
+ "M=10 #Kg #Mass of body\n",
+ "L=0.8 #m #Length of string\n",
+ "v=96.5 #m/s #Velocity of body\n",
+ "g=9.81 #acceleration due to gravity\n",
+ "\n",
+ "#Calculation\n",
+ "\n",
+ "#Velocity of Body after impact\n",
+ "V=(m*u-m*v)*M**-1 #m/s\n",
+ "\n",
+ "#Height \n",
+ "h=V**2*(2*g)**-1 #m\n",
+ "\n",
+ "#from geometry\n",
+ "theta=np.arccos((L-h)*L**-1)*(pi**-1*180)\n",
+ "\n",
+ "#Result\n",
+ "print\"Angle through which the body will swing\",round(theta,2),\"Degrees\""
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "Angle through which the body will swing 23.89 Degrees\n"
+ ]
+ }
+ ],
+ "prompt_number": 1
+ }
+ ],
+ "metadata": {}
+ }
+ ]
+}
\ No newline at end of file diff --git a/Engineering_Mechanics/chapter_2.ipynb b/Engineering_Mechanics/chapter_2.ipynb new file mode 100644 index 00000000..6dcfae81 --- /dev/null +++ b/Engineering_Mechanics/chapter_2.ipynb @@ -0,0 +1,648 @@ +{
+ "metadata": {
+ "name": "chapter_2.ipynb"
+ },
+ "nbformat": 3,
+ "nbformat_minor": 0,
+ "worksheets": [
+ {
+ "cells": [
+ {
+ "cell_type": "heading",
+ "level": 1,
+ "metadata": {},
+ "source": [
+ "Chapter 2:Coplanar Collinear And Concurrent Forces"
+ ]
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 2.1,Page No.30"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "\n",
+ "#Declaration Of Variables\n",
+ "\n",
+ "#Horizontal Forces\n",
+ "F1=200 #N\n",
+ "F2=100 #N\n",
+ "F3=300 #N\n",
+ "\n",
+ "#Calculations\n",
+ "\n",
+ "#Analytical Method\n",
+ "\n",
+ "#When all forces are acting in same Direction,resultant is\n",
+ "R=F1+F2+F3 #N\n",
+ "\n",
+ "#When Force 100 N is acting in opposite direction\n",
+ "R2=F1-F2+F3 #N\n",
+ "\n",
+ "#Graphical Method\n",
+ "\n",
+ "#Let P1,P2,P3 be the forces\n",
+ "#Suppose 100 N=1 cm\n",
+ "P1=F1*F2**-1 #cm\n",
+ "P2=F2*F2**-1 #cm\n",
+ "P3=F3*F2**-1 #cm\n",
+ "\n",
+ "#When All Forces act in same direction \n",
+ "ab=2 #cm to represent F1\n",
+ "bc=1 #cm to represent F2\n",
+ "cd=3 #cm to represent F3\n",
+ "\n",
+ "#by Measurement \n",
+ "ad=6 #cm\n",
+ "R3=6*F2 #N\n",
+ "\n",
+ "#When F2 acts in opposite direction \n",
+ "#draw bc in opposite Direction \n",
+ "#By Measurement,Length\n",
+ "ad=4 #cm\n",
+ "\n",
+ "R4=4*F2 #N\n",
+ "\n",
+ "#Result\n",
+ "print\"Resultant of forces analytically:When all forces are acting in same Direction\",round(R,2),\"N\"\n",
+ "print\" :When Force 100 N is acting in opposite direction\",round(R2,2),\"N\"\n",
+ "print\"Resultant of forces Graphically:When All Forces act in same direction\",round(R3,2),\"N\"\n",
+ "print\" :When Force 100 N is acting in opposite direction\",round(R4,2),\"N\""
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "Resultant of forces analytically:When all forces are acting in same Direction 600.0 N\n",
+ " :When Force 100 N is acting in opposite direction 400.0 N\n",
+ "Resultant of forces Graphically:When All Forces act in same direction 600.0 N\n",
+ " :When Force 100 N is acting in opposite direction 400.0 N\n"
+ ]
+ }
+ ],
+ "prompt_number": 1
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 2.2,Page No.34"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "from math import sin, cos, tan, radians, pi\n",
+ "import numpy as np\n",
+ "\n",
+ "#Declaration Of Variables\n",
+ "\n",
+ "#Forces\n",
+ "P=240 #N\n",
+ "Q=200 #N\n",
+ "alpha=60 #Degrees #Angle Between forces\n",
+ "\n",
+ "#Calculations\n",
+ "\n",
+ "#Magnitude of Resultant Force is \n",
+ "R=(P**2+Q**2+2*P*Q*cos(alpha*pi*180**-1))**0.5 #N\n",
+ "\n",
+ "#Using sine formula\n",
+ "#P*(sin(beta))**-1=Q*(sin(rho))**-1=R*(sin(180-alpha))**-1\n",
+ "\n",
+ "X=(P*sin((180-alpha)*180**-1*pi)*R**-1)\n",
+ "beta=np.arcsin(X)*(180*pi**-1) #degrees\n",
+ "\n",
+ "Y=(Q*sin((180-alpha)*180**-1*pi)*R**-1)\n",
+ "rho=np.arcsin(Y)*(180*pi**-1) #degrees\n",
+ "\n",
+ "#Result\n",
+ "print\"Magnitude of Resultant is\",round(R,2),\"N\"\n",
+ "print\"angle beta is\",round(beta,2),\"Degrees\"\n",
+ "print\"Angle rho is\",round(rho,3),\"Degrees\""
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "Magnitude of Resultant is 381.58 N\n",
+ "angle beta is 33.0 Degrees\n",
+ "Angle rho is 26.996 Degrees\n"
+ ]
+ }
+ ],
+ "prompt_number": 1
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 2.3,Page No.35"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "from math import sin, cos, tan, radians, pi\n",
+ "\n",
+ "#Declaration Of Variables\n",
+ "\n",
+ "R=400 #N #resultant\n",
+ "beta=35 #Degrees\n",
+ "rho=25 #Derees\n",
+ "\n",
+ "#Calculations\n",
+ "\n",
+ "#Angle Between two forces\n",
+ "alpha=beta+rho #Degrees\n",
+ "\n",
+ "#Using sine formula\n",
+ "#P*(sin(beta))**-1=Q*(sin(rho))**-1=R*(sin(180-alpha))**-1\n",
+ "#After further simplifying we get\n",
+ "\n",
+ "P=R*sin(beta*180**-1*pi)*(sin((180-alpha)*180**-1*pi))**-1 #N\n",
+ "Q=R*sin(rho*180**-1*pi)*(sin((180-alpha)*180**-1*pi))**-1 #N\n",
+ "\n",
+ "#Result\n",
+ "print\"Two forces Are:P\",round(P,2),\"P\"\n",
+ "print\" :Q\",round(Q,3),\"Q\""
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "Two forces Are:P 264.92 P\n",
+ " :Q 195.199 Q\n"
+ ]
+ }
+ ],
+ "prompt_number": 3
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 2.4,Page No.35"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "from math import sin, cos, tan, radians, pi\n",
+ "import numpy as np\n",
+ "\n",
+ "\n",
+ "#Declaration Of Variables\n",
+ "\n",
+ "#Forces\n",
+ "P=240 #N\n",
+ "Q=200 #N\n",
+ "R=400 #N\n",
+ "\n",
+ "#Calculations\n",
+ "\n",
+ "#Using Equation of Resultant,we get\n",
+ "#R=(P**2+Q**2+2*P*Q*cos(alpha))**0.5\n",
+ "#After Further simplifying we get\n",
+ "#Let cos(alpha)=X\n",
+ "X=(R**2-P**2-Q**2)*(2*P*Q)**-1 \n",
+ "alpha=np.arccos(X)*(180*pi**-1) #Degrees\n",
+ "\n",
+ "#Using sine formula\n",
+ "#P*(sin(beta))**-1=Q*(sin(rho))**-1=R*(sin(180-alpha))**-1\n",
+ "#After further simplifying we get\n",
+ "X=(P*sin((180-alpha)*180**-1*pi)*R**-1)\n",
+ "beta=np.arcsin(X)*(180*pi**-1) #degrees\n",
+ "\n",
+ "Y=(Q*sin((180-alpha)*180**-1*pi)*R**-1)\n",
+ "rho=np.arcsin(Y)*(180*pi**-1) #degrees\n",
+ "\n",
+ "#Result\n",
+ "print\"Values of:alpha\",round(alpha,2),\"Degrees\"\n",
+ "print\" :beta\",round(beta,2),\"Degrees\"\n",
+ "print\" :rho\",round(rho,2),\"Degrees\""
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "Values of:alpha 49.46 Degrees\n",
+ " :beta 27.13 Degrees\n",
+ " :rho 22.33 Degrees\n"
+ ]
+ }
+ ],
+ "prompt_number": 4
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 2.5,Page No.36"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "from math import sin, cos, tan, radians, pi\n",
+ "\n",
+ "#Declaration Of Variables\n",
+ "\n",
+ "F=100 #N\n",
+ "theta=30 #Degrees #Angle made by Force with axis\n",
+ "\n",
+ "#Calculations\n",
+ "\n",
+ "#Force acting in X-direction \n",
+ "F_x=F*cos(theta*180**-1*pi) #N\n",
+ "\n",
+ "#Force acting in Y-direction \n",
+ "F_y=F*sin(theta*180**-1*pi) #N\n",
+ "\n",
+ "#Result\n",
+ "print\"Components of Force along X directions\",round(F_x,2),\"N\"\n",
+ "print\"Components Of force along Y direction\",round(F_y,2),\"N\""
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "Components of Force along X directions 86.6 N\n",
+ "Components Of force along Y direction 50.0 N\n"
+ ]
+ }
+ ],
+ "prompt_number": 5
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 2.6,Page No.37"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "from math import sin, cos, tan, radians, pi\n",
+ "\n",
+ "#Declaration Of Variables\n",
+ "\n",
+ "W=100 #N #Weight\n",
+ "theta=30 #Degrees\n",
+ "\n",
+ "#Calculations\n",
+ "\n",
+ "#Component of weight perpendicular to plane\n",
+ "W1=W*cos(theta*180**-1*pi) #N\n",
+ "\n",
+ "#Component of weight parallel to plane\n",
+ "W2=W*sin(theta*180**-1*pi) #N\n",
+ "\n",
+ "#Result\n",
+ "print\"Component of weight:perpendicular to plane\",round(W1,2),\"N\"\n",
+ "print\" :parallel to plane\",round(W2,2),\"N\"\n",
+ "\n",
+ "#Answer for Component of weight:perpendicular to plane is incorrect"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "Component of weight:perpendicular to plane 86.6 N\n",
+ " :parallel to plane 50.0 N\n"
+ ]
+ }
+ ],
+ "prompt_number": 6
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 2.7,Page No.37"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "from math import sin, cos, tan, radians, pi\n",
+ "import numpy as np\n",
+ "\n",
+ "#Declaration Of Variables\n",
+ "\n",
+ "#Lengths\n",
+ "L_BA=50 #cm\n",
+ "L_AO=25 #cm\n",
+ "\n",
+ "theta=45 #Degrees #angle made by crank bith L_BO\n",
+ "\n",
+ "F1=2500 #N Force ererted on connecting rod\n",
+ "\n",
+ "#Calculations\n",
+ "\n",
+ "#Let alpha be the angle made by connecting rod with hte perpendicular drawn to L_BO\n",
+ "\n",
+ "L_AC=L_AO*sin(theta*pi*180**-1)\n",
+ "\n",
+ "alpha=np.arcsin(L_AC*L_BA**-1)*(180*pi**-1) #degrees\n",
+ "\n",
+ "#Horizontal force of connecting rod\n",
+ "H_A=F1*cos(round(alpha,2)*pi*180**-1)\n",
+ "\n",
+ "#Vertical force of connecting rod\n",
+ "V_A=F1*sin(round(alpha,2)*pi*180**-1)\n",
+ "\n",
+ "#Part-2\n",
+ "\n",
+ "#LEt angle OAD be beta\n",
+ "beta=theta+alpha #Degrees\n",
+ "\n",
+ "#Component of force AD along AO\n",
+ "F_AO1=F1*cos(round(beta,2)*pi*180**-1) #degrees\n",
+ "\n",
+ "#Component of force AD along AE\n",
+ "F_AO2=F1*sin(round(beta,2)*pi*180**-1) #degrees\n",
+ "\n",
+ "\n",
+ "#Result\n",
+ "print\"Resolving Forces of connecting rod:H_A\",round(H_A,2),\"KN\"\n",
+ "print\" :V_A\",round(V_A,2),\"KN\"\n",
+ "print\"Resolving forces of crank:F_AO2\",round(F_AO2,2),\"KN\"\n",
+ "print\" :F_AO1\",round(F_AO1,2),\"KN\""
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "Resolving Forces of connecting rod:H_A 2338.61 KN\n",
+ " :V_A 883.69 KN\n",
+ "Resolving forces of crank:F_AO2 2278.51 KN\n",
+ " :F_AO1 1028.79 KN\n"
+ ]
+ }
+ ],
+ "prompt_number": 7
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 2.8,Page No.38"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "from math import sin, cos, tan, radians, pi\n",
+ "import numpy as np\n",
+ "\n",
+ "#Declaration Of Variables\n",
+ "\n",
+ "#Forces\n",
+ "F1=104 #N\n",
+ "F2=156 #N\n",
+ "F3=252 #N\n",
+ "F4=228 #N\n",
+ "\n",
+ "#Angles\n",
+ "alpha1=10 #Degrees\n",
+ "alpha2=24 #Degrees\n",
+ "alpha3=3 #Degrees\n",
+ "alpha4=9 #Degrees\n",
+ "\n",
+ "#Calculations\n",
+ "\n",
+ "#Resolving force F1\n",
+ "F1_V=F1*sin(alpha1*pi*180**-1) #N\n",
+ "F1_H=F1*cos(alpha1*pi*180**-1) #N\n",
+ "\n",
+ "#Resolving Force F2\n",
+ "F2_V=F2*cos(alpha2*pi*180**-1) #N\n",
+ "F2_H=-F2*sin(alpha2*pi*180**-1) #N\n",
+ "\n",
+ "#Resolving Force F3\n",
+ "F3_H=-F3*cos(alpha3*pi*180**-1) #N\n",
+ "F3_V=F3*sin(alpha3*pi*180**-1) #N\n",
+ "\n",
+ "#Resolving Force F4\n",
+ "F4_H=-F4*sin(alpha4*pi*180**-1) #N\n",
+ "F4_V=F4*cos(alpha4*pi*180**-1) #N\n",
+ "\n",
+ "#Sum of Horizontal Forces\n",
+ "H=F1_H+F2_H+F3_H+F4_H #N\n",
+ "\n",
+ "#Sum of vertical Forces\n",
+ "V=F1_V+F2_V-F3_V-F4_V #N\n",
+ "\n",
+ "#Resultant\n",
+ "R=(H**2+V**2)**0.5\n",
+ "\n",
+ "#Direction\n",
+ "theta=np.arctan(V*H**-1)*(180*pi**-1)\n",
+ "\n",
+ "#Result\n",
+ "print\"Magnitude of Resultant\",round(R,2),\"N\"\n",
+ "print\"Direction of Resultant\",round(theta,2),\"Degrees\""
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "Magnitude of Resultant 260.26 N\n",
+ "Direction of Resultant 17.4 Degrees\n"
+ ]
+ }
+ ],
+ "prompt_number": 8
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 2.9,Page No.41"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "from math import sin, cos, tan, radians, pi\n",
+ "import numpy as np\n",
+ "\n",
+ "#Declaration Of Variables\n",
+ "\n",
+ "#Forces\n",
+ "F1=10 #KN \n",
+ "F3=20 #KN\n",
+ "F4=40 #KN\n",
+ "\n",
+ "#Inclination\n",
+ "theta1=30 #Degree\n",
+ "theta3=90 #degree\n",
+ "theta3=120 #degree\n",
+ "\n",
+ "R=72 #KN #Resultant\n",
+ "\n",
+ "#Calculations\n",
+ "\n",
+ "#Sum of horizontal Forces\n",
+ "#F2*cos(theta2)=11.34...................1\n",
+ "\n",
+ "#Sum of vertical Forces\n",
+ "#F2*sin(theta2)=12.36.....................2\n",
+ "\n",
+ "#Dividing equation 2 by 1 and further simplifying we get\n",
+ "\n",
+ "theta2=np.arctan(1.0899)*(180*pi**-1)\n",
+ "\n",
+ "#Force\n",
+ "F2=12.36*(sin(theta2*180**-1*pi))**-1 #KN\n",
+ "\n",
+ "#Result\n",
+ "print\"Magnitude of Force is\",round(F2,2),\"KN\"\n",
+ "print\"Direction of force is\",round(theta2,2),\"Degrees\""
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "Magnitude of Force is 16.77 KN\n",
+ "Direction of force is 47.46 Degrees\n"
+ ]
+ }
+ ],
+ "prompt_number": 2
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 2.10,Page No.41"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "from math import sin, cos, tan, radians, pi\n",
+ "import numpy as np\n",
+ "\n",
+ "#Declaration Of Variables\n",
+ "\n",
+ "#Lengths\n",
+ "L_OC=4 #m \n",
+ "L_BC=3 #m\n",
+ "\n",
+ "#Forces\n",
+ "F_O=20 #N\n",
+ "F_C=35 #N\n",
+ "F_B=25 #N \n",
+ "F_A=50 #N\n",
+ "\n",
+ "#Calculations\n",
+ "\n",
+ "#Resultant Forces\n",
+ "R1=(F_A**2+F_O**2)**0.5 #N\n",
+ "R2=(F_B**2+F_C**2)**0.5 #N\n",
+ "\n",
+ "#Angle\n",
+ "theta1=np.arctan(F_O*F_A**-1)*(180*pi**-1) #Degrees\n",
+ "theta2=np.arctan(F_B*F_C**-1)*(180*pi**-1) #Degrees\n",
+ "\n",
+ "#Angle between these two Forces\n",
+ "theta3=theta1+theta2 #Degrees\n",
+ "\n",
+ "#Resultant of Forces R1 & R2\n",
+ "P=(R1**2+R2**2+2*R1*R2*cos(theta3*pi*180**-1))**0.5 #N\n",
+ "\n",
+ "#Angle made by Resultant P with R1\n",
+ "S1=(R2*sin(theta3*pi*180**-1))\n",
+ "S2=R1+R2*cos(theta3*pi*180**-1)\n",
+ "alpha=np.arctan(S1*S2**-1)*(180*pi**-1)\n",
+ "\n",
+ "#Angle made by resultant P with vertical in anticlock wise direction\n",
+ "theta4=alpha-theta1 #Degrees\n",
+ "\n",
+ "#Result\n",
+ "print\"Magnitude of Force\",round(P,2),\"N\"\n",
+ "print\"Direction of force\",round(theta4,2),\"N\""
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "Magnitude of Force 85.15 N\n",
+ "Direction of force 3.37 N\n"
+ ]
+ }
+ ],
+ "prompt_number": 3
+ }
+ ],
+ "metadata": {}
+ }
+ ]
+}
\ No newline at end of file diff --git a/Engineering_Mechanics/chapter_20.ipynb b/Engineering_Mechanics/chapter_20.ipynb new file mode 100644 index 00000000..7512cbbd --- /dev/null +++ b/Engineering_Mechanics/chapter_20.ipynb @@ -0,0 +1,2599 @@ +{
+ "metadata": {
+ "name": "chapter_20.ipynb"
+ },
+ "nbformat": 3,
+ "nbformat_minor": 0,
+ "worksheets": [
+ {
+ "cells": [
+ {
+ "cell_type": "heading",
+ "level": 1,
+ "metadata": {},
+ "source": [
+ "Chapter 20:Beams (Shear Force And Bending Moment)"
+ ]
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 20.1,Page No.730"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "import matplotlib.pyplot as plt\n",
+ "\n",
+ "#Declaration Of Variables\n",
+ "\n",
+ "#Lengths\n",
+ "\n",
+ "L=2 #m #Span of beam\n",
+ "L_AB=0.5 #m\n",
+ "L_BC=0.7 #m\n",
+ "L_CD=0.8 #m\n",
+ "\n",
+ "#Point Load\n",
+ "F_D=800 #N\n",
+ "F_C=500 #N\n",
+ "F_B=300 #n\n",
+ "\n",
+ "#Calculations\n",
+ "\n",
+ "#Let R_A be the reactions at A \n",
+ "R_A=F_B+F_C+F_D #N\n",
+ "\n",
+ "#Shear Force Calculations\n",
+ "\n",
+ "#Shear Force at pt D\n",
+ "V_D=F_D #N\n",
+ "\n",
+ "#Shear Force at pt C\n",
+ "V_C1=V_D #N\n",
+ "V_C2=V_D+F_C #N\n",
+ "\n",
+ "#Shear force at pt B\n",
+ "V_B1=V_C2 #N\n",
+ "V_B2=V_C2+F_B\n",
+ "\n",
+ "#Shear Force at pt A\n",
+ "V_A=V_B2 #N\n",
+ "\n",
+ "#Bending Moment Calculations\n",
+ "\n",
+ "#B.M at D\n",
+ "M_D=F_D*0 #N.m\n",
+ "\n",
+ "#B.M at pt C\n",
+ "M_C=F_D*L_CD #N.m\n",
+ "\n",
+ "#B.M at pt B\n",
+ "M_B=F_D*(L_CD+L_BC)+F_C*L_BC #N.m\n",
+ "\n",
+ "#B.M at pt A\n",
+ "M_A=F_D*L+F_C*(L_BC+L_AB)+F_B*L_AB #N.m\n",
+ "\n",
+ "#Result\n",
+ "print \"The Shear Force and Bending Moment Diagrams are the results\"\n",
+ "\n",
+ "#Plotting the Shear Force Diagram\n",
+ "\n",
+ "X1=[0,L_CD,L_CD,L_CD+L_BC,L_CD+L_BC,L_CD+L_BC+L_AB]\n",
+ "Y1=[V_D,V_C1,V_C2,V_B1,V_B2,V_A]\n",
+ "Z1=[0,0,0,0,0,0]\n",
+ "plt.plot(X1,Y1,X1,Z1)\n",
+ "plt.xlabel(\"Length x in m\")\n",
+ "plt.ylabel(\"Shear Force in kN\")\n",
+ "plt.show()\n",
+ "\n",
+ "#Plotting the Bendimg Moment Diagram\n",
+ "\n",
+ "Y2=[M_D,M_C,M_B,M_A]\n",
+ "X2=[0,L_CD,L_CD+L_BC,L_CD+L_BC+L_AB]\n",
+ "Z2=[0,0,0,0]\n",
+ "plt.plot(X2,Y2)\n",
+ "plt.xlabel(\"Lenght in m\")\n",
+ "plt.ylabel(\"Bending Moment in kN.m\")\n",
+ "plt.show()"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "The Shear Force and Bending Moment Diagrams are the results\n"
+ ]
+ },
+ {
+ "metadata": {},
+ "output_type": "display_data",
+ "png": 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+ "text": [
+ "<matplotlib.figure.Figure at 0x55c44d0>"
+ ]
+ },
+ {
+ "metadata": {},
+ "output_type": "display_data",
+ "png": 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+ "text": [
+ "<matplotlib.figure.Figure at 0x55c45d0>"
+ ]
+ }
+ ],
+ "prompt_number": 1
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 20.2,Page No.733"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "import matplotlib.pyplot as plt\n",
+ "\n",
+ "#Declaration Of Variables\n",
+ "\n",
+ "#lengths\n",
+ "L_CB=1.5 #m \n",
+ "L_AC=0.5 #m\n",
+ "\n",
+ "#Loads\n",
+ "w=1 #KN/m #u.d.l\n",
+ "\n",
+ "#Calculations\n",
+ "\n",
+ "R_A=w*L_CB #KN\n",
+ "\n",
+ "#Shear Force Calculations\n",
+ "\n",
+ "#S.F at B\n",
+ "V_B=0\n",
+ "\n",
+ "#S.F at C\n",
+ "V_C=w*L_CB #KN\n",
+ "\n",
+ "#S.F at A\n",
+ "V_A=V_C #KN\n",
+ "\n",
+ "#Bending Moment Calculations\n",
+ "\n",
+ "#B.M at B\n",
+ "M_B=0\n",
+ "\n",
+ "#B.M at C\n",
+ "M_C=w*L_CB*L_CB*2**-1\n",
+ "\n",
+ "#B.M at A\n",
+ "M_A=w*L_CB*(L_CB*2**-1+L_AC) #KN\n",
+ "\n",
+ "#Result\n",
+ "print \"The Shear Force and Bending Moment Diagrams are the results\"\n",
+ "\n",
+ "#Plotting the Shear Force Diagram\n",
+ "\n",
+ "X1=[0,L_CB,L_CB+L_AC]\n",
+ "Y1=[V_B,V_C,V_A]\n",
+ "Z1=[0,0,0]\n",
+ "plt.plot(X1,Y1,X1,Z1)\n",
+ "plt.xlabel(\"Length x in m\")\n",
+ "plt.ylabel(\"Shear Force in kN\")\n",
+ "plt.show()\n",
+ "\n",
+ "#Plotting the Bendimg Moment Diagram\n",
+ "\n",
+ "Y2=[M_B,M_C,M_A]\n",
+ "X2=[0,L_CB,L_AC+L_CB]\n",
+ "Z2=[0,0,0]\n",
+ "plt.plot(X2,Y2)\n",
+ "plt.xlabel(\"Lenght in m\")\n",
+ "plt.ylabel(\"Bending Moment in kN.m\")\n",
+ "plt.show()"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "The Shear Force and Bending Moment Diagrams are the results\n"
+ ]
+ },
+ {
+ "metadata": {},
+ "output_type": "display_data",
+ "png": 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+ "text": [
+ "<matplotlib.figure.Figure at 0x55b4f50>"
+ ]
+ },
+ {
+ "metadata": {},
+ "output_type": "display_data",
+ "png": 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+ "text": [
+ "<matplotlib.figure.Figure at 0x567d030>"
+ ]
+ }
+ ],
+ "prompt_number": 2
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 20.3,Page No.734"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "import matplotlib.pyplot as plt\n",
+ "\n",
+ "#Declaration Of Variables\n",
+ "\n",
+ "#Lengths\n",
+ "L_AB=2 #m\n",
+ "\n",
+ "#Load\n",
+ "w=2 #KN/m \n",
+ "F_B=3 #KN\n",
+ "\n",
+ "#Calculations\n",
+ "\n",
+ "#LEt R_A be the reaction at pt A\n",
+ "R_A=F_B+w*L_AB\n",
+ "\n",
+ "#Shear Force Calculations\n",
+ "\n",
+ "#S.F at B\n",
+ "V_B=F_B #KN\n",
+ "\n",
+ "#S.F at A\n",
+ "V_A=V_B+w*L_AB #KN\n",
+ "\n",
+ "#Bending Moment Calculations\n",
+ "\n",
+ "#B.M at B\n",
+ "M_B=0 #KN.m\n",
+ "\n",
+ "#B.M at A\n",
+ "M_A=F_B*L_AB+w*L_AB*L_AB*2**-1 #KN.m\n",
+ "\n",
+ "\n",
+ "#Result\n",
+ "print \"The Shear Force and Bending Moment Diagrams are the results\"\n",
+ "\n",
+ "#Plotting the Shear Force Diagram\n",
+ "\n",
+ "X1=[0,L_AB]\n",
+ "Y1=[V_B,V_A]\n",
+ "Z1=[0,0]\n",
+ "plt.plot(X1,Y1,X1,Z1)\n",
+ "plt.xlabel(\"Length x in m\")\n",
+ "plt.ylabel(\"Shear Force in kN\")\n",
+ "plt.show()\n",
+ "\n",
+ "#Plotting the Bendimg Moment Diagram\n",
+ "\n",
+ "Y2=[M_B,M_A]\n",
+ "X2=[0,L_AB]\n",
+ "Z2=[0,0]\n",
+ "plt.plot(X2,Y2)\n",
+ "plt.xlabel(\"Lenght in m\")\n",
+ "plt.ylabel(\"Bending Moment in kN.m\")\n",
+ "plt.show()"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "The Shear Force and Bending Moment Diagrams are the results\n"
+ ]
+ },
+ {
+ "metadata": {},
+ "output_type": "display_data",
+ "png": 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+ "text": [
+ "<matplotlib.figure.Figure at 0x55c4ef0>"
+ ]
+ },
+ {
+ "metadata": {},
+ "output_type": "display_data",
+ "png": 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+ "text": [
+ "<matplotlib.figure.Figure at 0x583f090>"
+ ]
+ }
+ ],
+ "prompt_number": 3
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 20.4,Page No.736"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "import matplotlib.pyplot as plt\n",
+ "\n",
+ "#Declaration Of Variables\n",
+ "\n",
+ "#Lengths\n",
+ "L_CB=0.5 #m\n",
+ "L_AC=1.5 #m\n",
+ "L=2 #m \n",
+ "\n",
+ "#Loads\n",
+ "F_C=2 #KN\n",
+ "w=1.5 #KN/m\n",
+ "\n",
+ "#Calculations\n",
+ "\n",
+ "#Let R_A be the reaction at pt A\n",
+ "R_A=F_C+w*L #KN\n",
+ "\n",
+ "#Shear Force Calculations\n",
+ "\n",
+ "#S.F at pt B\n",
+ "V_B=0 #KN\n",
+ "\n",
+ "#S.F At pt C\n",
+ "V_C1=w*L_CB #KN\n",
+ "V_C2=V_C1+F_C #KN\n",
+ "\n",
+ "#S.F at pt A\n",
+ "V_A=F_C+w*L #KN\n",
+ "\n",
+ "#Bending Moment Calculations\n",
+ "\n",
+ "#B.M at pt B\n",
+ "M_B=0 #KN.m\n",
+ "\n",
+ "#B.M at pt C\n",
+ "M_C=w*L_CB*L_CB*2**-1\n",
+ "\n",
+ "#B.M at pt A\n",
+ "M_A=F_C*L_AC+w*L*L*2**-1 #KN.m\n",
+ "\n",
+ "#Result\n",
+ "print \"The Shear Force and Bending Moment Diagrams are the results\"\n",
+ "\n",
+ "#Plotting the Shear Force Diagram\n",
+ "\n",
+ "X1=[0,L_CB,L_CB,L_AC+L_AC]\n",
+ "Y1=[V_B,V_C1,V_C2,V_A]\n",
+ "Z1=[0,0,0,0]\n",
+ "plt.plot(X1,Y1,X1,Z1)\n",
+ "plt.xlabel(\"Length x in m\")\n",
+ "plt.ylabel(\"Shear Force in kN\")\n",
+ "plt.show()\n",
+ "\n",
+ "#Plotting the Bendimg Moment Diagram\n",
+ "\n",
+ "Y2=[M_B,M_C,M_A]\n",
+ "X2=[0,L_CB,L_AC+L_CB]\n",
+ "Z2=[0,0,0]\n",
+ "plt.plot(X2,Y2)\n",
+ "plt.xlabel(\"Lenght in m\")\n",
+ "plt.ylabel(\"Bending Moment in kN.m\")\n",
+ "plt.show()"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "The Shear Force and Bending Moment Diagrams are the results\n"
+ ]
+ },
+ {
+ "metadata": {},
+ "output_type": "display_data",
+ "png": 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+ "text": [
+ "<matplotlib.figure.Figure at 0x55c37d0>"
+ ]
+ },
+ {
+ "metadata": {},
+ "output_type": "display_data",
+ "png": 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+ "text": [
+ "<matplotlib.figure.Figure at 0x5686df0>"
+ ]
+ }
+ ],
+ "prompt_number": 4
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 20.5,Page No.738"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "import matplotlib.pyplot as plt\n",
+ "\n",
+ "#Declaration Of Variables\n",
+ "\n",
+ "#Lengths\n",
+ "L_CB=0.25 #m\n",
+ "L_DC=1 #m \n",
+ "L_AD=0.25 #m\n",
+ "L_DB=1.25 #m\n",
+ "L=1.5 #m\n",
+ "\n",
+ "#Loads\n",
+ "F_C=3 #KN #Point Load\n",
+ "w=2 #KN/m #u.d.l\n",
+ "\n",
+ "#Calculations\n",
+ "\n",
+ "#Let R_A be the reaction at A\n",
+ "R_A=F_C+w*(L_DC+L_CB)\n",
+ "\n",
+ "#Shear Force calculations\n",
+ "\n",
+ "#S.F at pt B\n",
+ "V_B=0\n",
+ "\n",
+ "#S.F at pt C\n",
+ "V_C1=w*L_CB #KN\n",
+ "V_C2=V_C1+F_C #KN\n",
+ "\n",
+ "#S.F at D\n",
+ "V_D=w*(L_DC+L_CB)+F_C #KN\n",
+ "\n",
+ "#S.F at pt A\n",
+ "V_A=V_D #KN\n",
+ "\n",
+ "#Bending Moment Calculations\n",
+ "\n",
+ "#B.M at pt B\n",
+ "M_B=0\n",
+ "\n",
+ "#B.M at pt C\n",
+ "M_C=w*L_CB*L_CB*2**-1 #KN.m\n",
+ "\n",
+ "#B.M at pt D\n",
+ "M_D=w*L_DB*L_DB*2**-1+F_C*L_DC #KN.m\n",
+ "\n",
+ "#B.M at pt A\n",
+ "M_A=w*L_DB*(L_DB*2**-1+L_AD)+F_C*(L_DC+L_AD) #KN.m\n",
+ "\n",
+ "\n",
+ "#Result\n",
+ "print \"The Shear Force and Bending Moment Diagrams are the results\"\n",
+ "\n",
+ "#Plotting the Shear Force Diagram\n",
+ "\n",
+ "X1=[0,L_CB,L_CB,L_CB+L_DB,L_CB+L_DB+L_AD]\n",
+ "Y1=[V_B,V_C1,V_C2,V_D,V_A]\n",
+ "Z1=[0,0,0,0,0]\n",
+ "plt.plot(X1,Y1,X1,Z1)\n",
+ "plt.xlabel(\"Length x in m\")\n",
+ "plt.ylabel(\"Shear Force in kN\")\n",
+ "plt.show()\n",
+ "\n",
+ "#Plotting the Bendimg Moment Diagram\n",
+ "\n",
+ "Y2=[M_B,M_C,M_D,M_A]\n",
+ "X2=[0,L_CB,L_DC+L_CB,L_DC+L_CB+L_AD]\n",
+ "Z2=[0,0,0,0]\n",
+ "plt.plot(X2,Y2)\n",
+ "plt.xlabel(\"Lenght in m\")\n",
+ "plt.ylabel(\"Bending Moment in kN.m\")\n",
+ "plt.show()"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "The Shear Force and Bending Moment Diagrams are the results\n"
+ ]
+ },
+ {
+ "metadata": {},
+ "output_type": "display_data",
+ "png": 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+ "text": [
+ "<matplotlib.figure.Figure at 0x55b4770>"
+ ]
+ },
+ {
+ "metadata": {},
+ "output_type": "display_data",
+ "png": 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+ "text": [
+ "<matplotlib.figure.Figure at 0x5686cb0>"
+ ]
+ }
+ ],
+ "prompt_number": 5
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 20.6,Page No.739"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "import matplotlib.pyplot as plt\n",
+ "\n",
+ "#Declaration Of Variables\n",
+ "\n",
+ "#Lengths\n",
+ "L_CB=0.5 #m\n",
+ "L_DC=2 #m\n",
+ "L_ED=1.5 #m\n",
+ "L_AE=1 #m\n",
+ "L=5 #m\n",
+ "\n",
+ "#Forces\n",
+ "F_B=2.5 #KN\n",
+ "F_E=3 #KN\n",
+ "w=1 #KN/m #u.d.l\n",
+ "\n",
+ "#Calculations\n",
+ "\n",
+ "#Let R_A be the reaction at A\n",
+ "R_A=F_B+F_E+w*L_DC #KN\n",
+ "\n",
+ "#Shear Force calculations\n",
+ "\n",
+ "#S.F at pt B\n",
+ "V_B=F_B\n",
+ "\n",
+ "#S.F at pt C\n",
+ "V_C=V_B #KN\n",
+ "\n",
+ "#S.F at pt D\n",
+ "V_D=V_C+w*L_DC #KN\n",
+ "\n",
+ "#S.F at pt E\n",
+ "V_E1=V_D #KN\n",
+ "V_E2=V_D+F_E #KN\n",
+ "\n",
+ "#S.F at pt A\n",
+ "V_A=V_E2 #KN\n",
+ "\n",
+ "#Bending Moment Calculations\n",
+ "\n",
+ "#B.M at pt B\n",
+ "M_B=0 #KN.m\n",
+ "\n",
+ "#B.M at pt C\n",
+ "M_C=F_B*L_CB #KN.m\n",
+ "\n",
+ "#B.M at pt D\n",
+ "M_D=w*L_DC*L_DC*2**-1+F_B*(L_CB+L_DC) #KN.m\n",
+ "\n",
+ "#B.M at pt E\n",
+ "M_E=F_B*(L_ED+L_DC+L_CB)+w*L_DC*(L_DC*2**-1+L_ED) #KN.m\n",
+ "\n",
+ "#B.M at pt A\n",
+ "M_A=F_B*L+w*L_DC*(L_DC*2**-1+L_ED+L_AE)+F_E*L_AE #KN.m\n",
+ "\n",
+ "#Result\n",
+ "print \"The Shear Force and Bending Moment Diagrams are the results\"\n",
+ "\n",
+ "#Plotting the Shear Force Diagram\n",
+ "\n",
+ "X1=[0,L_CB,L_CB+L_DC,L_CB+L_DC+L_ED,L_CB+L_DC+L_ED,L_CB+L_DC+L_ED+L_AE]\n",
+ "Y1=[V_B,V_C,V_D,V_E1,V_E2,V_A]\n",
+ "Z1=[0,0,0,0,0,0]\n",
+ "plt.plot(X1,Y1,X1,Z1)\n",
+ "plt.xlabel(\"Length x in m\")\n",
+ "plt.ylabel(\"Shear Force in kN\")\n",
+ "plt.show()\n",
+ "\n",
+ "#Plotting the Bendimg Moment Diagram\n",
+ "\n",
+ "Y2=[M_B,M_C,M_D,M_E,M_A]\n",
+ "X2=[0,L_CB,L_DC+L_CB,L_ED+L_DC+L_CB,L_ED+L_DC+L_CB+L_AE]\n",
+ "Z2=[0,0,0,0,0]\n",
+ "plt.plot(X2,Y2)\n",
+ "plt.xlabel(\"Lenght in m\")\n",
+ "plt.ylabel(\"Bending Moment in kN.m\")\n",
+ "plt.show()"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "The Shear Force and Bending Moment Diagrams are the results\n"
+ ]
+ },
+ {
+ "metadata": {},
+ "output_type": "display_data",
+ "png": 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+ "text": [
+ "<matplotlib.figure.Figure at 0x568fff0>"
+ ]
+ },
+ {
+ "metadata": {},
+ "output_type": "display_data",
+ "png": 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+ "text": [
+ "<matplotlib.figure.Figure at 0x583f810>"
+ ]
+ }
+ ],
+ "prompt_number": 6
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 20.7,Page No.741"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "import matplotlib.pyplot as plt\n",
+ "\n",
+ "#Declaration Of Variables\n",
+ "\n",
+ "L_AB=4 #m #Length of AC\n",
+ "w=2 #KN/m #u.v.l\n",
+ "\n",
+ "#Calculations\n",
+ "\n",
+ "#Shear force calculation\n",
+ "\n",
+ "#S.F at pt B\n",
+ "V_B=0 #KN\n",
+ "\n",
+ "#S.F at pt A\n",
+ "V_A=w*L_AB*2**-1 #KN\n",
+ "\n",
+ "#Bending Moment Calculations\n",
+ "\n",
+ "#B.M at pt B\n",
+ "M_B=0 #KN.m\n",
+ "\n",
+ "#B.M at pt A\n",
+ "M_A=w*L_AB**2*6**-1 #KN.m\n",
+ "\n",
+ "#Result\n",
+ "print \"The Shear Force and Bending Moment Diagrams are the results\"\n",
+ "\n",
+ "#Plotting the Shear Force Diagram\n",
+ "\n",
+ "X1=[0,L_AB]\n",
+ "Y1=[V_B,V_A]\n",
+ "Z1=[0,0]\n",
+ "plt.plot(X1,Y1,X1,Z1)\n",
+ "plt.xlabel(\"Length x in m\")\n",
+ "plt.ylabel(\"Shear Force in kN\")\n",
+ "plt.show()\n",
+ "\n",
+ "#Plotting the Bendimg Moment Diagram\n",
+ "\n",
+ "Y2=[M_B,M_A]\n",
+ "X2=[0,L_AB]\n",
+ "Z2=[0,0]\n",
+ "plt.plot(X2,Y2)\n",
+ "plt.xlabel(\"Lenght in m\")\n",
+ "plt.ylabel(\"Bending Moment in kN.m\")\n",
+ "plt.show()"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "The Shear Force and Bending Moment Diagrams are the results\n"
+ ]
+ },
+ {
+ "metadata": {},
+ "output_type": "display_data",
+ "png": 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+ "text": [
+ "<matplotlib.figure.Figure at 0x567d3b0>"
+ ]
+ },
+ {
+ "metadata": {},
+ "output_type": "display_data",
+ "png": 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+ "text": [
+ "<matplotlib.figure.Figure at 0x5815390>"
+ ]
+ }
+ ],
+ "prompt_number": 7
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 20.8,Page No.745"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "import matplotlib.pyplot as plt\n",
+ "\n",
+ "#Declaration Of Variables\n",
+ "\n",
+ "#Lengths\n",
+ "L_DB=L_CD=L_AC=2 #m\n",
+ "L=6 #m\n",
+ "\n",
+ "#Loads\n",
+ "F_C=3 #KN\n",
+ "F_D=6 #KN\n",
+ "\n",
+ "\n",
+ "#Calculations\n",
+ "\n",
+ "#Let R_A & R_B be the reactions at pt A & B respectively\n",
+ "#R_A+R_B=F_C+F_D\n",
+ "\n",
+ "#Taking Moment at pt A,M_A\n",
+ "R_B=(F_D*(L_AC+L_CD)+F_C*L_AC)*L**-1 #KN\n",
+ "R_A=(F_C+F_D)-R_B\n",
+ "\n",
+ "#Shear force calculations\n",
+ "\n",
+ "#S.F at pt B\n",
+ "V_B=R_B #KN\n",
+ "\n",
+ "#S.F at pt D\n",
+ "V_D1=R_B #KN\n",
+ "V_D2=V_D1-F_D #KN\n",
+ "\n",
+ "#S.F at C\n",
+ "V_C1=V_D2 #KN\n",
+ "V_C2=V_D2-F_C #KN\n",
+ "\n",
+ "#S.F at pt A\n",
+ "V_A1=V_C2 #KN\n",
+ "V_A2=V_C2+R_A #KN\n",
+ "\n",
+ "#Bending Moment calculations\n",
+ "\n",
+ "#B.M at pt B\n",
+ "M_B=0 #KNm\n",
+ "\n",
+ "#B.M at pt D\n",
+ "M_D=-R_B*L_DB #KN.m\n",
+ "\n",
+ "#B.M at pt C\n",
+ "M_C=F_D*L_CD-R_B*(L_DB+L_CD) #KN.m\n",
+ "\n",
+ "#B.M at pt A\n",
+ "M_A=-R_B*L+F_D*(L_CD+L_AC)+F_C*L_AC #KN.m\n",
+ "\n",
+ "#Result\n",
+ "print \"The Shear Force and Bending Moment Diagrams are the results\"\n",
+ "\n",
+ "#Plotting the Shear Force Diagram\n",
+ "\n",
+ "X1=[0,L_DB,L_DB,L_DB+L_CD,L_DB+L_CD,L_DB+L_CD+L_AC,L_DB+L_CD+L_AC]\n",
+ "Y1=[V_B,V_D1,V_D2,V_C1,V_C2,V_A1,V_A2]\n",
+ "Z1=[0,0,0,0,0,0,0]\n",
+ "plt.plot(X1,Y1,X1,Z1)\n",
+ "plt.xlabel(\"Length x in m\")\n",
+ "plt.ylabel(\"Shear Force in kN\")\n",
+ "plt.show()\n",
+ "\n",
+ "#Plotting the Bendimg Moment Diagram\n",
+ "\n",
+ "Y2=[M_B,M_D,M_C,M_A]\n",
+ "X2=[0,L_DB,L_CD+L_DB,L_AC+L_CD+L_DB]\n",
+ "Z2=[0,0,0,0]\n",
+ "plt.plot(X2,Y2)\n",
+ "plt.xlabel(\"Lenght in m\")\n",
+ "plt.ylabel(\"Bending Moment in kN.m\")\n",
+ "plt.show()"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "The Shear Force and Bending Moment Diagrams are the results\n"
+ ]
+ },
+ {
+ "metadata": {},
+ "output_type": "display_data",
+ "png": 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+ "text": [
+ "<matplotlib.figure.Figure at 0x58bbf90>"
+ ]
+ },
+ {
+ "metadata": {},
+ "output_type": "display_data",
+ "png": 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+ "text": [
+ "<matplotlib.figure.Figure at 0x56943f0>"
+ ]
+ }
+ ],
+ "prompt_number": 8
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 20.9,Page No.748"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "import matplotlib.pyplot as plt\n",
+ "\n",
+ "#Declaration Of Variables\n",
+ "\n",
+ "#LEngths\n",
+ "L_CB=3 #m\n",
+ "L_AC=6 #m\n",
+ "L= 9 #m\n",
+ "\n",
+ "#Loads\n",
+ "w=10 #KN/m \n",
+ "\n",
+ "#Calculations\n",
+ "\n",
+ "#Let R_A & R_B be the reactions at pt A & B respectively\n",
+ "#R_A+R_B=w*L_AC\n",
+ "\n",
+ "#Taking Moment at pt A,M_A\n",
+ "R_B=w*L_AC*L_AC*2**-1*L**-1 #KN.m\n",
+ "R_A=w*L_AC-R_B #KN.m\n",
+ "\n",
+ "#Shear force calculations\n",
+ "\n",
+ "#S.F at pt B\n",
+ "V_B1=0\n",
+ "V_B2=R_B #KN\n",
+ "\n",
+ "#S.F at pt C\n",
+ "V_C=V_B2 #KN\n",
+ "\n",
+ "#S.F at pt A\n",
+ "V_A1=V_C-w*L_AC #KN\n",
+ "V_A2=V_C-w*L_AC+R_A #KN\n",
+ "\n",
+ "#Bending Moment calculations\n",
+ "\n",
+ "#B.M at pt B\n",
+ "M_B=0 #KN.m\n",
+ "\n",
+ "#B.M at pt C\n",
+ "M_C=-R_B*L_CB #KN.m\n",
+ "\n",
+ "#B.M at pt A\n",
+ "M_A=-R_B*L+w*L_AC*L_AC*2**-1 #KN.m\n",
+ "\n",
+ "#Result\n",
+ "print \"The Shear Force and Bending Moment Diagrams are the results\"\n",
+ "\n",
+ "#Plotting the Shear Force Diagram\n",
+ "\n",
+ "X1=[0,0,L_CB,L_CB+L_AC,L_CB+L_AC]\n",
+ "Y1=[V_B1,V_B2,V_C,V_A1,V_A2]\n",
+ "Z1=[0,0,0,0,0]\n",
+ "plt.plot(X1,Y1,X1,Z1)\n",
+ "plt.xlabel(\"Length x in m\")\n",
+ "plt.ylabel(\"Shear Force in kN\")\n",
+ "plt.show()\n",
+ "\n",
+ "#Plotting the Bendimg Moment Diagram\n",
+ "\n",
+ "Y2=[M_B,M_C,M_A]\n",
+ "X2=[0,L_CB,L_CB+L_AC]\n",
+ "Z2=[0,0,0]\n",
+ "plt.plot(X2,Y2)\n",
+ "plt.xlabel(\"Lenght in m\")\n",
+ "plt.ylabel(\"Bending Moment in kN.m\")\n",
+ "plt.show()"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "The Shear Force and Bending Moment Diagrams are the results\n"
+ ]
+ },
+ {
+ "metadata": {},
+ "output_type": "display_data",
+ "png": 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48MEHRWtrq9Ijibi4OKHT6URUVJTYtWuX0cfx5DUiIpLZ1e4jIiKyLkaBiIhk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\n",
+ "text": [
+ "<matplotlib.figure.Figure at 0x58c5790>"
+ ]
+ },
+ {
+ "metadata": {},
+ "output_type": "display_data",
+ "png": 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+ "text": [
+ "<matplotlib.figure.Figure at 0x567d550>"
+ ]
+ }
+ ],
+ "prompt_number": 9
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 20.10,Page No.749"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "import matplotlib.pyplot as plt\n",
+ "\n",
+ "#Declaration Of Variables\n",
+ "\n",
+ "#Lengths\n",
+ "L_DB=3 #m\n",
+ "L_CD=4 #m\n",
+ "L_AC=1 #m\n",
+ "L=8 #m\n",
+ "\n",
+ "#Loads\n",
+ "w=10 #KN/m\n",
+ "\n",
+ "#Calculations\n",
+ "\n",
+ "#Let R_A & R_B be the reactions at A & B respectively\n",
+ "#R_A+R_B=w*L_CD\n",
+ "\n",
+ "#Taking moment at pt A,M_A\n",
+ "R_B=(w*L_CD*(L_CD*2**-1+L_AC))*L**-1 #KN\n",
+ "R_A=w*L_CD-R_B #KN\n",
+ "\n",
+ "#Shear Force calculations\n",
+ "\n",
+ "#S.F at pt B\n",
+ "V_B1=0\n",
+ "V_B2=R_B #KN\n",
+ "\n",
+ "#S.F at pt D\n",
+ "V_D=V_B2 #KN\n",
+ "\n",
+ "#S.F at pt C\n",
+ "V_C=-w*L_CD+R_B #KN\n",
+ "\n",
+ "#S.F at pt A\n",
+ "V_A1=V_C #KN\n",
+ "V_A2=V_C+R_A\n",
+ "\n",
+ "\n",
+ "#Bending Moment calculations\n",
+ "\n",
+ "#B.A at pt B\n",
+ "M_B=0\n",
+ "\n",
+ "#B.M at pt D\n",
+ "M_D=-R_B*L_DB #KN.m\n",
+ "\n",
+ "#B.M at pt C\n",
+ "M_C=-R_B*(L_DB+L_CD)+w*L_CD*L_CD*2**-1 #KN.m\n",
+ "\n",
+ "#B.M at pt A\n",
+ "M_A=-R_B*L+w*L_CD*(L_CD*2**-1+L_AC) #KN.m\n",
+ "\n",
+ "#Result\n",
+ "print \"The Shear Force and Bending Moment Diagrams are the results\"\n",
+ "\n",
+ "#Plotting the Shear Force Diagram\n",
+ "\n",
+ "X1=[0,0,L_DB,L_DB+L_CD,L_AC+L_DB+L_CD,L_AC+L_DB+L_CD]\n",
+ "Y1=[V_B1,V_B2,V_D,V_C,V_A1,V_A2]\n",
+ "Z1=[0,0,0,0,0,0]\n",
+ "plt.plot(X1,Y1,X1,Z1)\n",
+ "plt.xlabel(\"Length x in m\")\n",
+ "plt.ylabel(\"Shear Force in kN\")\n",
+ "plt.show()\n",
+ "\n",
+ "#Plotting the Bendimg Moment Diagram\n",
+ "\n",
+ "Y2=[M_B,M_D,M_C,M_A]\n",
+ "X2=[0,L_DB,L_DB+L_CD,L_AC+L_CD+L_DB]\n",
+ "Z2=[0,0,0,0]\n",
+ "plt.plot(X2,Y2)\n",
+ "plt.xlabel(\"Lenght in m\")\n",
+ "plt.ylabel(\"Bending Moment in kN.m\")\n",
+ "plt.show()"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "The Shear Force and Bending Moment Diagrams are the results\n"
+ ]
+ },
+ {
+ "metadata": {},
+ "output_type": "display_data",
+ "png": 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+ "text": [
+ "<matplotlib.figure.Figure at 0x5807d10>"
+ ]
+ },
+ {
+ "metadata": {},
+ "output_type": "display_data",
+ "png": 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+ "text": [
+ "<matplotlib.figure.Figure at 0x5694fd0>"
+ ]
+ }
+ ],
+ "prompt_number": 10
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 20.11,Page No.751"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "import matplotlib.pyplot as plt\n",
+ "\n",
+ "#Declaration Of Variables\n",
+ "\n",
+ "#Lengths\n",
+ "L_DB=2 #m \n",
+ "L_CD=2 #m\n",
+ "L_AC=3 #m\n",
+ "L=7 #m\n",
+ "\n",
+ "#Loads\n",
+ "w1=5 #KN/m\n",
+ "w2=10 #KN/m\n",
+ "\n",
+ "#Calculations\n",
+ "\n",
+ "#Let R_A & R_B be the reactions at A & B respectively\n",
+ "#R_A+R_B=w*L_AC+w*L_DB\n",
+ "\n",
+ "#Taking moment at pt A,M_A\n",
+ "R_B=(w1*L_DB*(L_DB*2**-1+L_CD+L_AC)+w2*L_AC*L_AC*2**-1)*L**-1 #KN\n",
+ "R_A=(w1*L_DB+w2*L_AC)-R_B\n",
+ "\n",
+ "#Shear Force Calculations\n",
+ "\n",
+ "#S.F at pt B\n",
+ "V_B1=0 #KN\n",
+ "V_B2=R_B #KN\n",
+ "\n",
+ "#S.F at pt D\n",
+ "V_D=R_B-w1*L_DB #KN\n",
+ "\n",
+ "#S.F at pt C\n",
+ "V_C=V_D #KN\n",
+ "\n",
+ "#S.F at pt A\n",
+ "V_A1=V_C-w2*L_AC #KN\n",
+ "V_A2=V_A1+R_A #KN\n",
+ "\n",
+ "#Bending Moment Calculations\n",
+ "\n",
+ "#B.M at pt B\n",
+ "M_B=0 #KN.m\n",
+ "\n",
+ "#B.M at pt D\n",
+ "M_D=w1*L_DB*L_DB*2**-1-R_B*L_DB #KN.m\n",
+ "\n",
+ "#B.M at pt C\n",
+ "M_C=-R_B*(L_CD+L_DB)+w1*L_DB*(L_DB*2**-1+L_CD) #KN.m\n",
+ "\n",
+ "#B.M at pt A\n",
+ "M_A=-R_B*L+w1*L_DB*(L_DB*2**-1+L_CD+L_AC)+w2*L_AC*L_AC*2**-1 #KN.m\n",
+ "\n",
+ "#Result\n",
+ "print \"The Shear Force and Bending Moment Diagrams are the results\"\n",
+ "\n",
+ "#Plotting the Shear Force Diagram\n",
+ "\n",
+ "X1=[0,0,L_DB,L_DB+L_CD,L_AC+L_CD+L_DB,L_AC+L_CD+L_DB]\n",
+ "Y1=[V_B1,V_B2,V_D,V_C,V_A1,V_A2]\n",
+ "Z1=[0,0,0,0,0,0]\n",
+ "plt.plot(X1,Y1,X1,Z1)\n",
+ "plt.xlabel(\"Length x in m\")\n",
+ "plt.ylabel(\"Shear Force in kN\")\n",
+ "plt.show()\n",
+ "\n",
+ "#Plotting the Bendimg Moment Diagram\n",
+ "\n",
+ "Y2=[M_B,M_D,M_C,M_A]\n",
+ "X2=[0,L_DB,L_CD+L_DB,L_AC+L_CD+L_DB]\n",
+ "Z2=[0,0,0,0]\n",
+ "plt.plot(X2,Y2)\n",
+ "plt.xlabel(\"Lenght in m\")\n",
+ "plt.ylabel(\"Bending Moment in kN.m\")\n",
+ "plt.show()"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "The Shear Force and Bending Moment Diagrams are the results\n"
+ ]
+ },
+ {
+ "metadata": {},
+ "output_type": "display_data",
+ "png": 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+ "text": [
+ "<matplotlib.figure.Figure at 0x569eb50>"
+ ]
+ },
+ {
+ "metadata": {},
+ "output_type": "display_data",
+ "png": 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+ "text": [
+ "<matplotlib.figure.Figure at 0x55c48f0>"
+ ]
+ }
+ ],
+ "prompt_number": 11
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 20.12,Page No.752"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "import matplotlib.pyplot as plt\n",
+ "\n",
+ "#Declaration Of Variables\n",
+ "\n",
+ "#Lengths\n",
+ "L_DB=4 #m\n",
+ "L_CD=4 #m\n",
+ "L_AC=2 #m\n",
+ "L=10 #m\n",
+ "\n",
+ "#Loads\n",
+ "F_D=40 #KN\n",
+ "F_C=50 #KN\n",
+ "w=10 #KN/m\n",
+ "\n",
+ "#Calculations\n",
+ "\n",
+ "\n",
+ "#Let R_A & R_B be the reactions at A & B respectively\n",
+ "#R_A+R_B=w*L_CD+F_C+F_D\n",
+ "\n",
+ "#Taking moment at pt A,M_A\n",
+ "R_B=(F_C*L_AC+w*L_CD*(L_CD*2**-1+L_AC)+F_D*(L_CD+L_AC))*L**-1 #KN\n",
+ "R_A=(w*L_CD+F_C+F_D)-R_B #KN\n",
+ "\n",
+ "#Shear Force calculations\n",
+ "\n",
+ "#S.F at pt B\n",
+ "V_B1=0 #KN\n",
+ "V_B2=R_B #KN\n",
+ "\n",
+ "#S.F at pt D\n",
+ "V_D1=V_B2 #KN\n",
+ "V_D2=V_B2-F_D #KN\n",
+ "\n",
+ "#S.F at pt C\n",
+ "V_C1=V_D2-w*L_CD #KN\n",
+ "V_C2=V_C1-F_C #KN\n",
+ "\n",
+ "#S.F at pt A\n",
+ "V_A1=V_C2 #KN\n",
+ "V_A2=V_C2+R_A #KN\n",
+ "\n",
+ "#Bending Moment calculations\n",
+ "\n",
+ "#B.M at pt B\n",
+ "M_B=0 #KN.m\n",
+ "\n",
+ "#B.M at pt D\n",
+ "M_D=-R_B*L_DB #KN.m\n",
+ "\n",
+ "#B.M at pt C\n",
+ "M_C=-R_B*(L_DB+L_CD)+F_D*L_CD+w*L_CD*L_CD*2**-1 #KN.m\n",
+ "\n",
+ "#B.M at pt A\n",
+ "M_A=-R_B*L+F_D*(L_CD+L_AC)+F_C*L_AC+w*L_CD*(L_CD*2**-1+L_AC)\n",
+ "\n",
+ "#Result\n",
+ "print \"The Shear Force and Bending Moment Diagrams are the results\"\n",
+ "\n",
+ "#Plotting the Shear Force Diagram\n",
+ "\n",
+ "X1=[0,0,L_DB,L_DB,L_DB+L_CD,L_DB+L_CD,L_DB+L_CD+L_AC,L_DB+L_CD+L_AC]\n",
+ "Y1=[V_B1,V_B2,V_D1,V_D2,V_C1,V_C2,V_A1,V_A2]\n",
+ "Z1=[0,0,0,0,0,0,0,0]\n",
+ "plt.plot(X1,Y1,X1,Z1)\n",
+ "plt.xlabel(\"Length x in m\")\n",
+ "plt.ylabel(\"Shear Force in kN\")\n",
+ "plt.show()\n",
+ "\n",
+ "#Plotting the Bendimg Moment Diagram\n",
+ "\n",
+ "Y2=[M_B,M_D,M_C,M_A]\n",
+ "X2=[0,L_DB,L_DB+L_CD,L_AC+L_CD+L_DB]\n",
+ "Z2=[0,0,0,0]\n",
+ "plt.plot(X2,Y2)\n",
+ "plt.xlabel(\"Lenght in m\")\n",
+ "plt.ylabel(\"Bending Moment in kN.m\")\n",
+ "plt.show()"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "The Shear Force and Bending Moment Diagrams are the results\n"
+ ]
+ },
+ {
+ "metadata": {},
+ "output_type": "display_data",
+ "png": 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xzTffYOrUqbj55pvh7OyM2bNn4+uvv5YdSyp3d3fzGS5qamowbNiwTl9vVwUx\nfvx4lJeXo6KiAg0NDcjIyEB0dLTsWFIIIfDQQw9Bq9XiiSeekB1HquXLl8NoNMJgMGDbtm2YPn06\n3n//fdmxpPDw8MCIESNQVlYGANizZw8CAwMlp5LD398fBQUFOH/+PIQQ2LNnD7RarexYUkVHRyM9\nPR0AkJ6ebvkPyy6fJ0OyXbt2CT8/P+Ht7S2WL18uO440e/fuFSqVSowZM0YEBweL4OBg8dlnn8mO\nJZ1erxdRUVGyY0j173//W4wfP16MHj1azJo1S9TX18uOJM2KFSuEVqsVQUFB4sEHHxQNDQ2yI9nM\nfffdJ4YPHy7UarXQaDRi06ZN4uTJkyI8PFz4+voKnU4nTp061el7cKIcEREpsqshJiIish0WBBER\nKWJBEBGRIhYEEREpYkEQEZEiFgQRESliQVCvYu3TjaxevRrnz5/v9s/75JNPHPr09dQzcR4E9SoD\nBgzA//73P6u9/8iRI/HNN9/g5ptvtsnnEcnELQjq9Y4ePYq7774b48ePx5133onDhw8DABYsWIDF\nixfj9ttvh7e3NzIzMwEAzc3NSE5ORkBAACIiInDPPfcgMzMT69atQ3V1NcLCwhAeHm5+/xdffBHB\nwcGYMmUKfvrpp3af/8QTT+CVV14BAPzzn//EXXfd1e417733Hh5//PFOc7VWUVEBf39/JCYmYtSo\nUZg/fz52796N22+/HX5+figqKrr+L47IBjO+iWzG1dW13bLp06eL8vJyIYQQBQUFYvr06UIIIRIS\nEkRcXJwQQojS0lLh4+MjhBBix44dIjIyUgghxPHjx8WgQYNEZmamEEIILy8vcfLkSfN7q1QqsXPn\nTiGEEEuWLBGvvvpqu88/d+6cCAwMFHl5eWLUqFHi2LFj7V7z3nvviccee6zTXK0ZDAbh7Owsvvvu\nO9Hc3CzGjRsnFi5cKIQQIisrS8TExFj8rogscZZdUETWdPbsWezbtw9z5841L2toaABgOt1xy8nK\nAgICzOfGz8/PR1xcHADT2S/DwsI6fH8XFxfcc889AIBx48YhNze33WtuvPFGvPvuu5g2bRrWrFmD\nkSNHdpq5o1xXGjlypPlEfIGBgeZrHQQFBaGioqLTzyC6GiwI6tWam5sxcOBAlJSUKD7v4uJivi9+\n2R2nUqnaXFdCdLKbTq1Wm+87OTmhsbFR8XUHDhzA0KFDr/oCV0q5rtS3b982n92yTmc5iLqC+yCo\nV3Nzc8OGyRbRAAABH0lEQVTIkSPx4YcfAjD92B44cKDTdW6//XZkZmZCCIHa2lp8+eWX5ucGDBiA\nM2fOdCnDDz/8gDfeeAMlJSX47LPPUFhY2O41nZUQkSwsCOpVzp07hxEjRphvq1evxtatW7Fx40YE\nBwcjKCgI2dnZ5te3vqJWy/05c+ZAo9FAq9XigQcewNixY83XdV60aBF+85vfmHdSX7n+lVfoEkIg\nKSkJq1atgoeHBzZu3IikpCTzMFdH63Z0/8p1OnrMqy9Sd+BhrkQKfv75Z/Tv3x8nT57EpEmT8PXX\nX1u8+hZRb8N9EEQK7r33XtTX16OhoQEvvfQSy4EcErcgiIhIEfdBEBGRIhYEEREpYkEQEZEiFgQR\nESliQRARkSIWBBERKfp/qsHjWC7FrDIAAAAASUVORK5CYII=\n",
+ "text": [
+ "<matplotlib.figure.Figure at 0x58b4310>"
+ ]
+ },
+ {
+ "metadata": {},
+ "output_type": "display_data",
+ "png": 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+ "text": [
+ "<matplotlib.figure.Figure at 0x5837050>"
+ ]
+ }
+ ],
+ "prompt_number": 12
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 20.13,Page No.758"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "import matplotlib.pyplot as plt\n",
+ "\n",
+ "#Declaration Of Variables\n",
+ "\n",
+ "L_AB=5 #m #Length of AB\n",
+ "F_1=800 #N u.d.l\n",
+ "F_2=1600 #N u.v.l\n",
+ "\n",
+ "#Calculations\n",
+ "\n",
+ "#Load on beam due to u.d.l of 800 N/m\n",
+ "w1=F_1*L_AB #N\n",
+ "\n",
+ "#Load on beam due to triangular Loading\n",
+ "w2=F_1*L_AB*2**-1 #N\n",
+ "\n",
+ "#Calculation of reactions R_A & R_B\n",
+ "#Taking moment about A,we get\n",
+ "#R_B=w1*L_AB*2**-1+w2**(2*5**-1of5)\n",
+ "#After further simplifying we get\n",
+ "R_B=2000+1333.33 #N\n",
+ "R_A=(w1+w2)-R_B #N\n",
+ "\n",
+ "#Consider any section X-X at a distance x from A.\n",
+ "#Rate of Loading at the section X-X\n",
+ "#w_x=800+160*x\n",
+ "\n",
+ "#Total Load on length AX\n",
+ "#W=800*x+80*x**2\n",
+ "\n",
+ "#Now the S.F at the section X-X is given by,\n",
+ "#F_x=R_A-Load on length AX\n",
+ "#After sub values and further simplifying we get\n",
+ "#F_x=2666.67-800*x-80*x**2 ............................(1)\n",
+ "\n",
+ "#Equation 1 shows that shear force between A & B \n",
+ "#At A\n",
+ "x=0\n",
+ "F_x1=F_x=2666.67-800*x-80*x**2 #N\n",
+ "\n",
+ "#At B\n",
+ "x=5\n",
+ "F_x2=F_x=2666.67-800*x-80*x**2 #N\n",
+ "\n",
+ "#Finding the position of zero shear.Equating S.F equal to zero in eqn(1)\n",
+ "#0=2666.67-800*x-80*x**2\n",
+ "#Further simplifying we get\n",
+ "#x**2+10*x-33.33=0\n",
+ "a=1\n",
+ "b=10\n",
+ "c=-33.33\n",
+ "\n",
+ "X=b**2-4*a*c\n",
+ "\n",
+ "x1=(-b+X**0.5)*(2*a)**-1 #m\n",
+ "x2=(-b-X**0.5)*(2*a)**-1 #m\n",
+ "\n",
+ "#B.M Diagram\n",
+ "#B.M at the section X-X is given by\n",
+ "#M_x=R_A*x-800*x**2*2**-1-x**3*80*3**-1\n",
+ "#Further simplifyng we get\n",
+ "#M_x=2666.67*x-400*x**2-80*3**-1*x**3 ............2\n",
+ "\n",
+ "#Equation 2 shows that B.M between A & B varies \n",
+ "#At A\n",
+ "x=0\n",
+ "M_x1=2666.67*x-400*x**2-80*3**-1*x**3 #KN/m\n",
+ "\n",
+ "#At B\n",
+ "x=5\n",
+ "M_x2=2666.67*x-400*x**2-80*3**-1*x**3 #KN/m\n",
+ "\n",
+ "#value of M_X2 is very small .i.e equal to zero\n",
+ "#MAx B.M occurs where S.F is zero.\n",
+ "#But shear force is zero at distance of 2.637m from A.\n",
+ "#hence max B.M is Obtained by sub \n",
+ "x=2.637 #m\n",
+ "M_x=2666.67*x-400*x**2-80*3**-1*x**3\n",
+ "\n",
+ "#Plotting the Shear Force Diagram\n",
+ "\n",
+ "X1=[0,L_AB]\n",
+ "Y1=[F_x1,F_x2]\n",
+ "Z1=[0,0,]\n",
+ "plt.plot(X1,Y1,X1,Z1)\n",
+ "plt.xlabel(\"Length x in m\")\n",
+ "plt.ylabel(\"Shear Force in kN\")\n",
+ "plt.show()\n",
+ "\n",
+ "#Plotting the Bendimg Moment Diagram\n",
+ "\n",
+ "Y2=[M_x1,M_x2]\n",
+ "X2=[0,L_AB]\n",
+ "Z2=[0,0]\n",
+ "plt.plot(X2,Y2,X2,Z2)\n",
+ "plt.xlabel(\"Length in m\")\n",
+ "plt.ylabel(\"Bending Moment in kN.m\")\n",
+ "plt.show()"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "metadata": {},
+ "output_type": "display_data",
+ "png": 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+ "text": [
+ "<matplotlib.figure.Figure at 0x5694ed0>"
+ ]
+ },
+ {
+ "metadata": {},
+ "output_type": "display_data",
+ "png": 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QNSzZq0q4U26uNlvq+HFYvBhuvVXviISoH848O2tNHIcPH+aTTz4hJSWF7t27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\ngg==\n",
+ "text": [
+ "<matplotlib.figure.Figure at 0x569df30>"
+ ]
+ }
+ ],
+ "prompt_number": 13
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 20.14,Page No.760"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "import matplotlib.pyplot as plt\n",
+ "\n",
+ "#Declaration Of Variables\n",
+ "\n",
+ "L_AB=4 #m\n",
+ "L_BC=2 #m\n",
+ "L=6 #m\n",
+ "w=2 #KN/m #u.d.l\n",
+ "\n",
+ "#Calculations\n",
+ "\n",
+ "#Let R_A and R_B be the reactions at A & B respectively\n",
+ "#R_A+R_B=w*L\n",
+ " \n",
+ "#Taking Moment at A,M_A\n",
+ "R_B=(w*L*L*2**-1)*L_AB**-1 #KN\n",
+ "R_A=w*L-R_B #KN\n",
+ "\n",
+ "#Shear Force calculations \n",
+ "\n",
+ "#S.f at pt C\n",
+ "V_C=0\n",
+ "\n",
+ "#S.F at pt B\n",
+ "V_B1=-w*L_BC #KN\n",
+ "V_B2=V_B1+R_B #KN\n",
+ "\n",
+ "#S.F at pt A\n",
+ "V_A1=V_B2-w*L_AB #KN\n",
+ "V_A2=V_A1+R_A #KN\n",
+ "\n",
+ "#Bending Moment Calculations\n",
+ "\n",
+ "#B.M at pt C\n",
+ "M_C=0 #KN.m\n",
+ "\n",
+ "#B.M at pt B\n",
+ "M_B=w*L_BC #KN.m\n",
+ "\n",
+ "#B.M at pt A\n",
+ "M_A=w*L*L*2**-1-R_B*L_AB #KN.m\n",
+ "\n",
+ "\n",
+ "#Result\n",
+ "print \"The Shear Force and Bending Moment Diagrams are the results\"\n",
+ "\n",
+ "#Plotting the Shear Force Diagram\n",
+ "\n",
+ "X1=[0,L_BC,L_BC,L_BC+L_AB,L_BC+L_AB]\n",
+ "Y1=[V_C,V_B1,V_B2,V_A1,V_A2]\n",
+ "Z1=[0,0,0,0,0]\n",
+ "plt.plot(X1,Y1,X1,Z1)\n",
+ "plt.xlabel(\"Length x in m\")\n",
+ "plt.ylabel(\"Shear Force in kN\")\n",
+ "plt.show()\n",
+ "\n",
+ "#Plotting the Bendimg Moment Diagram\n",
+ "\n",
+ "Y2=[M_C,M_B,M_A]\n",
+ "X2=[0,L_BC,L_BC+L_AB]\n",
+ "Z2=[0,0,0]\n",
+ "plt.plot(X2,Y2)\n",
+ "plt.xlabel(\"Lenght in m\")\n",
+ "plt.ylabel(\"Bending Moment in kN.m\")\n",
+ "plt.show()"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "The Shear Force and Bending Moment Diagrams are the results\n"
+ ]
+ },
+ {
+ "metadata": {},
+ "output_type": "display_data",
+ "png": 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+ "text": [
+ "<matplotlib.figure.Figure at 0x5804eb0>"
+ ]
+ },
+ {
+ "metadata": {},
+ "output_type": "display_data",
+ "png": 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+ "text": [
+ "<matplotlib.figure.Figure at 0x569eed0>"
+ ]
+ }
+ ],
+ "prompt_number": 14
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 20.15,Page No.762"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "import matplotlib.pyplot as plt\n",
+ "\n",
+ "#Declaration Of Variables\n",
+ "\n",
+ "#Lengths\n",
+ "L_AB=4 #m\n",
+ "L_BC=2 #m\n",
+ "L=6 #m\n",
+ "\n",
+ "#Loads\n",
+ "w=2 #KN/m\n",
+ "F_C=2 #KN\n",
+ "\n",
+ "#Calculations\n",
+ "\n",
+ "#Let R_A and R_B be the reactions at A & B respectively\n",
+ "#R_A+R_B=w*L+F_C\n",
+ " \n",
+ "#Taking Moment at A,M_A\n",
+ "R_B=(F_C*L+w*L*L*2**-1)*L_AB**-1 #KN\n",
+ "R_A=(w*L+F_C)-R_B #KN\n",
+ "\n",
+ "#Shear Force calculations\n",
+ "\n",
+ "#S.F at pt C\n",
+ "V_C1=0 #KN\n",
+ "V_C2=F_C #KN\n",
+ "\n",
+ "#S.F at pt B\n",
+ "V_B1=-w*L_BC-F_C #KN\n",
+ "V_B2=V_B1+R_B #KN\n",
+ "\n",
+ "#S.F at pt A\n",
+ "V_A1=V_B2-w*L_AB #KN\n",
+ "V_A2=V_A1+R_A #KN\n",
+ "\n",
+ "#Bending Moment Calculations\n",
+ "\n",
+ "#B.M at pt C\n",
+ "M_C=0 #KN.m\n",
+ "\n",
+ "#B.M at pt B\n",
+ "M_B=w*L_BC*L_BC*2**-1+F_C*L_BC #KN.m\n",
+ "\n",
+ "#B.M at pt A\n",
+ "M_A=F_C*L+w*L*L*2**-1-R_B*L_AB #KN.m\n",
+ "\n",
+ "#Result\n",
+ "print\"The Shear Force and Bending Moment are the Results\"\n",
+ "\n",
+ "#Plotting Shear Force Diagram\n",
+ "\n",
+ "X1=[0,0,L_BC,L_BC,L_BC+L_AB,L_AB+L_BC]\n",
+ "Y1=[V_C1,V_C2,V_B1,V_B2,V_A1,V_A2]\n",
+ "Z1=[0,0,0,0,0,0]\n",
+ "plt.plot(X1,Y1,X1,Z1)\n",
+ "plt.xlabel(\"Length in m\")\n",
+ "plt.ylabel(\"Shear Force in KN\")\n",
+ "plt.show()\n",
+ "\n",
+ "#plotting the Bending Moment Diagram\n",
+ "\n",
+ "X2=[0,L_BC,L_BC+L_AB]\n",
+ "Y2=[M_C,M_B,M_A]\n",
+ "Z2=[0,0,0]\n",
+ "plt.plot(X2,Y2,X2,Z2)\n",
+ "plt.xlabel(\"Length in m\")\n",
+ "plt.ylabel(\"Bending Moment in KN.m\")\n",
+ "plt.show()"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "The Shear Force and Bending Moment are the Results\n"
+ ]
+ },
+ {
+ "metadata": {},
+ "output_type": "display_data",
+ "png": 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+ "text": [
+ "<matplotlib.figure.Figure at 0x55b4b90>"
+ ]
+ },
+ {
+ "metadata": {},
+ "output_type": "display_data",
+ "png": 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+ "text": [
+ "<matplotlib.figure.Figure at 0x569d830>"
+ ]
+ }
+ ],
+ "prompt_number": 15
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 20.16,Page No.763"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "import matplotlib.pyplot as plt\n",
+ "\n",
+ "#Declaration Of Variables\n",
+ "\n",
+ "#Lengths\n",
+ "L_BD=L_CA=2 #m\n",
+ "L_AB=8 #m\n",
+ "L=12 #m\n",
+ "\n",
+ "#Loads\n",
+ "F_D=F_C=1000 #N\n",
+ "\n",
+ "#Calculations\n",
+ "\n",
+ "#Let R_A & R_b be the reactions at A & B respectively\n",
+ "#As the Load on the beam is symmetrical,R_A and R_B will be equal\n",
+ "#Their magnitude will be half of the total Load\n",
+ "\n",
+ "R_A=R_B=(F_C+F_D)*2**-1 #N\n",
+ "\n",
+ "#Shear force calculations\n",
+ "\n",
+ "#S.F at pt D\n",
+ "V_D1=0 #N\n",
+ "V_D2=-F_D #N\n",
+ "\n",
+ "#s.F at pt B\n",
+ "V_B1=V_D2 #N\n",
+ "V_B2=V_B1+R_B #N\n",
+ "\n",
+ "#S.F at pt A\n",
+ "V_A1=V_B2 #N\n",
+ "V_A2=V_A1+R_A #N\n",
+ "\n",
+ "#S.F at pt C\n",
+ "V_C1=V_A2 #N\n",
+ "V_C2=V_C1-F_C\n",
+ "\n",
+ "#Bending Moment Calculations\n",
+ "\n",
+ "#B.M at pt D\n",
+ "M_D=0 #KN.m\n",
+ "\n",
+ "#B.M at pt B\n",
+ "M_B=F_D*L_BD #KN.m\n",
+ "\n",
+ "#B.M at pt A\n",
+ "M_A=F_D*(L_BD+L_AB)-R_B*L_AB #KN.m\n",
+ "\n",
+ "#B.M at pt C\n",
+ "M_C=F_D*L-R_B*(L_AB+L_CA)-R_A*L_CA #KN.m\n",
+ "\n",
+ "\n",
+ "#Result\n",
+ "print\"The Shear Force And Bending Moment diagrams are the Results\"\n",
+ "\n",
+ "#plotting Shear Force Diagram\n",
+ "\n",
+ "X1=[0,0,L_BD,L_BD,L_BD+L_AB,L_BD+L_AB,L_CA+L_BD+L_AB,L_CA+L_BD+L_AB]\n",
+ "Y1=[V_D1,V_D2,V_B1,V_B2,V_A1,V_A2,V_C1,V_C2]\n",
+ "Z1=[0,0,0,0,0,0,0,0]\n",
+ "plt.plot(X1,Y1,X1,Z1)\n",
+ "plt.xlabel(\"Length in m\")\n",
+ "plt.ylabel(\"Shear force in N\")\n",
+ "plt.show()\n",
+ "\n",
+ "#Plotting Bending Moment diagram\n",
+ "\n",
+ "X2=[0,L_BD,L_BD+L_AB,L_CA+L_AB+L_BD]\n",
+ "Y2=[M_D,M_B,M_A,M_C]\n",
+ "Z2=[0,0,0,0]\n",
+ "plt.plot(X2,Y2,X2,Z2)\n",
+ "plt.xlabel(\"Length in m\")\n",
+ "plt.ylabel(\"Bending Moment in N.m\")\n",
+ "plt.show()"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "The Shear Force And Bending Moment diagrams are the Results\n"
+ ]
+ },
+ {
+ "metadata": {},
+ "output_type": "display_data",
+ "png": 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+ "text": [
+ "<matplotlib.figure.Figure at 0x55c4fd0>"
+ ]
+ },
+ {
+ "metadata": {},
+ "output_type": "display_data",
+ "png": 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IyOjwnICAAAEAH3zwwQcfPXgEBAT06PvYJAiCAJVrbW3Fbbfdhn/961+49dZb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\nEBGR0/4fEsvDXVDtsKwAAAAASUVORK5CYII=\n",
+ "text": [
+ "<matplotlib.figure.Figure at 0x582cd70>"
+ ]
+ }
+ ],
+ "prompt_number": 16
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 20.17,Page No.765"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "import matplotlib.pyplot as plt\n",
+ "\n",
+ "#Declaration Of Variables\n",
+ "\n",
+ "#Lengths\n",
+ "L_BE=2 #m\n",
+ "L_DB=L_CA=3 #m\n",
+ "L_AD=5 #m\n",
+ "L_AB=8 #m\n",
+ "L=13 #m\n",
+ "\n",
+ "#Loads\n",
+ "F_E=1000 #N\n",
+ "F_C=800 #N\n",
+ "F_D=2000 #N\n",
+ "\n",
+ "#Calculations\n",
+ "\n",
+ "#Let R_A and R_B be the reactions at pt A and B respectively\n",
+ "#Taking Moment at pt A\n",
+ "R_B=(-F_C*L_CA+F_D*L_AD+F_E*(L_AD+L_DB+L_BE))*L_AB**-1 #KN\n",
+ "R_A=(F_C+F_D+F_E)-R_B #KN\n",
+ "\n",
+ "#Shear Force Calculations\n",
+ "\n",
+ "#S.F at pt E\n",
+ "V_E1=0 #KN\n",
+ "V_E2=-F_E #KN\n",
+ "\n",
+ "#S.F at pt B\n",
+ "V_B1=V_E2 #KN\n",
+ "V_B2=V_B1+R_B #KN\n",
+ "\n",
+ "#S.F at pt D\n",
+ "V_D1=V_B2 #KN\n",
+ "V_D2=V_D1-F_D #KN\n",
+ "\n",
+ "#S.F at pt A\n",
+ "V_A1=V_D2 #KN\n",
+ "V_A2=V_A1+R_A #KN\n",
+ "\n",
+ "#S.F at pt C\n",
+ "V_C1=V_A2 #KN\n",
+ "V_C2=V_C1-F_C #KN\n",
+ " \n",
+ "#Bending Moment Calculations\n",
+ "\n",
+ "#B.M at pt E\n",
+ "M_E=0 #KN.m \n",
+ "\n",
+ "#B.M at pt B\n",
+ "M_B=F_E*L_BE #KN,m\n",
+ "\n",
+ "#B.M at pt D\n",
+ "M_D=F_E*(L_BE+L_DB)-R_B*L_DB #KN.m\n",
+ "\n",
+ "#B.M at pt A\n",
+ "M_A=F_D*L_AD+F_E*(L_AD+L_DB+L_BE)-R_B*(L_DB+L_AD) #KN.m\n",
+ "\n",
+ "#B.M at pt C\n",
+ "M_C=F_E*L+F_D*(L_AD+L_CA)-R_A*L_CA-R_B*(L_CA+L_AD+L_DB) #KN.m\n",
+ "\n",
+ "#Result\n",
+ "print\"The Shear Force and Bending Moment diagrams are the results\"\n",
+ "\n",
+ "#Plotting Shear force Diagrams\n",
+ "\n",
+ "X1=[0,0,L_BE,L_BE,L_BE+L_DB,L_BE+L_DB,L_AD+L_BE+L_DB,L_AD+L_BE+L_DB,L_AD+L_BE+L_DB+L_CA,L_AD+L_BE+L_DB+L_CA]\n",
+ "Y1=[V_E1,V_E2,V_B1,V_B2,V_D1,V_D2,V_A1,V_A2,V_C1,V_C2]\n",
+ "Z1=[0,0,0,0,0,0,0,0,0,0]\n",
+ "plt.plot(X1,Y1,X1,Z1)\n",
+ "plt.xlabel(\"Length in m\")\n",
+ "plt.ylabel(\"Shear Force in KN\")\n",
+ "plt.show()\n",
+ "\n",
+ "#Plotting the Bendimg Moment Diagram\n",
+ "\n",
+ "Y2=[M_E,M_B,M_D,M_A,M_C]\n",
+ "X2=[0,L_BE,L_BE+L_DB,L_BE+L_DB+L_AD,L_BE+L_DB+L_AD+L_CA]\n",
+ "Z2=[0,0,0,0,0]\n",
+ "plt.plot(X2,Y2,X2,Z2)\n",
+ "plt.xlabel(\"Length in m\")\n",
+ "plt.ylabel(\"Bending Moment in kN.m\")\n",
+ "plt.show()"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "The Shear Force and Bending Moment diagrams are the results\n"
+ ]
+ },
+ {
+ "metadata": {},
+ "output_type": "display_data",
+ "png": 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+ "text": [
+ "<matplotlib.figure.Figure at 0x569de30>"
+ ]
+ },
+ {
+ "metadata": {},
+ "output_type": "display_data",
+ "png": 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NREVFIS0tDcOHD8epU6eg0Wjg7++PS5cuaUv1A7r/YhjjM73mzze/TaxKSoBW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\nyeWQkBBER0dDrVZDrVYjISEBABAdHQ0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+ "text": [
+ "<matplotlib.figure.Figure at 0x5837c10>"
+ ]
+ }
+ ],
+ "prompt_number": 17
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 20.18,Page No.766"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "import matplotlib.pyplot as plt\n",
+ "\n",
+ "#Declaration Of Variables \n",
+ "L=10 #m #span\n",
+ "w=1 #KN/m #u.d.l\n",
+ "l=6 #m #Span betwen A & B\n",
+ "l_AC=2.23 #m #Length AC\n",
+ "l_BD=1.77 #m #LEngth BD\n",
+ "\n",
+ "#Calculations\n",
+ "\n",
+ "#Let R_A & R_B be the reactions at A & B respectively\n",
+ "#Taking moment at A\n",
+ "#x**2*x*2**-1+R_B*l=(10-x)**2*2**-1\n",
+ "#After simplifying we get,\n",
+ "#R_A=5*3**-1*(5-x)\n",
+ "#R_B=5*3**-1*(1+x)\n",
+ "\n",
+ "#Let y be the distance at which B.M is maximum at section ABfrom C\n",
+ "#S.F at section AB \n",
+ "#R_A=y\n",
+ "#Substituting value of R_A from above equation\n",
+ "#y=5*3**-1*(1+x)...................................1\n",
+ "\n",
+ "#B.M at A\n",
+ "#M_A=x**2*2**-1 \n",
+ "\n",
+ "#B.M at distance y from C\n",
+ "#M_C=y**2*2**-1+R_A*(y-x)....................2\n",
+ "#After further simplifying we get\n",
+ "#M_C=5*18**-1*(-x**2+4*x+5).............................3\n",
+ "\n",
+ "#EQuating equations 1 & 2,we get quadratic equation as\n",
+ "#14x**2-20x-25=0\n",
+ "a=14\n",
+ "b=-20\n",
+ "c=-25\n",
+ "\n",
+ "X=b**2-4*a*c\n",
+ "x=(-b+X**0.5)*(2*a)**-1\n",
+ "\n",
+ "#Substituing value of x in equation 1 we get\n",
+ "y=5*3**-1*(1+x)\n",
+ "\n",
+ "#Sub values of x & y we get values of R_A & R_B as follows\n",
+ "R_B=5*3**-1*(5-x)\n",
+ "R_A=5*3**-1*(1+x)\n",
+ "\n",
+ "#Shear Force calculations\n",
+ "\n",
+ "#S.F at pt C\n",
+ "V_C=0\n",
+ "\n",
+ "#S.F at A\n",
+ "V_A1=-w*l_AC #KN\n",
+ "V_A2=V_A1+R_A #KN\n",
+ "\n",
+ "#S.F at pt B\n",
+ "V_B1=V_A2-1*l #KN\n",
+ "V_B2=V_B1+R_B #KN\n",
+ "\n",
+ "#S.F at D\n",
+ "V_D=V_B2-l_BD\n",
+ "\n",
+ "#BEnding Moment calculations\n",
+ "\n",
+ "#B.M at C\n",
+ "M_C=0\n",
+ "\n",
+ "#B.M at A\n",
+ "M_A=-w*l_AC**2*2**-1 #KNm\n",
+ "\n",
+ "#B.M at E i.e at y=5.38 m\n",
+ "M_E=-w*y**2*2**-1+R_A*(y-l_AC)\n",
+ "\n",
+ "#B.M at B\n",
+ "M_B=-w*(l_AC+l)**2*2**-1+R_A*l\n",
+ "\n",
+ "#Result\n",
+ "print \"The Shear Force and Bending Moment Diagrams are the results\"\n",
+ "\n",
+ "#Plotting the Shear Force Diagram\n",
+ "\n",
+ "X1=[0,l_AC,l_AC,l_AC+l,l_AC+l,l_AC+l+l_BD]\n",
+ "Y1=[V_C,V_A1,V_A2,V_B1,V_B2,V_D]\n",
+ "Z1=[0,0,0,0,0,0]\n",
+ "plt.plot(X1,Y1,X1,Z1)\n",
+ "plt.xlabel(\"Length x in m\")\n",
+ "plt.ylabel(\"Shear Force in kN\")\n",
+ "plt.show()\n",
+ "\n",
+ "#Plotting the Bendimg Moment Diagram\n",
+ "\n",
+ "Y2=[M_C,M_A,M_E,M_B]\n",
+ "X2=[0,l_AC,l_AC+y,l_AC+l]\n",
+ "Z2=[0,0,0,0]\n",
+ "plt.plot(X2,Y2,X2,Z2)\n",
+ "plt.xlabel(\"Length in m\")\n",
+ "plt.ylabel(\"Bending Moment in kN.m\")\n",
+ "plt.show()"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "The Shear Force and Bending Moment Diagrams are the results\n"
+ ]
+ },
+ {
+ "metadata": {},
+ "output_type": "display_data",
+ "png": 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VM8jLoi/MQSY9YQ6yfGwEGlU+B/n772VXQ1QzzEGWi41Aw+w5yI8/Lm4TaRlz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\ng2MjICIyuP8H+JpvorKE/gUAAAAASUVORK5CYII=\n",
+ "text": [
+ "<matplotlib.figure.Figure at 0x58c8610>"
+ ]
+ },
+ {
+ "metadata": {},
+ "output_type": "display_data",
+ "png": 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ekbXxzJ8cVkpKCvr06YMOHTrg8ccfx6lTpwAATz31FKZOnYrOnTvD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\nAElFTkSuQmCC\n",
+ "text": [
+ "<matplotlib.figure.Figure at 0x569d0f0>"
+ ]
+ }
+ ],
+ "prompt_number": 18
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 20.19,Page No.770"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "import matplotlib.pyplot as plt\n",
+ "from math import sin, cos, radians, pi\n",
+ "\n",
+ "#Declaration Of Variables\n",
+ "\n",
+ "#Lengths\n",
+ "L_EB=L_DE=L_CD=L_AC=1 #m\n",
+ "L=4 #m\n",
+ "\n",
+ "#Loads\n",
+ "#point Load\n",
+ "\n",
+ "#At pt D\n",
+ "F_D1=200*sin(45*pi*180**-1)\n",
+ "F_D2=200*cos(45*pi*180**-1)\n",
+ "\n",
+ "#At pt C\n",
+ "F_C1=100*sin(60*pi*180**-1)\n",
+ "F_C2=100*cos(60*pi*180**-1)\n",
+ "\n",
+ "#At pt E\n",
+ "F_E1=300*sin(30*pi*180**-1)\n",
+ "F_E2=300*cos(30*pi*180**-1)\n",
+ "\n",
+ "#Calculations\n",
+ "\n",
+ "#Let R_A and R_B be the reactions at pt A and B respectively\n",
+ "#R_A+R_B=F_D1+F_C1+F_E1 #KN\n",
+ "\n",
+ "#Taking Moment at pt A\n",
+ "R_B=(F_E1*(L_AC+L_CD+L_DE)+F_D1*(L_AC+L_CD)+F_C1*L_AC)*L**-1 #KN\n",
+ "R_A=(F_D1+F_C1+F_E1)-R_B #KN\n",
+ "\n",
+ "#Shear Force Calculations\n",
+ "\n",
+ "#S.F at pt B\n",
+ "V_B1=0 #N\n",
+ "V_B2=R_B #N\n",
+ "\n",
+ "#S.F at pt E\n",
+ "V_E1=V_B2 #N\n",
+ "V_E2=V_E1-F_E1 #N\n",
+ "\n",
+ "#S.F at pt D\n",
+ "V_D1=V_E2 #N\n",
+ "V_D2=V_D1-F_D1 #N\n",
+ "\n",
+ "#S.F at pt C\n",
+ "V_C1=V_D2 #N\n",
+ "V_C2=V_C1-F_C1 #N\n",
+ "\n",
+ "#S.F at pt A\n",
+ "V_A1=V_C2 #N\n",
+ "V_A2=V_A1+R_A\n",
+ "\n",
+ "#Bending Moment Diagrams\n",
+ "\n",
+ "#B.M At pt B\n",
+ "M_B=0 #KN.m\n",
+ "\n",
+ "#B.M at pt E\n",
+ "M_E=-R_B*L_EB #KN.m\n",
+ "\n",
+ "#B.M at pt D\n",
+ "M_D=-R_B*(L_DE+L_EB)+F_E1*L_DE #KN.m\n",
+ "\n",
+ "#B.M at pt C\n",
+ "M_C=-R_B*(L_CD+L_DE+L_EB)+F_E1*(L_CD+L_DE)+F_D1*L_CD #KN.m\n",
+ "\n",
+ "#B.M at pt A\n",
+ "M_A=-R_B*L+F_E1*(L_CD+L_DE+L_AC)+F_D1*(L_AC+L_CD)+F_C1*L_AC #KN.m\n",
+ "\n",
+ "#Result\n",
+ "print \"The Shear Force and Bending Moment Diagrams are the results\"\n",
+ "\n",
+ "#Plotting the Shear Force Diagram\n",
+ "\n",
+ "X1=[0,0,L_EB,L_EB,L_EB+L_DE,L_EB+L_DE,L_EB+L_DE+L_CD,L_EB+L_DE+L_CD,L_EB+L_DE+L_CD,L_EB+L_DE+L_CD]\n",
+ "Y1=[V_B1,V_B2,V_E1,V_E2,V_D1,V_D2,V_C1,V_C2,V_A1,V_A2]\n",
+ "Z1=[0,0,0,0,0,0,0,0,0,0]\n",
+ "plt.plot(X1,Y1,X1,Z1)\n",
+ "plt.xlabel(\"Length x in m\")\n",
+ "plt.ylabel(\"Shear Force in kN\")\n",
+ "plt.show()\n",
+ "\n",
+ "#Plotting the Bendimg Moment Diagram\n",
+ "\n",
+ "Y2=[M_B,M_E,M_D,M_C,M_A]\n",
+ "X2=[0,L_EB,L_DE+L_EB,L_DE+L_EB+L_CD,L_DE+L_EB+L_CD+L_AC]\n",
+ "Z2=[0,0,0,0,0]\n",
+ "plt.plot(X2,Y2,X2,Z2)\n",
+ "plt.xlabel(\"Length in m\")\n",
+ "plt.ylabel(\"Bending Moment in kN.m\")\n",
+ "plt.show()"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "The Shear Force and Bending Moment Diagrams are the results\n"
+ ]
+ },
+ {
+ "metadata": {},
+ "output_type": "display_data",
+ "png": 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+ "text": [
+ "<matplotlib.figure.Figure at 0x55cd530>"
+ ]
+ },
+ {
+ "metadata": {},
+ "output_type": "display_data",
+ "png": 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+ "text": [
+ "<matplotlib.figure.Figure at 0x55cd3f0>"
+ ]
+ }
+ ],
+ "prompt_number": 23
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 20.20,Page No.772"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "import matplotlib.pyplot as plt\n",
+ "\n",
+ "#Declaration Of Variables\n",
+ "\n",
+ "#Lengths\n",
+ "L_AC=L_CD=L_DE=L_EB=2 #m\n",
+ "L=8 #m\n",
+ "\n",
+ "#Loads\n",
+ "#point Load\n",
+ "\n",
+ "#At pt E\n",
+ "F_E1=6*sin(pi*180**-1*45) #KN\n",
+ "F_E2=6*cos(pi*180**-1*45) #KN\n",
+ "\n",
+ "#At pt D\n",
+ "F_D1=8*sin(pi*180**-1*60) #KN\n",
+ "F_D2=8*cos(pi*180**-1*60) #KN\n",
+ "\n",
+ "#At pt C\n",
+ "F_C1=4*sin(pi*180**-1*30) #KN\n",
+ "F_C2=4*cos(pi*180**-1*30) #KN\n",
+ "\n",
+ "#Calculations\n",
+ "\n",
+ "#Let R_A and R_B be the reactions at pt A and B respectively\n",
+ "#R_A+R_B=F_D1+F_C1+F_E1 #KN\n",
+ "\n",
+ "#Taking Moment at pt A\n",
+ "R_B=(F_E1*(L_AC+L_CD+L_DE)+F_D1*(L_AC+L_CD)+F_C1*L_AC)*L**-1 #KN\n",
+ "R_A=(F_D1+F_C1+F_E1)-R_B #KN\n",
+ "\n",
+ "#Shear Force Calculations\n",
+ "\n",
+ "#S.F at pt B\n",
+ "V_B1=0 #N\n",
+ "V_B2=R_B #N\n",
+ "\n",
+ "#S.F at pt E\n",
+ "V_E1=V_B2 #N\n",
+ "V_E2=V_E1-F_E1 #N\n",
+ "\n",
+ "#S.F at pt D\n",
+ "V_D1=V_E2 #N\n",
+ "V_D2=V_D1-F_D1 #N\n",
+ "\n",
+ "#S.F at pt C\n",
+ "V_C1=V_D2 #N\n",
+ "V_C2=V_C1-F_C1 #N\n",
+ "\n",
+ "#S.F at pt A\n",
+ "V_A1=V_C2 #N\n",
+ "V_A2=V_A1+R_A\n",
+ "\n",
+ "#Bending Moment Diagrams\n",
+ "\n",
+ "#B.M At pt B\n",
+ "M_B=0 #KN.m\n",
+ "\n",
+ "#B.M at pt E\n",
+ "M_E=-R_B*L_EB #KN.m\n",
+ "\n",
+ "#B.M at pt D\n",
+ "M_D=-R_B*(L_DE+L_EB)+F_E1*L_DE #KN.m\n",
+ "\n",
+ "#B.M at pt C\n",
+ "M_C=-R_B*(L_CD+L_DE+L_EB)+F_E1*(L_CD+L_DE)+F_D1*L_CD #KN.m\n",
+ "\n",
+ "#B.M at pt A\n",
+ "M_A=-R_B*L+F_E1*(L_CD+L_DE+L_AC)+F_D1*(L_AC+L_CD)+F_C1*L_AC #KN.m\n",
+ "\n",
+ "\n",
+ "#Result\n",
+ "print \"The Shear Force and Bending Moment Diagrams are the results\"\n",
+ "\n",
+ "#Plotting the Shear Force Diagram\n",
+ "\n",
+ "X1=[0,0,L_EB,L_EB,L_EB+L_DE,L_EB+L_DE,L_EB+L_DE+L_CD,L_EB+L_DE+L_CD,L_EB+L_DE+L_CD,L_EB+L_DE+L_CD]\n",
+ "Y1=[V_B1,V_B2,V_E1,V_E2,V_D1,V_D2,V_C1,V_C2,V_A1,V_A2]\n",
+ "Z1=[0,0,0,0,0,0,0,0,0,0]\n",
+ "plt.plot(X1,Y1,X1,Z1)\n",
+ "plt.xlabel(\"Length x in m\")\n",
+ "plt.ylabel(\"Shear Force in kN\")\n",
+ "plt.show()\n",
+ "\n",
+ "#Plotting the Bendimg Moment Diagram\n",
+ "\n",
+ "Y2=[M_B,M_E,M_D,M_C,M_A]\n",
+ "X2=[0,L_EB,L_DE+L_EB,L_DE+L_EB+L_CD,L_DE+L_EB+L_CD+L_AC]\n",
+ "Z2=[0,0,0,0,0]\n",
+ "plt.plot(X2,Y2,X2,Z2)\n",
+ "plt.xlabel(\"Length in m\")\n",
+ "plt.ylabel(\"Bending Moment in kN.m\")\n",
+ "plt.show()"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "The Shear Force and Bending Moment Diagrams are the results\n"
+ ]
+ },
+ {
+ "metadata": {},
+ "output_type": "display_data",
+ "png": 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+ "text": [
+ "<matplotlib.figure.Figure at 0x58c0630>"
+ ]
+ },
+ {
+ "metadata": {},
+ "output_type": "display_data",
+ "png": 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O5TNopNCtWzfk5+cjOzsbWVlZPKSOqk2nE4ubx4+LY7q9vMTNXZwNNJ5Tp4CO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\nNGnSBLVr18aAAQNw8ODBMh9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+ "text": [
+ "<matplotlib.figure.Figure at 0x5804cd0>"
+ ]
+ }
+ ],
+ "prompt_number": 20
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 20.21,Page No.774"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "import matplotlib.pyplot as plt\n",
+ "\n",
+ "#Declaration Of Variables\n",
+ "\n",
+ "#Lengths\n",
+ "L_CB=4 #m\n",
+ "L_AC=2 #m\n",
+ "L=6 #m\n",
+ "\n",
+ "#Loads\n",
+ "m=24 #KN.m #couple\n",
+ "\n",
+ "#Calculations\n",
+ "\n",
+ "#Let R_A and R_B be the reactions at pt A and B respectively\n",
+ "#R_A+R_B=0\n",
+ "#Taking Moment at pt A\n",
+ "R_B=m*L**-1 #KN\n",
+ "R_A=-R_B #KN\n",
+ "\n",
+ "#Shear Force Calculations\n",
+ "\n",
+ "#S.f at pt B\n",
+ "V_B1=0 #KN\n",
+ "V_B2=R_B #KN\n",
+ "\n",
+ "#S.F at pt C\n",
+ "V_C=V_B2 #KN\n",
+ "\n",
+ "#S.F at pt A\n",
+ "V_A1=V_C #KN\n",
+ "V_A2=V_A1+R_A #KN\n",
+ "\n",
+ "#Bending Moment Calculations\n",
+ "\n",
+ "#B.M at pt B\n",
+ "M_B=0 #KN.m\n",
+ "\n",
+ "#B.M at pt C\n",
+ "M_C1=-R_B*L_CB #KN.m\n",
+ "M_C2=M_C1+m #KN.m\n",
+ "\n",
+ "#B.M at pt A\n",
+ "M_A=-R_B*L+m #KN.m\n",
+ "\n",
+ "#Result\n",
+ "print\"The Shear Force and Bending Moment are the results\"\n",
+ "\n",
+ "#Plotting Shear Force Diagram\n",
+ "\n",
+ "X1=[0,0,L_CB,L_CB+L_AC,L_CB+L_AC]\n",
+ "Y1=[V_B1,V_B2,V_C,V_A1,V_A2]\n",
+ "Z1=[0,0,0,0,0]\n",
+ "plt.plot(X1,Y1,X1,Z1)\n",
+ "plt.xlabel(\"Length in m\")\n",
+ "plt.ylabel(\"Shear Force in KN\")\n",
+ "plt.show()\n",
+ "\n",
+ "#Plotting Bending Moment Diagram\n",
+ "\n",
+ "X1=[0,L_CB,L_CB,L_CB+L_AC]\n",
+ "Y1=[M_B,M_C1,M_C2,M_A]\n",
+ "Z1=[0,0,0,0]\n",
+ "plt.plot(X1,Y1,X1,Z1)\n",
+ "plt.xlabel(\"Length in m\")\n",
+ "plt.ylabel(\"Bending Moment in KN.m\")\n",
+ "plt.show()"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "The Shear Force and Bending Moment are the results\n"
+ ]
+ },
+ {
+ "metadata": {},
+ "output_type": "display_data",
+ "png": 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+ "text": [
+ "<matplotlib.figure.Figure at 0x568bbb0>"
+ ]
+ },
+ {
+ "metadata": {},
+ "output_type": "display_data",
+ "png": 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+ "text": [
+ "<matplotlib.figure.Figure at 0x5694910>"
+ ]
+ }
+ ],
+ "prompt_number": 21
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 20.22,Page No.775"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "import matplotlib.pyplot as plt\n",
+ "\n",
+ "#Declaration Of Variables\n",
+ "\n",
+ "#Lengths\n",
+ "L_DB=L_CD=2.5 #m\n",
+ "L_AC=5 #m\n",
+ "L=L=10 #m\n",
+ "\n",
+ "#Loads\n",
+ "m=15000 #Nm #couple\n",
+ "w=1000 #N/m #u.d.l\n",
+ "\n",
+ "#Calculations\n",
+ "\n",
+ "#Let R_A and R_B be the reactions at pt A and B respectively\n",
+ "#R_A+R_B=w*L_AC\n",
+ "#Taking Moment at pt A\n",
+ "R_B=(w*L_AC*L_AC*2**-1-m)*L**-1 #KN\n",
+ "R_A=w*L_AC-R_B #KN\n",
+ "\n",
+ "#Shear Force Calculations\n",
+ "\n",
+ "#S.F at pt B\n",
+ "V_B1=0 #KN\n",
+ "V_B2=R_B #KN\n",
+ "\n",
+ "#S.F at pt D\n",
+ "V_D=V_B2 #KN\n",
+ "\n",
+ "#S.F at pt C\n",
+ "V_C=V_D #KN\n",
+ "\n",
+ "#S.F at pt A\n",
+ "V_A1=V_C-w*L_AC #KN\n",
+ "V_A2=V_A1+R_A #KN\n",
+ "\n",
+ "#Bending Moment Calculations\n",
+ "\n",
+ "#B.M at pt B\n",
+ "M_B=0 #KN.m\n",
+ "\n",
+ "#B.M at pt D\n",
+ "M_D1=-R_B*L_DB #KN.m\n",
+ "M_D2=M_D1-m #KN.m\n",
+ "\n",
+ "#B.M at pt C\n",
+ "M_C=-R_B*(L_CD+L_DB)-m #KN.m\n",
+ "\n",
+ "#B.M at pt A\n",
+ "M_A=-R_B*L-m+w*L_AC*L_AC*2**-1 #KN.m\n",
+ "\n",
+ "#Result\n",
+ "print\"The Shear Force and Bending Moment Diagrams are the results\"\n",
+ "\n",
+ "#Plotting the Shear Force Diagram\n",
+ "\n",
+ "X1=[0,0,L_DB,L_CD+L_DB,L_CD+L_DB+L_AC,L_CD+L_DB+L_AC]\n",
+ "Y1=[V_B1,V_B2,V_D,V_C,V_A1,V_A2]\n",
+ "Z1=[0,0,0,0,0,0]\n",
+ "plt.plot(X1,Y1,X1,Z1)\n",
+ "plt.xlabel(\"Length x in m\")\n",
+ "plt.ylabel(\"Shear Force in kN\")\n",
+ "plt.show()\n",
+ "\n",
+ "#Plotting the Bendimg Moment Diagram\n",
+ "\n",
+ "Y2=[M_B,M_D1,M_D2,M_C,M_A]\n",
+ "X2=[0,L_DB,L_DB,L_DB+L_CD,L_AC+L_CD+L_DB]\n",
+ "Z2=[0,0,0,0,0]\n",
+ "plt.plot(X2,Y2,X2,Z2)\n",
+ "plt.xlabel(\"Length in m\")\n",
+ "plt.ylabel(\"Bending Moment in kN.m\")\n",
+ "plt.show()"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "The Shear Force and Bending Moment Diagrams are the results\n"
+ ]
+ },
+ {
+ "metadata": {},
+ "output_type": "display_data",
+ "png": 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+ "text": [
+ "<matplotlib.figure.Figure at 0x567dc90>"
+ ]
+ },
+ {
+ "metadata": {},
+ "output_type": "display_data",
+ "png": 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5c60jCsiI0UIIR3rxRdiwQcKmsakxcKp2ExZCCEdZsgTeeQdSU6FDB72rEXVJ\nxlUVQtQby5dDTAx89hnYcUAToRMJHCFEvbBiBURHa2HTqZPe1Qh7kMARQuhu1Sp49VXtNFqVoRFF\nI2MzcJYvX16tN4LBYKBt27b4+/vTq1cvuxcohGjc3nwTXnpJC5u77tK7GmFPNqcnSE9P51//+hf5\n+flYLBbeeOMNtm7dyp///GeWLl3qiBqFEI3U6tXwwgvafTZduuhdjbA3m0c4ubm5ZGRk0Lp1awAW\nLFhAWFgYn332Gf7+/jKpmRCiVtauhblz4dNPwcND72qEI9gMnOPHj9OiylR6zs7OHDt2jFtvvZVb\nZCIKIUQtvPcePP20FjaennpXIxzFZuA89NBD9O/fn5EjR6KUYsuWLTz44IOcPXsWb29vR9QohGhE\n4uPhySe1sdG8vPSuRjjSdQ3euWfPHr766isMBgP33nsvffv2dURtDiND29QNGdpG2LJxozanTXIy\n9OihdzXiZtTp0DZV9enTxzqJmcFg4OjRo9x55521KlII0TQlJMC0adrkaRI2TZPNwHnttdeYP38+\nHTp0oHnz5tb2b7/91q6FCSEaj48+0qaG/vhj6N1b72qEXmwGzquvvsr3339f41TTQghxLUlJMHky\nbNkCjexsvLhBNu/DufPOO63TE9SV9evX4+PjQ/PmzcnIyKi2bPHixZjNZry8vEhOTra2p6en4+fn\nh9lsZubMmdb2srIyoqKiMJvNBAYGcuTIEeuy2NhYPD098fT0ZO3atXX6GYQQtm3fDhMmwObN0L+/\n3tUIvdk8wunSpQsDBgxg2LBh1u7RNzsfjp+fH5s2beKxxx6r1p6ZmUl8fDyZmZlYLBYGDx5MVlYW\nBoOBqVOnEhMTQ0BAAGFhYSQlJREaGkpMTAyurq5kZWURHx/PnDlziIuLo6ioiAULFpCeng6Av78/\n4eHhtGvXrtZ1CyGu386d8OCDWkeBe+7RuxpRH1zXEc7gwYMpLy/nzJkzlJSUUFJSclM79fLywvMq\nne8TEhIYO3Yszs7OdO7cGQ8PD9LS0igoKKCkpISAgAAAJkyYwObNmwFITExk4sSJAERERLBjxw4A\ntm3bRkhICO3ataNdu3YEBweTlJR0U3ULIa7P559DZCR88AH84Q96VyPqC5tHOI6cFyc/P5/AwEDr\na5PJhMViwdnZGVOVEf2MRiMWiwUAi8WCu7s7AE5OTrRt25YTJ06Qn59fbZ1L2xJC2NeuXTB6NLz/\nPgQF6V2ZEQgkAAAXzUlEQVSNqE9qDJyZM2eyYsUKhg8ffsUyg8FAYmLiNTccHBxMYWHhFe2LFi26\n6jb1VjVYg4KCCJL/pwhxw9LSYORIWLcOBg/WuxpRl1JTU0lNTb2pbdQYOOPHjwfgySefrNWGU1JS\nbngdo9FIbm6u9XVeXh4mkwmj0UheXt4V7ZfWOXr0qPU+oeLiYlxdXTEajdW+nNzcXAYOHFjjvmWG\nUyFuzt69MHw4rFkDQ4boXY2oa5f/IT5//vwb34jSUVBQkNq7d6/19YEDB1TPnj1VWVmZ+vHHH1XX\nrl1VZWWlUkqpgIAAtXv3blVZWamGDh2qtm7dqpRSatWqVeovf/mLUkqp999/X0VFRSmllDpx4oTq\n0qWLOnnypCoqKrI+vxqdv4ZGIy1NqX799K5C6CEjQ6kOHZRKSNC7EuEotfndrPEIx8/Pr8aQMhgM\n7N+//8bT7RebNm1ixowZ/PzzzwwbNozevXuzdetWvL29iYyMxNvbGycnJ6KjozEYDABER0czadIk\nSktLCQsLIzQ0FIApU6Ywfvx4zGYzrq6uxMXFAdC+fXuee+45+vXrB8Dzzz8vPdSEsIP//heGDoXX\nX4fwcL2rEfVZjWOp5eTkANoPPWin2JRSvPvuuwCNai4cGUutbshYak3Pd99BcLA2PXRkpN7VCEeq\nze+mzcE7e/XqxTfffFOtrXfv3uzbt+/GK6ynJHDqhgRO03LwIAwaBC+/rN1vI5qW2vxu2rwPRynF\nl19+aX391VdfyY+zEE3c999rRzZLlkjYiOtn8z6c1atX8/DDD1NcXAxAu3btePvtt+1emBCifjp0\nSOvyvGCBNmyNENfLZuD4+/uzf/9+a+C0bdvW7kUJIeqn7GztNNpzz2kDcgpxI2wGzvnz59m4cSM5\nOTlUVFQA2rm7uXPn2r04IUT9ceQIDBwIc+ZoUw0IcaNsBs6IESNo164d/v7+3HLLLY6oSQhRz+Tm\namEza5Y2iZoQtWEzcCwWC9u2bXNELUKIeshi0cLmr3+FGTP0rkY0ZDZ7qd1zzz03dZOnEKLhKijQ\nwuaRR+AmZiQRAriOI5wvvviCt99+my5dutCyZUvg5kcaEELUf8eOaR0Exo/XrtsIcbNsBs7WrVsd\nUYcQoh45flzr+hwZCf/4h97ViMbC5im1zp07k5uby86dO+ncuTOtWrWSGz+FaMROnNDCJjwcnn9e\n72pEY2IzcObNm8dLL73E4sWLASgvL2fcuHF2L0wI4XgnT2ojCAwZAi++CL+MnStEnbAZOJs2bSIh\nIYFWrVoB2vwzNzvFtBCi/jl1CkJCtFk6ly6VsBF1z2bgtGzZkmbNfn3b2bNn7VqQEMLxTp+G0FC4\n+25YvlzCRtiHzcAZM2YMjz32GKdOneLNN99k0KBBPPLII46oTQjhAGfOQFgY9O6tTTMgYSPsxeb0\nBADJyckkJycDMGTIEIKDg+1emCPJ9AR1Q6YnaHjOntXCxtMT3ngDmtn8E1QIjV2mJwAICQnh5Zdf\nZs6cOQwePLhWxVW1fv16fHx8aN68Oenp6db2lJQU+vbtS48ePejbty87d+60LktPT8fPzw+z2czM\nmTOt7WVlZURFRWE2mwkMDOTIkSPWZbGxsXh6euLp6cnatWtvum4hGpNz52D4cOjaVcJGOEhNc0/v\n2rVL3X///eqBBx5QGRkZysfHR3Xs2FHdcccd6pNPPrnhuayrOnjwoPr+++9VUFCQSk9Pt7bv27dP\nFRQUKKWU+u6775TRaLQu69evn0pLS1NKKTV06FC1detWpZRSq1atUlOnTlVKKRUXF6eioqKUUkqd\nOHFCde3aVZ08eVKdPHnS+vxqrvE1iBuQlqZUv356VyGuR2mpUsHBSo0bp1RFhd7ViIaoNr+bNf5N\nM336dJ599lnGjh3LgAED+Pe//01hYSGff/45zzzzzE2FnJeXF56enle09+rVCzc3NwC8vb0pLS3l\nwoULFBQUUFJSQkBAAAATJkxg8+bNACQmJjJx4kQAIiIi2LFjBwDbtm0jJCSEdu3a0a5dO4KDg0lK\nSrqpuoVoDMrK4IEHwNUV3n4bmjfXuyLRVNQYOBcvXiQkJIQxY8bw29/+lsDAQEALC4MDripu3LgR\nf39/nJ2dsVgsmEwm6zKj0YjFYgG0wUXd3d0BcHJyom3btpw4cYL8/Pxq65hMJus6QjRV5eUQEQGt\nW8O6deBkc6wRIepOjf+5VQ2V2kxLEBwcTGFh4RXtixYtYvjw4ddc98CBAzz99NOkpKTc8H5ra968\nedbnQUFBBAUFOWzfQjjChQsQFQXOzvDeexI24sakpqaSmpp6U9uo8T+5/fv306ZNGwBKS0utzy+9\ntqW2YZGXl8eoUaNYt24dXbp0AbQjmry8vGrvuXT0YjQaOXr0KJ06daKiooLi4mJcXV0xGo3Vvpzc\n3FwGDhxY436rBo4Qjc2FCzB2LFy8CBs2aKEjxI24/A/x+fPn3/A2rnlKraSkhJKSEioqKqzPL72u\nK6pKt7pTp04xbNgwli5dyt13321t/+1vf4uLiwtpaWkopVi3bh0jRowAIDw8nNjYWAA2bNjAoEGD\nAK1nXXJyMqdOneLkyZOkpKQwZMiQOqtbiIaiokIb8fncOVi/Hlq00Lsi0WTVedeF6/Dhhx8qk8mk\nbrnlFtWxY0cVGhqqlFLqhRdeUK1atVK9evWyPo4fP66UUmrv3r3K19dXdevWTT3++OPWbZ0/f16N\nGTNGeXh4qP79+6vs7GzrstWrVysPDw/l4eGh1qxZU2M9On0NjY70Uqt/KiqUeughrUdaaane1YjG\npDa/m9d142djJzd+1g258bN+qayEyZO16aG3bIFbb9W7ItGY1OZ3Uy4bCtEIVVbCo49CdjZ88omE\njagfJHCEaGSUgmnT4H//g6Qk+GWgdyF0J4EjRCOiFDz+OPz3v7Btm3a/jRD1hQSOEI2EUjB7tnYN\nLSUFXFz0rkiI6iRwhGgElIKnnoLPP4ft26FtW70rEuJKEjhCNHBKwd//rh3VfPop3Hab3hUJcXUS\nOEI0cPPmad2ed+6E9u31rkaImkngCNGAvfCCNlTNzp1w++16VyPEtUngCNFALVkC774LqanQoYPe\n1QhhmwSOEA3Q8uUQEwOffQa/TCElRL0ngSNEA7NiBURHa2HTqZPe1Qhx/SRwhGhAVq2CV1/VTqNV\nmV9QiAZBAkeIBuLNN+Gll7SwuesuvasR4sZJ4AjRAKxerfVI27kTfpmXUIgGRwJHiHouNhbmztVu\n6vTw0LsaIWpPAkeIeuy99+CZZ7Sw8fTUuxohbk6NU0zb0/r16/Hx8aF58+ZkZGRcsfzo0aO0bt2a\n5cuXW9vS09Px8/PDbDYzc+ZMa3tZWRlRUVGYzWYCAwM5cuSIdVlsbCyenp54enqydu1a+34oIWqp\nogIKCmDfPm06gTVrtHtspk2DJ5/Uhqzx8tK7SiFuni5HOH5+fmzatInHHnvsqstnz57NsGHDqrVN\nnTqVmJgYAgICCAsLIykpidDQUGJiYnB1dSUrK4v4+HjmzJlDXFwcRUVFLFiwgPT0dAD8/f0JDw+n\nXbt2dv98QlRWQlERFBZqj2PHrv68sBBOntSGpHFz0x4dO2r/enhoXZ/lyEY0FroEjtc1/lzbvHkz\nXbt2pVWVWaMKCgooKSkhICAAgAkTJrB582ZCQ0NJTExk/vz5AERERDB9+nQAtm3bRkhIiDVggoOD\nSUpK4k9/+pO9PpZo5JSC06erh0VNQXL8uDYXzaUQqRokvr6/Pndz04akcZKT26IJqFf/mZ85c4aX\nXnqJ7du3s2zZMmu7xWLBVOWmA6PRiMVisS5zd3cHwMnJibZt23LixAny8/OrrWMymazrCFHV2bPX\nPgKp+rpFi+phcen5PfdUf92hA7RsqfcnE6J+sVvgBAcHU1hYeEX7okWLGD58+FXXmTdvHrNmzeLW\nW29FKWWv0mrc9yVBQUEEBQU5dP+ibpWVaUFxPUFSUVE9LC4979Wr+uuOHWW6ZtF0paamkpqaelPb\nsFvgpKSk3PA6X3/9NRs3buSpp57i1KlTNGvWjN/85jeMGjWKvLw86/vy8vKsRy9Go5GjR4/SqVMn\nKioqKC4uxtXVFaPRWO3Lyc3NZeDAgTXuu2rgiPqpokI7VXWtU1mXnp85ox1lXB4knp5w333Vg8TF\nBQwGvT+dEPXb5X+IX7qUcSN0P6VW9Ujm888/tz6fP38+bdq0Ydq0aQC4uLiQlpZGQEAA69atY8aM\nGQCEh4cTGxtLYGAgGzZsYNCgQQCEhITw7LPPcurUKZRSpKSksHTpUgd+MnE9ql5cv9aprGPHtPdd\n7eK6uzv07Vv9esltt0EzXfpgCiFqokvgbNq0iRkzZvDzzz8zbNgwevfuzdatW6+5TnR0NJMmTaK0\ntJSwsDBCQ0MBmDJlCuPHj8dsNuPq6kpcXBwA7du357nnnqNfv34APP/889JDzUEuv7h+rdNacnFd\niKbDoBx9saQeMhgMDr9m1Bh98412pOHkVPPF9ctfy8V1IRqm2vxuSuAggVNXlAKLRTudJRfXhWjc\nJHBqSQJHCCFuTG1+N+WyqhBCCIeQwBFCCOEQEjhCCCEcQgJHCCGEQ0jgCCGEcAgJHCGEEA4hgSOE\nEMIhJHCEEEI4hASOEEIIh5DAEUII4RASOEIIIRxCAkcIIYRDSOAIIYRwCF0CZ/369fj4+NC8eXMy\nMjKqLdu/fz933303vr6+9OjRg/LycgDS09Px8/PDbDYzc+ZM6/vLysqIiorCbDYTGBjIkSNHrMti\nY2Px9PTE09OTtWvXOubDCSGEuDqlg4MHD6rvv/9eBQUFqfT0dGv7hQsXVI8ePdT+/fuVUkoVFRWp\nixcvKqWU6tevn0pLS1NKKTV06FC1detWpZRSq1atUlOnTlVKKRUXF6eioqKUUkqdOHFCde3aVZ08\neVKdPHnS+vxqdPoa6qWdO3fqXUK9Id+FRr6HX8l38ava/G7qcoTj5eWFp6fnFe3Jycn06NEDPz8/\nAG677TaaNWtGQUEBJSUlBAQEADBhwgQ2b94MQGJiIhMnTgQgIiKCHTt2ALBt2zZCQkJo164d7dq1\nIzg4mKSkJEd8vAYtNTVV7xLqDfkuNPI9/Eq+i5tTr67hZGVlYTAYCA0Nxd/fn2XLlgFgsVgwmUzW\n9xmNRiwWi3WZu7s7AE5OTrRt25YTJ06Qn59fbR2TyWRdRwghhOM52WvDwcHBFBYWXtG+aNEihg8f\nftV1Lly4wJdffsnevXv5zW9+w6BBg/D396dt27b2KlMIIYSD2C1wUlJSbngdd3d37rvvPtq3bw9A\nWFgYGRkZjBs3jry8POv78vLyrEcvRqORo0eP0qlTJyoqKiguLsbV1RWj0Vjt8Dc3N5eBAwdedb/d\nunXDYDDccL2N1fz58/Uuod6Q70Ij38Ov5LvQdOvW7YbX0f2UmqoyJ/aQIUP49ttvKS0tpaKigs8+\n+wwfHx/c3NxwcXEhLS0NpRTr1q1jxIgRAISHhxMbGwvAhg0bGDRoEAAhISEkJydz6tQpTp48SUpK\nCkOGDLlqDYcOHUIpJQ95yEMe8rjOx6FDh2r1g+9wH374oTKZTOqWW25RHTt2VKGhodZl77zzjvLx\n8VG+vr5qzpw51va9e/cqX19f1a1bN/X4449b28+fP6/GjBmjPDw8VP/+/VV2drZ12erVq5WHh4fy\n8PBQa9ascchnE0IIcXUGpZSyHUtCCCHEzdH9lJqekpKS8PLywmw2s3TpUr3L0U1ubi4DBgzAx8cH\nX19fVq5cqXdJurt48SK9e/eusYNLU3Hq1ClGjx5N9+7d8fb2Zvfu3XqXpJvFixfj4+ODn58fDz74\nIGVlZXqX5DCTJ0+mY8eO1ltWAIqKiggODsbT05OQkBBOnTplcztNNnAuXrzI9OnTSUpKIjMzk/ff\nf5+DBw/qXZYunJ2deeWVVzhw4AC7d+9m1apVTfa7uGTFihV4e3s3+c4kM2fOJCwsjIMHD7J//366\nd++ud0m6yMnJ4a233iIjI4Nvv/2WixcvEhcXp3dZDvPwww9fcR/jkiVLCA4O5ocffmDQoEEsWbLE\n5naabOB8/fXXeHh40LlzZ5ydnfnTn/5EQkKC3mXpws3NjV69egHQunVrunfvTn5+vs5V6ScvL49P\nPvmERx55hKZ8xrm4uJgvvviCyZMnA7/e59YUubi44OzszLlz56ioqODcuXMYjUa9y3KYP/zhD9x2\n223V2qredD9x4kTrzfjX0mQDp+oNoyA3hl6Sk5PDvn376N+/v96l6GbWrFksW7aMZs2a7P89AMjO\nzuaOO+7g4Ycfpk+fPvz5z3/m3Llzepeli/bt2/Pkk09y55130qlTJ9q1a8fgwYP1LktXx44do2PH\njgB07NiRY8eO2Vynyf4/qqmfKrmaM2fOMHr0aFasWEHr1q31LkcXH330ER06dKB3795N+ugGoKKi\ngoyMDKZNm0ZGRgatWrW6rtMmjdHhw4d59dVXycnJIT8/nzNnzvDuu+/qXVa9YTAYrus3tckGjtFo\nJDc31/o6Nze32lA4Tc2FCxeIiIhg3LhxjBw5Uu9ydLNr1y4SExPp0qULY8eO5dNPP2XChAl6l6UL\nk8mEyWSiX79+AIwePfqK0d2bir1793LPPffg6uqKk5MTo0aNYteuXXqXpauOHTtaR5MpKCigQ4cO\nNtdpsoHTt29fsrKyyMnJoby8nPj4eMLDw/UuSxdKKaZMmYK3tzdPPPGE3uXoatGiReTm5pKdnU1c\nXBwDBw5sslNbuLm54e7uzg8//ADA9u3b8fHx0bkqfXh5ebF7925KS0tRSrF9+3a8vb31LktXVW+6\nj42Nva4/VO02tE195+TkxD//+U+GDBnCxYsXmTJlSpPtgfPVV1/xzjvv0KNHD3r37g1oXUBDQ0N1\nrkx/Tf3U62uvvcZDDz1EeXk53bp14+2339a7JF307NmTCRMm0LdvX5o1a0afPn149NFH9S7LYcaO\nHctnn33Gzz//jLu7OwsWLODpp58mMjKSmJgYOnfuzAcffGBzO3LjpxBCCIdosqfUhBBCOJYEjhBC\nCIeQwBFCCOEQEjhCCCEcQgJHCCGEQ0jgCCGEcAgJHCFugL2H/Hn11VcpLS29of1t2bKlSU+vIRoO\nuQ9HiBvQpk0bSkpK7Lb9Ll26sHfvXlxdXR2yPyEcSY5whLhJhw8fZujQofTt25f77ruP77//HoBJ\nkyYxc+ZM7r33Xrp168bGjRsBqKysZNq0aXTv3p2QkBCGDRvGxo0bee2118jPz2fAgAEMGjTIuv1/\n/OMf9OrVi7vvvpuffvrpiv2vWbOGxx9//Jr7rConJwcvLy8efvhhfve73/HQQw+RnJzMvffei6en\nJ3v27LHH1ySEBI4QN+vRRx/ltddeY+/evSxbtoxp06ZZlxUWFvLVV1/x0Ucf8fTTTwPw4YcfcuTI\nEQ4ePMi6dev4z3/+g8Fg4PHHH6dTp06kpqayY8cOAM6ePcvdd9/NN998w3333cdbb711xf4vH37n\navu83OHDh/nb3/7G//73P77//nvi4+P56quvePnll1m0aFFdfTVCVNNkx1IToi6cOXOG//znP4wZ\nM8baVl5eDmhBcGlAw+7du1vnC/nyyy+JjIwEtBF3BwwYUOP2W7RowbBhwwDw9/cnJSXlmvXUtM/L\ndenSxToQp4+Pj3VuF19fX3Jycq65DyFqSwJHiJtQWVlJu3bt2Ldv31WXt2jRwvr80uVSg8FQba6d\na11GdXZ2tj5v1qwZFRUVNmu62j4v17Jly2rbvbTO9e5DiNqQU2pC3AQXFxe6dOnChg0bAO0Hfv/+\n/ddc595772Xjxo0opTh27BifffaZdVmbNm04ffr0DdUg/X5EQyGBI8QNOHfuHO7u7tbHq6++yrvv\nvktMTAy9evXC19eXxMRE6/urXl+59DwiIgKTyYS3tzfjx4+nT58+tG3bFtCuB4WGhlo7DVy+/tWm\nS7i8vabnl69T0+umPiWDsB/pFi2EDs6ePUurVq04ceIE/fv3Z9euXdc1Y6IQDZlcwxFCB3/84x85\ndeoU5eXlzJ07V8JGNAlyhCOEEMIh5BqOEEIIh5DAEUII4RASOEIIIRxCAkcIIYRDSOAIIYRwCAkc\nIYQQDvH/Aft+XWP0flPgAAAAAElFTkSuQmCC\n",
+ "text": [
+ "<matplotlib.figure.Figure at 0x58d5f90>"
+ ]
+ }
+ ],
+ "prompt_number": 22
+ }
+ ],
+ "metadata": {}
+ }
+ ]
+}
\ No newline at end of file diff --git a/Engineering_Mechanics/chapter_3.ipynb b/Engineering_Mechanics/chapter_3.ipynb new file mode 100644 index 00000000..f584173d --- /dev/null +++ b/Engineering_Mechanics/chapter_3.ipynb @@ -0,0 +1,591 @@ +{
+ "metadata": {
+ "name": "chapter_3.ipynb"
+ },
+ "nbformat": 3,
+ "nbformat_minor": 0,
+ "worksheets": [
+ {
+ "cells": [
+ {
+ "cell_type": "heading",
+ "level": 1,
+ "metadata": {},
+ "source": [
+ "Chapter 3:Coplanar Parallel forces"
+ ]
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 3.1,Page No.48"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "\n",
+ "#Declaration Of Variables\n",
+ "\n",
+ "#Lengths\n",
+ "L_AB=L_BC=L_CD=L_DA=2 #m\n",
+ "\n",
+ "#Loads\n",
+ "F_B=10 #N\n",
+ "F_C=20 #N\n",
+ "F_D=30 #N\n",
+ "F_A=40 #N\n",
+ "\n",
+ "#Calculations\n",
+ "\n",
+ "#Taking Moment at point A\n",
+ "#As the Forces F_A & F_B pass through point A,these Forces will be zero\n",
+ "#Resultant Moment of all Forces\n",
+ "M_A=-(-F_D*L_DA-F_C*L_CD) #N.m\n",
+ "\n",
+ "#Result\n",
+ "print\"Resultant Moment about point A is\",round(M_A,2),\"N.m (Anticlockwise)\""
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "Resultant Moment about point A is 100.0 N.m (Anticlockwise)\n"
+ ]
+ }
+ ],
+ "prompt_number": 1
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 3.2,Page No.50"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "from math import sin, cos, tan, radians, pi\n",
+ "\n",
+ "#Declaration Of Variables\n",
+ "F_A=100 #N\n",
+ "OCB=60 #Degrees\n",
+ "L_OC=3 #m\n",
+ "\n",
+ "#Calculations\n",
+ "\n",
+ "#Triangle OBC is a right Angled triangle\n",
+ "L_OB=L_OC*sin(60*pi*180**-1)\n",
+ "\n",
+ "#Moment of force 100 #N about o\n",
+ "M_O=F_A*L_OB #Nm\n",
+ "\n",
+ "#Result\n",
+ "print\"Moment of Force about O is\",round(M_O,2),\"Nm\""
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "Moment of Force about O is 259.81 Nm\n"
+ ]
+ }
+ ],
+ "prompt_number": 2
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 3.3,Page No.54"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "\n",
+ "#Declaration Of Variables\n",
+ "\n",
+ "#Lengths\n",
+ "L_AB=30 #cm\n",
+ "L_BC=40 #cm\n",
+ "\n",
+ "#Loads\n",
+ "F_A=100 #N\n",
+ "F_B=200 #N\n",
+ "F_C=300 #N\n",
+ "\n",
+ "#Calculations\n",
+ "\n",
+ "#resultant of all forces\n",
+ "R=F_A+F_B+F_C #N\n",
+ "\n",
+ "#Let resultant be acting at distance x from point A\n",
+ "\n",
+ "#Now taking moments at point A\n",
+ "M_A=-(-F_C*(L_AB+L_BC)-F_B*L_AB) #N.m\n",
+ "\n",
+ "#Moment of resultant R about A\n",
+ "#M_R=R*x\n",
+ "\n",
+ "#But algebraic sum of moments of all forces about A = Moment of resultant about A\n",
+ "x=M_A*R**-1\n",
+ "\n",
+ "#Result\n",
+ "print\"Resultant is\",round(R,2),\"N\"\n",
+ "print\"Distance of resultant from point A\",round(x,2),\"cm\""
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "Resultant is 600.0 N\n",
+ "Distance of resultant from point A 45.0 cm\n"
+ ]
+ }
+ ],
+ "prompt_number": 3
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 3.4,Page No.54"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "\n",
+ "#Declaration Of Variables\n",
+ "\n",
+ "#Lengths\n",
+ "L_AC=4 #m\n",
+ "L_CD=3 #m\n",
+ "L_AD=7 #m\n",
+ "\n",
+ "#Forces\n",
+ "F_A=50 #N\n",
+ "F_D=100 #N\n",
+ "F_B=200 #N\n",
+ "R=250 #N #Resultant \n",
+ "\n",
+ "#Calculations\n",
+ "\n",
+ "#Part-1\n",
+ "#Magnitude of Force F_B\n",
+ "F=R-F_A-F_D #N\n",
+ "\n",
+ "#Part-2\n",
+ "#Distance from pt A\n",
+ "#Taking Moment of all forces at pt A\n",
+ "#M_A=0\n",
+ "#Now moments of all forces = Moment of Resultant\n",
+ "#After simplifying further we get\n",
+ "x=(R*L_AC-F_D*L_AD)*F_B**-1 #m\n",
+ "\n",
+ "#Result\n",
+ "print\"Magnitude of Force F is\",round(F,2),\"N\"\n",
+ "print\"Distance of force f from A is\",round(x,2),\"m\""
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "Magnitude of Force F is 100.0 N\n",
+ "Distance of force f from A is 1.5 m\n"
+ ]
+ }
+ ],
+ "prompt_number": 1
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 3.5,Page No.55"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "\n",
+ "#Declaration Of Variables\n",
+ "\n",
+ "#Lengths\n",
+ "L_AB=0.9 #m\n",
+ "L_BC=1.2 #m\n",
+ "L_CD=0.75 #m\n",
+ "L=L_AB+L_BC+L_CD #m\n",
+ "\n",
+ "#Forces\n",
+ "F_A=100 #N\n",
+ "F_B=150 #N\n",
+ "F_C=25 #N\n",
+ "F_D=200 #N\n",
+ "\n",
+ "#Calculations\n",
+ "\n",
+ "#Part-1\n",
+ "#Magnitude of Resultant\n",
+ "R=F_A-F_B-F_C+F_D #N\n",
+ "\n",
+ "#Part-2\n",
+ "#Let x be the distance of Resultant from A\n",
+ "x=-(F_B*L_AB+F_C*(L_AB+L_BC)-F_D*L)*R**-1 #m\n",
+ "\n",
+ "#Result\n",
+ "print\"Magnitude of Resultant\",round(R,2),\"N\"\n",
+ "print\"Distance of Resultant from x is\",round(x,2),\"m\""
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "Magnitude of Resultant 125.0 N\n",
+ "Distance of Resultant from x is 3.06 m\n"
+ ]
+ }
+ ],
+ "prompt_number": 5
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 3.6,Page No.57"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "\n",
+ "#Declaration Of Variables\n",
+ "\n",
+ "#Lengths\n",
+ "L_AC=L_CD=1 #m\n",
+ "L_DB=1.5 #m\n",
+ "L=3.5 #m\n",
+ "\n",
+ "#Forces\n",
+ "F_A=32.5 #N\n",
+ "F_C=150 #N\n",
+ "F_D=67.5 #N\n",
+ "F_B=10 #N\n",
+ "\n",
+ "#Calculations\n",
+ "\n",
+ "#Part-1\n",
+ "\n",
+ "#Single Force ststem\n",
+ "R=-(F_A-F_C+F_D-F_B) #N\n",
+ "\n",
+ "#Let x be the distance of Resultant from A\n",
+ "x=-(F_C*L_AC-F_D*(L_AC+L_CD)+F_B*L)*R**-1 #m\n",
+ "\n",
+ "#Part-2\n",
+ "\n",
+ "#Single Force is given By R\n",
+ "\n",
+ "#Now moment of couple at pt A\n",
+ "M_A=-R*round(x,2) #N.m\n",
+ "\n",
+ "#Part-3\n",
+ "\n",
+ "#Now couple at B\n",
+ "L_BE=L+x\n",
+ "M_B=R*round(L_BE,3) #N.m\n",
+ "\n",
+ "#Result\n",
+ "print\"Single Force is\",round(R,2),\"N\"\n",
+ "print\"Couple at A\",round(M_A,2),\"N.m\"\n",
+ "print\"Couple at B\",round(M_B,2),\"N.m\""
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "Single Force is 60.0 N\n",
+ "Couple at A 49.8 N.m\n",
+ "Couple at B 160.02 N.m\n"
+ ]
+ }
+ ],
+ "prompt_number": 6
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 3.7,Page No.59"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "\n",
+ "#Declaration Of Variables\n",
+ "\n",
+ "#Lengths\n",
+ "L_AB=L_DE=0.6 #m\n",
+ "L_BC=0.9 #m\n",
+ "L_CD=1.2 #m\n",
+ "\n",
+ "#Forces\n",
+ "F_A=4 #N\n",
+ "F_B=8 #N\n",
+ "F_C=8 #N\n",
+ "F_D=16 #N\n",
+ "F_E=12 #N\n",
+ "\n",
+ "#Calculations\n",
+ "\n",
+ "#Resultant Of All Forces\n",
+ "R=-F_A+F_B-F_C+F_D-F_E #N\n",
+ "\n",
+ "#As the Resultatn Force is zero,tere will be two possibilities.The system will have a resultant coup\n",
+ "#Algebraic sum of moments of all forces about A\n",
+ "M_A=-F_B*L_AB+F_C*(L_AB+L_BC)-F_D*(L_AB+L_BC+L_CD)+F_E*(L_AB+L_BC+L_CD+L_DE) #N.m\n",
+ "\n",
+ "#As the algebraic sum of moments of all forces is not zero,the ststem will have couple of magnitude 3.6 #N.m\n",
+ "\n",
+ "#Result\n",
+ "print\"Resultant of Parallel Forces is\",round(R,2),\"N\""
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "Resultant of Parallel Forces is 0.0 N\n"
+ ]
+ }
+ ],
+ "prompt_number": 7
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 3.8,Page No.59"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "\n",
+ "#Declaration Of Variables\n",
+ "\n",
+ "L_AB=L_DE=2 #m\n",
+ "L_BC=0.5 #m\n",
+ "L_CD=0.5 #m\n",
+ "\n",
+ "#Forces\n",
+ "F_A=20 #N\n",
+ "F_B=20 #N\n",
+ "F_C=40 #N\n",
+ "F_D=30 #N\n",
+ "F_E=10 #N\n",
+ "\n",
+ "\n",
+ "#Calculations\n",
+ "\n",
+ "#Resultant Of All Forces\n",
+ "R=-F_A+F_B+F_C-F_D-F_E #N\n",
+ "\n",
+ "#As the Resultant is zero and also the resultant force on the body is zero,the body will be in equilibrium\n",
+ "\n",
+ "#Result\n",
+ "print\"Resultant of Parallel Forces is\",round(R,2),\"N\""
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "Resultant of Parallel Forces is 0.0 N\n"
+ ]
+ }
+ ],
+ "prompt_number": 8
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 3.9,Page No.60"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "from math import sin, cos, tan, radians, pi\n",
+ "\n",
+ "#Declaration Of Variables\n",
+ "\n",
+ "#Distances\n",
+ "L_OA=200 #mm\n",
+ "L_OB=100 #mm\n",
+ "L_BC=200 #mm\n",
+ "\n",
+ "COA=90 #Degrees\n",
+ "\n",
+ "#Forces\n",
+ "F_A=2000 #N\n",
+ "F_B=1500 #N\n",
+ "F_C=1000 #N\n",
+ "\n",
+ "#Calculations\n",
+ "\n",
+ "#Resolving FOrce A in two components\n",
+ "F_A1=F_A*cos(30*pi*180**-1) #Component along x-axis\n",
+ "F_A2=F_A*sin(30*pi*180**-1) #Component along y-axis\n",
+ "\n",
+ "#Resolving all forces along X-axis\n",
+ "F_x=F_A1-F_B-F_C\n",
+ "F_y=F_A2\n",
+ "\n",
+ "#Resultant \n",
+ "R=(F_x**2+F_y**2)**0.5 #N\n",
+ "\n",
+ "#Taking Moments of all forces about pt O\n",
+ "M_o=-(F_y*L_OA-F_B*L_OB-F_C*(L_BC+L_OB)) #N.mm\n",
+ "\n",
+ "#Result\n",
+ "print\"Equivalent system through point O is:Resultant\",round(R,2),\"N\"\n",
+ "print\" :Moment\",round(M_o,2),\"N.mm\""
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "Equivalent system through point O is:Resultant 1260.85 N\n",
+ " :Moment 250000.0 N.mm\n"
+ ]
+ }
+ ],
+ "prompt_number": 9
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 3.10,Page No.61"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "\n",
+ "#Declaration Of Variables\n",
+ "\n",
+ "#Lengths\n",
+ "L_AC=1 #m\n",
+ "L_CB=1.5 #m\n",
+ "L_CD=0.8 #m\n",
+ "L_DB=0.7 #m\n",
+ "L=2.5 #m\n",
+ "\n",
+ "#Forces\n",
+ "F_C=4000 #N\n",
+ "F_B=2500 #N\n",
+ "M_D=2000 #N*m\n",
+ "\n",
+ "#Calculations\n",
+ "\n",
+ "#Resultant of all forces\n",
+ "R=-F_C+F_B #N\n",
+ "\n",
+ "#As the Force is acting in downward direction,so negative sign\n",
+ "R2=-R\n",
+ "\n",
+ "#Sum of Moments of all Forces\n",
+ "M=(F_C*L_AC+M_D-F_B*L)\n",
+ "M2=-M #Anticlockwise\n",
+ "\n",
+ "#Now distance of resultant from x is\n",
+ "x=(F_C*L_AC+M_D-F_B*L)*R2**-1\n",
+ "\n",
+ "#Negative sign indicates that it acts left of A\n",
+ "x2=-x\n",
+ "\n",
+ "#Result\n",
+ "print\"Resultant of the system\",round(R2,2),\"N\"\n",
+ "print\"Equivalent system through A\",round(M2,2),\"N.m (Anticlockwise)\""
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "Resultant of the system 1500.0 N\n",
+ "Equivalent system through A 250.0 N.m (Anticlockwise)\n"
+ ]
+ }
+ ],
+ "prompt_number": 10
+ }
+ ],
+ "metadata": {}
+ }
+ ]
+}
\ No newline at end of file diff --git a/Engineering_Mechanics/chapter_4.ipynb b/Engineering_Mechanics/chapter_4.ipynb new file mode 100644 index 00000000..023a8e04 --- /dev/null +++ b/Engineering_Mechanics/chapter_4.ipynb @@ -0,0 +1,1051 @@ +{
+ "metadata": {
+ "name": "chapter_4.ipynb"
+ },
+ "nbformat": 3,
+ "nbformat_minor": 0,
+ "worksheets": [
+ {
+ "cells": [
+ {
+ "cell_type": "heading",
+ "level": 1,
+ "metadata": {},
+ "source": [
+ "Chapter 4:Conditions Of Equilibrium"
+ ]
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 4.1,Page No.68"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "\n",
+ "#Declaration Of Variables\n",
+ "F1=100 #N #Force acting on body\n",
+ "\n",
+ "#Calculations\n",
+ "\n",
+ "#As the Force F1 & F2 are acting on the same body and at same point but in opposite directions\n",
+ "#These two forces will be equal\n",
+ "F2=F1\n",
+ "\n",
+ "#Result\n",
+ "print\"Magnitude of Force F2 is\",round(F2,2),\"N\""
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "Magnitude of Force F2 is 100.0 N\n"
+ ]
+ }
+ ],
+ "prompt_number": 1
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 4.2,Page No.68"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "from math import sin, cos, tan, radians, pi\n",
+ "\n",
+ "#Declaration Of Variables\n",
+ "\n",
+ "#Force\n",
+ "F3=400 #N\n",
+ "theta1=30 #Degree #Angle made by forces F2 & F3\n",
+ "\n",
+ "#Calculations\n",
+ "\n",
+ "#By Lami's Theorem\n",
+ "#F1*sin(120)**-1=F2*sin(120)**-1=F3*sin(120)**-1\n",
+ "F2=F3*sin(120*pi*180**-1)**-1*sin(120*pi*180**-1)\n",
+ "F1=F2*sin(120*pi*180**-1)**-1*sin(120*pi*180**-1)\n",
+ "\n",
+ "#Result\n",
+ "print\"Magnitude of Forces:F1\",round(F1,2),\"N\"\n",
+ "print\" :F2\",round(F2,2),\"N\""
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "Magnitude of Forces:F1 400.0 N\n",
+ " :F2 400.0 N\n"
+ ]
+ }
+ ],
+ "prompt_number": 2
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 4.3,Page No.69"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "\n",
+ "#Declaration Of Variables\n",
+ "\n",
+ "#FOrces\n",
+ "F1=250 #N\n",
+ "F3=1000 #N\n",
+ "L_AB=1 #m #Length of AB\n",
+ "\n",
+ "#Calculations\n",
+ "\n",
+ "#Sum of forces in y direction\n",
+ "F2=F1+F3 #N\n",
+ "\n",
+ "#Moment at pt A\n",
+ "#-F2*L_AB+F3*(L_AB+x)=0\n",
+ "#After further simplifying we get\n",
+ "x=F2*L_AB*F3**-1-L_AB\n",
+ "\n",
+ "#Result\n",
+ "print\"Magnitude of Force F2 is\",round(F2,2),\"N\"\n",
+ "print\"Distance of F2 From F3 is\",round(x,2),\"N\""
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "Magnitude of Force F2 is 1250.0 N\n",
+ "Distance of F2 From F3 is 0.25 N\n"
+ ]
+ }
+ ],
+ "prompt_number": 3
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 4.4,Page No.69"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "from math import sin, cos, tan, radians, pi\n",
+ "import numpy as np\n",
+ "\n",
+ "#Declaration Of Variables\n",
+ "\n",
+ "#Forces\n",
+ "F1=18 #N\n",
+ "F2=22.5 #N\n",
+ "F3=15 #N\n",
+ "F4=30 #N\n",
+ "\n",
+ "#Angles\n",
+ "theta2=45 #Degree\n",
+ "theta3=90 #Degree\n",
+ "theta4=30 #Degree\n",
+ "\n",
+ "#Calculations\n",
+ "\n",
+ "#Sum of Forces in x-direction\n",
+ "#F1+F2*cos(45)-F4*cos(30)-F5*cos(theta5)=0\n",
+ "#After further simplifying we get\n",
+ "#F5*cos(theta5)=F1+F2*cos(45)-F4*cos(30)....................1\n",
+ "\n",
+ "#Sum of Forces in y-direction\n",
+ "#F3+F2*sin(45)-F4*sin(30)-F5*sin(theta5)=0\n",
+ "#After further simplifying we get\n",
+ "#F5*sin(theta5)=F3+F2*sin(45)-F4*sin(30)....................2\n",
+ "\n",
+ "#Dividing equation 2 and 1 we get\n",
+ "X=F3+F2*sin(45*pi*180**-1)-F4*sin(30*pi*180**-1)\n",
+ "Y=F1+F2*cos(45*pi*180**-1)-F4*cos(30*pi*180**-1)\n",
+ "theta=np.arctan((X)*(Y)**-1)*(pi**-1*180)\n",
+ "\n",
+ "F5=(F1+F2*cos(45*pi*180**-1)-F4*cos(30*pi*180**-1))*(cos(theta*pi*180**-1))**-1\n",
+ "\n",
+ "\n",
+ "#Result\n",
+ "print\"Magnitude of force F5 is\",round(F5,2),\"N\"\n",
+ "print\"Direction of F5 is\",round(theta,2),\"Degrees\""
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "Magnitude of force F5 is 17.78 N\n",
+ "Direction of F5 is 63.51 Degrees\n"
+ ]
+ }
+ ],
+ "prompt_number": 4
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 4.5,Page No.71"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "from math import sin, cos, tan, radians, pi\n",
+ "import numpy as np\n",
+ "\n",
+ "#Declaration Of Variables \n",
+ "\n",
+ "#Forces\n",
+ "F_C=1500 #N\n",
+ "theta_C=60 #degrees\n",
+ "\n",
+ "F_B=1805 #N\n",
+ "theta_B=33.67 #Degrees\n",
+ "\n",
+ "F_A=2240 #N\n",
+ "theta_A=63.43 #Degrees\n",
+ "\n",
+ "#Distances of forces from D\n",
+ "L_DC=2 #m\n",
+ "L_DB=3 #m\n",
+ "L_DE=4 #m\n",
+ "L_DO=3 #m\n",
+ "\n",
+ "\n",
+ "#Calculations\n",
+ "\n",
+ "#NEt forces along Y-axis\n",
+ "R_y=-F_C*cos(theta_C*pi*180**-1)-F_B*cos(theta_B*pi*180**-1)+F_A*cos(theta_A*pi*180**-1)\n",
+ "\n",
+ "#Net Forces along x-axis\n",
+ "R_x=F_C*sin(theta_C*pi*180**-1)-F_B*sin(theta_B*pi*180**-1)-F_A*sin(theta_A*pi*180**-1)\n",
+ "\n",
+ "#Resultant Forces\n",
+ "R=(R_x**2+R_y**2)**0.5 #N\n",
+ "\n",
+ "#Angle made by resultant\n",
+ "theta=np.arctan(R_y*R_x**-1)*(pi**-1*180) #Degrees\n",
+ "\n",
+ "#Net Moment about point O\n",
+ "M_O=-F_C*cos(theta_C*pi*180**-1)*L_DO-F_B*cos(theta_B*pi*180**-1)*L_DO-F_C*sin(theta_C*pi*180**-1)*L_DC+F_B*sin(theta_B*pi*180**-1)*L_DB+F_A*sin(theta_A*pi*180**-1)*L_DE\n",
+ "\n",
+ "\n",
+ "#Moment of R about O\n",
+ "\n",
+ "#X-intercept\n",
+ "x=M_O*-R_x**-1\n",
+ "\n",
+ "#Y-intercept\n",
+ "y=M_O*-R_y**-1\n",
+ "\n",
+ "#Result\n",
+ "print\"Resultant is\",round(R,2),\"N\"\n",
+ "print\"X intercept is\",round(x,2),\"m\"\n",
+ "print\"Y intercept is\",round(y,2),\"m\""
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "Resultant is 2114.37 N\n",
+ "X intercept is 0.97 m\n",
+ "Y intercept is 1.33 m\n"
+ ]
+ }
+ ],
+ "prompt_number": 5
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 4.6,Page No.73"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "from math import sin, cos, tan, radians, pi\n",
+ "\n",
+ "#Declaration Of Variables\n",
+ "theta=60 #Degrees #Angle made by chain with ceiling\n",
+ "W=5 #N #Weight of lamp\n",
+ "theta2=120 #Degree #Angle made by chain with cord\n",
+ "theta3=150 #Degree #Angle made by chain with wire holding lamp\n",
+ "theta4=90 #Degree #Angle made by cord with wire holding lamp\n",
+ "\n",
+ "#Calculations\n",
+ "\n",
+ "#LEt T1=tension in cord\n",
+ "#T2=tension in chain\n",
+ "\n",
+ "#By lami's theorem\n",
+ "#T1*sin(theta3)**-1=T2*sin(theta4)**-1=W*sin(theta2)**-1\n",
+ "\n",
+ "T1=W*sin(theta2*pi*180**-1)**-1*sin(theta3*pi*180**-1) #N\n",
+ "T2=W*sin(theta2*pi*180**-1)**-1*sin(theta4*pi*180**-1) #N\n",
+ "\n",
+ "#Result\n",
+ "print\"Tension in chain is\",round(T2,2),\"N\"\n",
+ "print\"Tension in cord is\",round(T1,2),\"N\""
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "Tension in chain is 5.77 N\n",
+ "Tension in cord is 2.89 N\n"
+ ]
+ }
+ ],
+ "prompt_number": 6
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 4.7,Page No.74"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "from math import sin, cos, tan, radians, pi\n",
+ "import numpy as np\n",
+ "\n",
+ "#Declaration Of Variables\n",
+ "\n",
+ "#Forces\n",
+ "F_P=1000 #N\n",
+ "F_Q=1500 #N\n",
+ "F_R=1000 #N\n",
+ "F_S=500 #N\n",
+ "\n",
+ "theta=90 #Degree #Angle made by F_P with PS\n",
+ "theta2=60 #Degree #Angle made by F_Q with QS\n",
+ "theta3=45 #Degree #Angle made by F_R with RS\n",
+ "theta4=30 #Degree #Angle made by F_S with PS\n",
+ "\n",
+ "#Calculations\n",
+ "\n",
+ "#Resultant of forces along x-axis\n",
+ "R_x=-F_Q*cos(theta2*pi*180**-1)-F_R*cos(theta3*pi*180**-1)-F_S*cos(theta4*pi*180**-1)\n",
+ "\n",
+ "#Resultant of forces along y-axis\n",
+ "R_y=-F_P*sin(theta*pi*180**-1)-F_Q*sin(theta2*pi*180**-1)-F_R*sin(theta3*pi*180**-1)-F_S*sin(theta4*pi*180**-1)\n",
+ "\n",
+ "#Resultant\n",
+ "R=(R_x**2+R_y**2)**0.5 #N\n",
+ "\n",
+ "#Direction of resultant\n",
+ "theta=np.arctan(R_y*R_x**-1)*(180*pi**-1) #Degree\n",
+ "\n",
+ "#Result\n",
+ "print\"Magnitude of Resultant is\",round(R,2),\"N\"\n",
+ "print\"Direction of Resultant is\",round(theta,2),\"degree\""
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "Magnitude of Resultant is 3764.97 N\n",
+ "Direction of Resultant is 59.87 degree\n"
+ ]
+ }
+ ],
+ "prompt_number": 7
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 4.9,Page No.78"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "from math import sin, cos, tan, radians, pi\n",
+ "import numpy as np\n",
+ "\n",
+ "#Declaration Of Variables\n",
+ "W=100 #N #Weight of roller\n",
+ "L_BC=10 #cm #Radius of roller\n",
+ "L_AB=20 #cm #Length of tie rod\n",
+ "\n",
+ "#Calculations\n",
+ "\n",
+ "theta=np.arcsin(L_BC*L_AB**-1)*(pi**-1*180) #Degrees\n",
+ "\n",
+ "F=W*cos(theta*pi*180**-1)**-1 #N #Force in tie rod\n",
+ "R_C=F*sin(theta*pi*180**-1)\n",
+ "\n",
+ "#Result \n",
+ "print\"Force in tie rod is\",round(F,2),\"N\"\n",
+ "print\"Reaction at C is\",round(R_C,2),\"N\""
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "Force in tie rod is 115.47 N\n",
+ "Reaction at C is 57.74 N\n"
+ ]
+ }
+ ],
+ "prompt_number": 8
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 4.11,Page No.79"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "from math import sin, cos, tan, radians, pi\n",
+ "\n",
+ "#Declaration Of Variables\n",
+ "W=120 #N #Weight of ball\n",
+ "theta=30 #Degrees #angle made by groove\n",
+ "theta2=60 #Degrees #Angle made by groove\n",
+ "\n",
+ "#Calculations\n",
+ "\n",
+ "#LEt R_A and R_B be the reactions at A and B respectively\n",
+ "#by LAmi's theorem\n",
+ "#R_B*sin(120)**-1=R_A*sin(150)**-1=W*sin(90)**-1\n",
+ "\n",
+ "R_C=W*sin(90*pi*180**-1)**-1*sin(120*pi*180**-1) #N\n",
+ "R_A=W*sin(90*pi*180**-1)**-1*sin(150*pi*180**-1) #N\n",
+ "\n",
+ "\n",
+ "#Result\n",
+ "print\"Reaction at A is\",round(R_A,2),\"N\"\n",
+ "print\"Reaction at c is\",round(R_C,2),\"N\""
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "Reaction at A is 60.0 N\n",
+ "Reaction at c is 103.92 N\n"
+ ]
+ }
+ ],
+ "prompt_number": 9
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 4.11(A),Page No.81"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "from math import sin, cos, tan, radians, pi\n",
+ "\n",
+ "#Declaration Of Variables\n",
+ "W=100 #N #weight of roller\n",
+ "\n",
+ "#Calculations\n",
+ "\n",
+ "#LEt R_A and R_B be the reactions at A and B respectively\n",
+ "theta=45 #Degrees #Angle made by R_B with horizontal\n",
+ "theta2=30 #Degrees #Angle made by R_A with horizontal\n",
+ "\n",
+ "#by LAmi's theorem\n",
+ "#R_B*sin(120)**-1=R_A*sin(135)**-1=W*sin(105)**-1\n",
+ "\n",
+ "R_B=W*sin(105*pi*180**-1)**-1*sin(120*pi*180**-1) #N\n",
+ "R_A=W*sin(105*pi*180**-1)**-1*sin(135*pi*180**-1) #N\n",
+ "\n",
+ "#Result\n",
+ "print\"Reaction at A is\",round(R_A,2),\"N\"\n",
+ "print\"Reaction at B is\",round(R_B,2),\"N\""
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "Reaction at A is 73.21 N\n",
+ "Reaction at B is 89.66 N\n"
+ ]
+ }
+ ],
+ "prompt_number": 10
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 4.12,Page No.81"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "from math import sin, cos, tan, radians, pi\n",
+ "import numpy as np\n",
+ "\n",
+ "#Declaration Of Variables\n",
+ "W=100 #N #Weight of roller\n",
+ "F=200 #N #Horizontal Force\n",
+ "L_AB=10 #cm #LEngth of bar AB\n",
+ "L_BC=5 #cm #radius of roller\n",
+ "\n",
+ "#Calculations\n",
+ "\n",
+ "theta=np.arcsin(L_BC*L_AB**-1)*(pi**-1*180)\n",
+ "\n",
+ "#LEt R_C be the reaction at c\n",
+ "\n",
+ "#sum of Forces along x-axis\n",
+ "F_AB=F*cos(theta*pi*180**-1)**-1 #N\n",
+ "\n",
+ "#sum of forces along y-axis\n",
+ "R_C=W+F_AB*sin(theta*pi*180**-1)\n",
+ "\n",
+ "#Result\n",
+ "print\"Force in bar AB is\",round(F_AB,2),\"N\"\n",
+ "print\"Reaction at C is\",round(R_C,2),\"N\""
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "Force in bar AB is 230.94 N\n",
+ "Reaction at C is 215.47 N\n"
+ ]
+ }
+ ],
+ "prompt_number": 11
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 4.14,Page No.84"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "from math import sin, cos, tan, radians, pi\n",
+ "\n",
+ "#Declaration Of Variables\n",
+ "W=1000 #N #Weight of rollers\n",
+ "theta=30 #Degree #Angle made by groove\n",
+ "\n",
+ "#Calculations\n",
+ "\n",
+ "#LEt R_A,R_B,R_C,R_D be the reactions at A,B,C,D respectively\n",
+ "\n",
+ "#Roller-2\n",
+ "R_D=W*sin(90*pi*180**-1)*sin(150*pi*180**-1) #N\n",
+ "R_A=W*sin(90*pi*180**-1)*sin(120*pi*180**-1) #N\n",
+ "\n",
+ "#ROller-1\n",
+ "R_B=(W+R_D*sin(theta*pi*180**-1))*sin(60*pi*180**-1)**-1 #N\n",
+ "R_C=R_B*cos(60*pi*180**-1)+R_D*cos(theta*pi*180**-1)\n",
+ "\n",
+ "#Result\n",
+ "print\"Reactions at A:R_A\",round(R_A,2),\"N\"\n",
+ "print\" B:R_B\",round(R_B,2),\"N\"\n",
+ "print\" C:R_C\",round(R_C,2),\"N\""
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "Reactions at A:R_A 866.03 N\n",
+ " B:R_B 1443.38 N\n",
+ " C:R_C 1154.7 N\n"
+ ]
+ }
+ ],
+ "prompt_number": 12
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 4.15,Page No.85"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "from math import sin, cos, tan, radians, pi\n",
+ "import numpy as np\n",
+ "\n",
+ "#Declaration Of Variables\n",
+ "W=1000 #N #Weight of each sphere\n",
+ "L_AF=L_BF=L_FD=L_DE=L_CE=25 #cm\n",
+ "L=90 #Width of channel\n",
+ "L_FG=40 #cm\n",
+ "L_EF=L_FD+L_DE #cm\n",
+ "\n",
+ "#Calculations\n",
+ "\n",
+ "theta=np.arcsin(L_FG*L_EF**-1)*(180*pi**-1) #Degrees\n",
+ "\n",
+ "#LEt R_A,R_B,R_C,R_D be the reactions at A,B,C,D respectively\n",
+ "\n",
+ "#Roller-2\n",
+ "R_D=W*(cos(theta*pi*180**-1))**-1 #N\n",
+ "R_C=R_D*sin(theta*pi*180**-1) #N\n",
+ "\n",
+ "#Roller-1\n",
+ "R_A=R_D*sin(theta*pi*180**-1) #N\n",
+ "R_B=R_D*cos(theta*pi*180**-1)+W #N\n",
+ "\n",
+ "#Result\n",
+ "print\"Reactions at A:R_A\",round(R_A,2),\"N\"\n",
+ "print\" B:R_B\",round(R_B,2),\"N\"\n",
+ "print\" C:R_C\",round(R_C,2),\"N\""
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "Reactions at A:R_A 1333.33 N\n",
+ " B:R_B 2000.0 N\n",
+ " C:R_C 1333.33 N\n"
+ ]
+ }
+ ],
+ "prompt_number": 13
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 4.16,Page No.87"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "from math import sin, cos, tan, radians, pi\n",
+ "import numpy as np\n",
+ "\n",
+ "#Declaration Of Variables\n",
+ "W=1000 #N #Weight of 2 circular cyclinders\n",
+ "L_AF=L_FC=L_CG=L_GB=15 #cm\n",
+ "W2=2000 #N #Weight of 3rd cyclinder\n",
+ "r2=15 #cm\n",
+ "L_AB=40 #cm\n",
+ "L_AH=L_HB=20 #cm\n",
+ "\n",
+ "#Calculations\n",
+ "\n",
+ "theta=np.arcsin(L_AH*(L_AF+L_FC)**-1)*(pi**-1*180) #Degrees\n",
+ "\n",
+ "#Let R_G,R_F,R_D,R_E be the reactions at G,F,D,E \n",
+ "\n",
+ "R_F=W2*(2*cos(theta*pi*180**-1))**-1 #N\n",
+ "R_G=R_F #N\n",
+ "\n",
+ "#Roller-1\n",
+ "\n",
+ "R_D=W+R_F*cos(theta*pi*180**-1) #N\n",
+ "S=R_F*sin(theta*pi*180**-1) #N\n",
+ "\n",
+ "#Roller-2\n",
+ "\n",
+ "R_E=W+R_G*cos(41.81*pi*180**-1) #N\n",
+ "\n",
+ "#Result\n",
+ "print\"Reaction at E is \",round(R_E,2),\"N\"\n",
+ "print\"Reactions at D is\",round(R_D,2),\"N\"\n",
+ "print\"Force S in the string is \",round(S,2),\"N\""
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "Reaction at E is 2000.0 N\n",
+ "Reactions at D is 2000.0 N\n",
+ "Force S in the string is 894.43 N\n"
+ ]
+ }
+ ],
+ "prompt_number": 14
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 4.17,Page No.88"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "from math import sin, cos, tan, radians, pi\n",
+ "import numpy as np\n",
+ "\n",
+ "#Declaration Of Variables\n",
+ "L_OB=L_OC=L_OA=40 #cm #Radius of roller\n",
+ "h=20 #cm #Height of block\n",
+ "L_OD=L_OA-h #cm #Length \n",
+ "W=3000 #N #Weight of roller\n",
+ "\n",
+ "#Calculations\n",
+ "\n",
+ "#LEt R_B be the reaction at B\n",
+ "L_BD=((L_OB**2-L_OD**2)**0.5) #cm\n",
+ "theta=np.arctan(L_BD*(L_OC+L_OD)**-1)*(180*pi**-1) #degree\n",
+ "\n",
+ "#Sum of all vertical Forces\n",
+ "R_B=W*(cos(theta*pi*180**-1))**-1 #N\n",
+ "\n",
+ "#Sum of all horizontal Forces\n",
+ "P=R_B*sin(theta*pi*180**-1) #N\n",
+ "\n",
+ "#Result\n",
+ "print\"Reaction at B is\",round(R_B,2),\"N\"\n",
+ "print\"Horizontal Reaction at C is\",round(P,2),\"N\""
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "Reaction at B is 3464.1 N\n",
+ "Horizontal Reaction at C is 1732.05 N\n"
+ ]
+ }
+ ],
+ "prompt_number": 15
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 4.18,Page No.89"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "from math import sin, cos, tan, radians, pi\n",
+ "import numpy as np\n",
+ "\n",
+ "#Declaration Of Variables\n",
+ "#Declaration Of Variables\n",
+ "L_OB=L_OC=L_OA=40 #cm #Radius of roller\n",
+ "h=20 #cm #Height of block\n",
+ "L_OD=L_OA-h #cm #Length \n",
+ "W=3000 #N #Weight of roller\n",
+ "\n",
+ "#Calculations\n",
+ "\n",
+ "theta=np.arccos(L_OD*L_OB**-1)*(pi**-1*180) #N\n",
+ "\n",
+ "R_B=W*(cos(theta*pi*180**-1))**-1 #N\n",
+ "P=R_B*sin(theta*pi*180**-1) #N\n",
+ "\n",
+ "#LEt P_min be the least Force applied\n",
+ "#let alpha be the angle made by least force\n",
+ "#P_min=W*L_BD*L_BC**-1\n",
+ "\n",
+ "L_BD=((L_OB**2-L_OD**2)**0.5) #cm\n",
+ "\n",
+ "#But L_BC=L_BO*sin(alpha) \n",
+ "\n",
+ "#Force P will be min when sin(Alpha) is max.\n",
+ "#thus sin(alpha)=90 or sin(alpha)=0. therefore sub value in above equation,we get min Force\n",
+ "#LEt P_min be the Least Force to be applied\n",
+ "P_min=W*L_BD*(L_OB*1)**-1 #N\n",
+ "\n",
+ "#Direction of least force is right angle to L_BO\n",
+ "\n",
+ "#Result\n",
+ "print\"Minimum least force is\",round(P_min,2),\"N\"\n",
+ "print\"Magnitude of force applied horizontally at centre of roller\",round(P,2),\"N\""
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "Minimum least force is 2598.08 N\n",
+ "Magnitude of force applied horizontally at centre of roller 5196.15 N\n"
+ ]
+ }
+ ],
+ "prompt_number": 16
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 4.19,Page No.91"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "from math import sin, cos, tan, radians, pi\n",
+ "import numpy as np\n",
+ "\n",
+ "#Declaration Of Variables\n",
+ "L_BC=25 #cm \n",
+ "L_AB=40 #cm\n",
+ "\n",
+ "#Calculations\n",
+ "\n",
+ "#Let alpha be the angle made by force F so that body will be in equilibrium\n",
+ "#Theta is angle made by R_A with horizontal,so Force F has to make same angle with horizontal\n",
+ "alpha=np.arctan(L_AB*L_BC**-1)*(pi**-1*180) #degrees\n",
+ "theta=alpha\n",
+ "\n",
+ "#Result\n",
+ "print\"Angle theta is\",round(theta,2),\"Degrees\""
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "Angle theta is 57.99 Degrees\n"
+ ]
+ }
+ ],
+ "prompt_number": 17
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 4.20,Page No.91"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "from math import sin, cos, tan, radians, pi\n",
+ "\n",
+ "#Declaration Of Variables\n",
+ "L_AB=1.6 #m\n",
+ "L_BD=1.2 #m\n",
+ "L_BC=0.8 #m\n",
+ "L_CD=0.4 #m\n",
+ "F_C=200 #N #Force t C\n",
+ "theta=60 #Degrees\n",
+ "\n",
+ "#Calculations\n",
+ "\n",
+ "\n",
+ "\n",
+ "#Sum of all forces in x-direction\n",
+ "R_Bx=F_C #N\n",
+ "\n",
+ "L_BD2=L_BD*sin(theta*pi*180**-1) #m\n",
+ "L_DD=L_BD*cos(theta*pi*180**-1) #m\n",
+ "L_BC2=sin(theta*pi*180**-1)*L_BC #m\n",
+ "\n",
+ "R_D=F_C*L_BC2*L_DD**-1 #N\n",
+ "R_By=R_D\n",
+ "\n",
+ "#Resultant reaction at B\n",
+ "R_B=(R_Bx**2+R_By**2)**0.5 #N\n",
+ "\n",
+ "#Sum of moments at A\n",
+ "M_A=R_By*L_AB\n",
+ "\n",
+ "\n",
+ "#Result\n",
+ "print\"Couple to be apllied to hold the system is\",round(M_A,2),\"N\"\n",
+ "print\"Magnitude of pin reaction at B\",round(R_B,2),\"N\""
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "Couple to be apllied to hold the system is 369.5 N\n",
+ "Magnitude of pin reaction at B 305.51 N\n"
+ ]
+ }
+ ],
+ "prompt_number": 18
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 4.21,Page No.93"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "from math import sin, cos, tan, radians, pi\n",
+ "import numpy as np\n",
+ "\n",
+ "#Declaration Of Variables\n",
+ "W=2000 #N #Weight of chain\n",
+ "L_AB=2 #m\n",
+ "F_B=320 #N\n",
+ "\n",
+ "#Calculations\n",
+ "\n",
+ "#By LAmi's theorem\n",
+ "#F_A*sin(90)=W*sin(180-theta)**-1=F_B*sin(90+theta)**-1\n",
+ "#But sin(180-theta)=sin(theta),sin(90+theta)=cos(theta)\n",
+ "#Tan(theta)=W*F_B**-1\n",
+ "theta=np.arctan(W*F_B**-1)*(180*pi**-1) #Degrees\n",
+ "\n",
+ "F_A=W*(sin(theta*pi*180**-1))**-1 #N\n",
+ "#Let x be the lateral distance\n",
+ "x=cos(theta*pi*180**-1)*2\n",
+ "\n",
+ "#Result\n",
+ "print\"Force in the chain is\",round(F_A,2),\"N\"\n",
+ "print\"Horizontal displacement is\",round(x,2),\"m\""
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "Force in the chain is 2025.44 N\n",
+ "Horizontal displacement is 0.32 m\n"
+ ]
+ }
+ ],
+ "prompt_number": 15
+ }
+ ],
+ "metadata": {}
+ }
+ ]
+}
\ No newline at end of file diff --git a/Engineering_Mechanics/chapter_5.ipynb b/Engineering_Mechanics/chapter_5.ipynb new file mode 100644 index 00000000..1b989f4f --- /dev/null +++ b/Engineering_Mechanics/chapter_5.ipynb @@ -0,0 +1,851 @@ +{
+ "metadata": {
+ "name": "chapter_5.ipynb"
+ },
+ "nbformat": 3,
+ "nbformat_minor": 0,
+ "worksheets": [
+ {
+ "cells": [
+ {
+ "cell_type": "heading",
+ "level": 1,
+ "metadata": {},
+ "source": [
+ "Chapter 5:Support Reactions"
+ ]
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 5.1,Page No.101"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "\n",
+ "#Declaration Of Variables\n",
+ "\n",
+ "#Lengths\n",
+ "L=6 #m\n",
+ "L_AC=2 #m\n",
+ "L_AD=4 #m\n",
+ "L_CD=L_DB=2 #m\n",
+ "\n",
+ "#Forces\n",
+ "F_C=3 #KN\n",
+ "F_D=6 #KN\n",
+ "\n",
+ "#Calculations\n",
+ "\n",
+ "#LEt R_A and R_B be the reactions at A & B respectively\n",
+ "#R_A+R_B=F_C+F_D\n",
+ "#Taking Moment at pt A\n",
+ "R_B=(F_D*(L_AC+L_CD)+F_C*L_AC)*L**-1 #KN\n",
+ "R_A=(F_C+F_D)-R_B #KN\n",
+ "\n",
+ "#Result\n",
+ "print\"Reaction at A is\",round(R_A,2),\"KN\"\n",
+ "print\"Reaction at B is\",round(R_B,2),\"KN\""
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "Reaction at A is 4.0 KN\n",
+ "Reaction at B is 5.0 KN\n"
+ ]
+ }
+ ],
+ "prompt_number": 1
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 5.2,Page No102 "
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "\n",
+ "#Declaration Of Variables\n",
+ "\n",
+ "#Lengths\n",
+ "L_AC=6 #m\n",
+ "L_AB=9 #m\n",
+ "\n",
+ "#Load\n",
+ "w=10 #KN/m #u.d.l\n",
+ "\n",
+ "#Calculations\n",
+ "\n",
+ "#LEt R_A and R_B be the reactions at A & B respectively\n",
+ "#R_A+R_B=w*L_AC\n",
+ "#Taking Moment at pt A\n",
+ "R_B=w*L_AC*L_AC*2**-1*L_AB**-1 #KN\n",
+ "R_A=w*L_AC-R_B\n",
+ "\n",
+ "#Result\n",
+ "print\"Reaction at A is\",round(R_A,2),\"KN\"\n",
+ "print\"Reaction at B is\",round(R_B,2),\"KN\""
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "Reaction at A is 40.0 KN\n",
+ "Reaction at B is 20.0 KN\n"
+ ]
+ }
+ ],
+ "prompt_number": 2
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 5.3,Page No.103"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "\n",
+ "#Declaration Of Variables\n",
+ "\n",
+ "#Lengths\n",
+ "L_AC=2 #m\n",
+ "L_CD=L_DB=4 #m\n",
+ "L=10 #m #span\n",
+ "\n",
+ "#Forces & Loads\n",
+ "F_C=50 #KN\n",
+ "F_D=40 #KN\n",
+ "w=10 #KN/m #u.d.l\n",
+ "\n",
+ "#Calculations\n",
+ "\n",
+ "#LEt R_A and R_B be the reactions at A & B respectively\n",
+ "#R_A+R_B=w*L_CD-F_C-F_D\n",
+ "#Taking Moment at pt A\n",
+ "R_B=(F_C*L_AC+F_D*(L_AC+L_CD)+w*L_CD*(L_CD*2**-1+L_AC))*L**-1 #KN\n",
+ "R_A=w*L_CD+F_C+F_D-R_B #KN\n",
+ "\n",
+ "#Result\n",
+ "print\"Reaction at A is\",round(R_A,2),\"KN\"\n",
+ "print\"Reaction at B is\",round(R_B,2),\"KN\""
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "Reaction at A is 80.0 KN\n",
+ "Reaction at B is 50.0 KN\n"
+ ]
+ }
+ ],
+ "prompt_number": 3
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 5.4,Page No.103 "
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "\n",
+ "#Declaration Of Variables\n",
+ "\n",
+ "#Length\n",
+ "L_AB=9 #m\n",
+ "\n",
+ "#Load\n",
+ "w=900 #N/m #u.v.l\n",
+ "\n",
+ "#Calculations\n",
+ "\n",
+ "#LEt R_A and R_B be the reactions at A & B respectively\n",
+ "#R_A+R_B=w*L_AB*2**-1\n",
+ "#Taking Moment at pt A\n",
+ "R_B=w*L_AB*2**-1*2*3**-1*L_AB*L_AB**-1 #KN\n",
+ "R_A=w*L_AB*2**-1-R_B\n",
+ "\n",
+ "#Result\n",
+ "print\"Reaction at A is\",round(R_A,2),\"KN\"\n",
+ "print\"Reaction at B is\",round(R_B,2),\"KN\""
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "Reaction at A is 1350.0 KN\n",
+ "Reaction at B is 2700.0 KN\n"
+ ]
+ }
+ ],
+ "prompt_number": 4
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 5.5,Page No.104 "
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "\n",
+ "#Declaration Of Variables\n",
+ "\n",
+ "#Length\n",
+ "L_AB=5 #m\n",
+ "\n",
+ "#Loads\n",
+ "w1=800 #N/m #At A\n",
+ "w2=1600 #N/m #At B\n",
+ "\n",
+ "#Calculations\n",
+ "\n",
+ "#LEt R_A and R_B be the reactions at A & B respectively\n",
+ "#R_A+R_B=w2*2**-1*L_AB*2**-1+w1*L_AB\n",
+ "#Taking Moment at pt A\n",
+ "R_B=(w1*L_AB*L_AB*2**-1+w2*2**-1*L_AB*2**-1*2*3**-1*L_AB)*L_AB**-1 #KN\n",
+ "R_A=w2*2**-1*L_AB*2**-1+w1*L_AB-R_B\n",
+ "\n",
+ "#Result\n",
+ "print\"Reaction at A is\",round(R_A,2),\"KN\"\n",
+ "print\"Reaction at B is\",round(R_B,2),\"KN\""
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "Reaction at A is 2666.67 KN\n",
+ "Reaction at B is 3333.33 KN\n"
+ ]
+ }
+ ],
+ "prompt_number": 5
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 5.6,Page No.105 "
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "\n",
+ "#Declaration Of Variables\n",
+ "\n",
+ "#LEt the ends of beams be C and D respectively\n",
+ "#Lengths\n",
+ "L_CA=3 #m\n",
+ "L_AB=8 #m\n",
+ "L_BD=2 #m\n",
+ "\n",
+ "#Let the Force 2000 acting be E\n",
+ "L_AE=5 #m\n",
+ "L_EB=3 #m\n",
+ "\n",
+ "#Forces\n",
+ "F_C=800 #N\n",
+ "F_E=2000 #N\n",
+ "F_D=1000 #N\n",
+ "\n",
+ "#Calculations\n",
+ "\n",
+ "#LEt R_A and R_B be the reactions at A & B respectively\n",
+ "#R_A+R_B=(F_C+F_E+F_D)\n",
+ "#Taking Moment at pt A\n",
+ "R_B=(F_E*L_AE+F_D*(L_BD+L_AB)-F_C*L_CA)*L_AB**-1 #KN\n",
+ "R_A=(F_C+F_E+F_D)-R_B\n",
+ "\n",
+ "#Result\n",
+ "print\"Reaction at A is\",round(R_A,2),\"KN\"\n",
+ "print\"Reaction at B is\",round(R_B,2),\"KN\""
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "Reaction at A is 1600.0 KN\n",
+ "Reaction at B is 2200.0 KN\n"
+ ]
+ }
+ ],
+ "prompt_number": 6
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 5.7,Page No.106 "
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "\n",
+ "#Declaration Of Variables\n",
+ "\n",
+ "#Lengths\n",
+ "L_AB=4 #m\n",
+ "L_BC=2 #m\n",
+ "L_AC=6 #m\n",
+ "\n",
+ "#Loads\n",
+ "F_C=2 #KN\n",
+ "w=2 #KN/m #u.d.l\n",
+ "\n",
+ "#Calculations\n",
+ "\n",
+ "#LEt R_A and R_B be the reactions at A & B respectively\n",
+ "#R_A+R_B=w*L_AC\n",
+ "#Taking Moment at pt A\n",
+ "R_B=(F_C*L_AC+w*L_AC*L_AC*2**-1)*L_AB**-1 #KN\n",
+ "R_A=w*L_AC-R_B+F_C #KN\n",
+ "\n",
+ "#Result\n",
+ "print\"Reaction at A is\",round(R_A,2),\"KN\"\n",
+ "print\"Reaction at B is\",round(R_B,2),\"KN\""
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "Reaction at A is 2.0 KN\n",
+ "Reaction at B is 12.0 KN\n"
+ ]
+ }
+ ],
+ "prompt_number": 7
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 5.8,Page No.106 "
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "from math import sin, cos, tan, radians, pi\n",
+ "\n",
+ "#Declaration Of Variables\n",
+ "\n",
+ "#lengths\n",
+ "L_AC=20 #cm\n",
+ "L_CD=L_EB=40 #cm\n",
+ "L_DE=70 #cm\n",
+ "L_AB=L_AC+L_CD+L_EB+L_DE #cm\n",
+ "\n",
+ "#Forces\n",
+ "F_C=50 #N\n",
+ "\n",
+ "#At pt D\n",
+ "F_D1=20*sin(pi*180**-1*60) #N\n",
+ "F_D2=20*cos(pi*180**-1*60) #N\n",
+ "\n",
+ "#At pt E\n",
+ "F_E1=30*sin(pi*180**-1*45) #N\n",
+ "F_E2=30*cos(pi*180**-1*45) #N\n",
+ "\n",
+ "#At pt B\n",
+ "F_B1=15*sin(pi*180**-1*80) #N\n",
+ "F_B2=15*cos(pi*180**-1*80) #N\n",
+ "\n",
+ "#Calculations\n",
+ "\n",
+ "#LEt R and R_B be the reactions at A & B respectively\n",
+ "#R_A+R_B=F_C+F_D1+F_E1+F_B1\n",
+ "#Taking Moment at pt A\n",
+ "R_B=(F_C*L_AC+F_D1*(L_AC+L_CD)+F_E1*(L_AC+L_CD+L_DE)+F_B1*(L_AC+L_CD+L_DE+L_EB))*L_AB**-1\n",
+ "\n",
+ "#Vertical component of A\n",
+ "R_AY=F_C+F_D1+F_E1+F_B1-R_B #N\n",
+ "\n",
+ "#Now horizontal component of A\n",
+ "R_AX=-(F_D2-F_E2+F_B2) #N\n",
+ "#the direction of R_AX will be towards left of A\n",
+ "\n",
+ "#Reaction At A\n",
+ "R=(R_AY**2+R_AX**2)**0.5 #N\n",
+ "\n",
+ "#Result\n",
+ "print\"Reaction at A is:R\",round(R,2),\"N\"\n",
+ "print\"Reaction at B is\",round(R_B,2),\"N\""
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "Reaction at A is:R 60.93 N\n",
+ "Reaction at B is 42.99 N\n"
+ ]
+ }
+ ],
+ "prompt_number": 1
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 5.9,Page No.108"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "from math import sin, cos, tan, radians, pi\n",
+ "\n",
+ "#Declaration Of Variables\n",
+ "\n",
+ "#Lengths\n",
+ "L_AC=2 #m\n",
+ "L_CD=2 #m\n",
+ "L_DB=2 #m\n",
+ "L=6 #m\n",
+ "\n",
+ "#Loads\n",
+ "w=1.5 #KN/m\n",
+ "F_C=5 #KN\n",
+ "\n",
+ "#At pt D\n",
+ "F_D1=4*sin(pi*180**-1*(180-135))\n",
+ "F_D2=4*sin(pi*180**-1*(180-135))\n",
+ "\n",
+ "#Calculations\n",
+ "\n",
+ "#LEt R and R_B be the reactions at A & B respectively\n",
+ "#R_A+R_B=F_C+F_D1+F_E1+F_B1\n",
+ "#Taking Moment at pt A\n",
+ "R_B=((F_C*L_AC)+w*L_CD*(L_CD*2**-1+L_AC)+F_D1*(L_AC+L_CD))*L**-1\n",
+ "\n",
+ "#Vertical component of A\n",
+ "R_AY=F_C+F_D1+w*L_AC-R_B #KN\n",
+ "\n",
+ "#Now horizontal component of A\n",
+ "R_AX=(F_D2) #KN\n",
+ "#the direction of R_AX will be towards left of A\n",
+ "\n",
+ "#Reaction At A\n",
+ "R=(R_AY**2+R_AX**2)**0.5 #KN\n",
+ "\n",
+ "\n",
+ "#Result\n",
+ "print\"Reaction at A is:R\",round(R,2),\"KN\"\n",
+ "print\"Reaction at B is\",round(R_B,2),\"KN\""
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "Reaction at A is:R 6.43 KN\n",
+ "Reaction at B is 5.05 KN\n"
+ ]
+ }
+ ],
+ "prompt_number": 2
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 5.10,Page No.110 "
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "from math import sin, cos, tan, radians, pi\n",
+ "\n",
+ "#Declaration Of Variables\n",
+ "\n",
+ "#Lengths\n",
+ "L=10 #m\n",
+ "L_AC=2.5 #m\n",
+ "L_CD=2.5 #m\n",
+ "L_DE=3 #m\n",
+ "L_EB=2 #m\n",
+ "\n",
+ "#Forces\n",
+ "F_C=4 #KN\n",
+ "\n",
+ "#At pt D\n",
+ "F_D1=5*sin(pi*180**-1*45)\n",
+ "F_D2=5*cos(pi*180**-1*45)\n",
+ "\n",
+ "F_E=5 #KN\n",
+ "\n",
+ "#Calculations\n",
+ "\n",
+ "#Let R and R_B be the reactions at A & B respectively\n",
+ "\n",
+ "#Resolving R_B into R_B1 & R_B2\n",
+ "#R_B1*sin(30*pi*180**-1)\n",
+ "#R_B2*cos(30*pi*180**-1)\n",
+ "\n",
+ "#R_A+R_B=F_C+F_D1+F_E\n",
+ "#Taking Moment at pt A\n",
+ "R_B1=(F_C*L_AC+F_D1*(L_AC+L_CD)+F_E*(L_AC+L_CD+L_DE))*(L*cos(pi*180**-1*30))**-1 #KN\n",
+ "R_B2=R_B1*sin(30*pi*180**-1) #KN\n",
+ "\n",
+ "#Vertical component of A\n",
+ "R_AY=(F_C+F_D1+F_E-R_B1*cos(30*pi*180**-1)) #KN\n",
+ "\n",
+ "#Now horizontal component of A\n",
+ "R_AX=(-F_D2+R_B2) #KN\n",
+ "#the direction of R_AX will be towards left of A\n",
+ "\n",
+ "#Reaction At A\n",
+ "R=(R_AY**2+R_AX**2)**0.5 #KN\n",
+ "\n",
+ "\n",
+ "#Result\n",
+ "print\"Reaction at A is:R\",round(R,2),\"KN\"\n",
+ "print\"Reaction at B is\",round(R_B1,2),\"KN\""
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "Reaction at A is:R 5.78 KN\n",
+ "Reaction at B is 7.81 KN\n"
+ ]
+ }
+ ],
+ "prompt_number": 3
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 5.11,Page No.111"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "from math import sin, cos, tan, radians, pi\n",
+ "\n",
+ "#Declaration Of Variables\n",
+ "\n",
+ "#Lengths\n",
+ "L_AC=L_CD=5 #m\n",
+ "L_AD=10 #m\n",
+ "\n",
+ "#Forces\n",
+ "F_C=F_D=500 #N\n",
+ "\n",
+ "#Calculations\n",
+ "\n",
+ "#LEt R_A & R_B be the reactions at pt A & B respectively\n",
+ "\n",
+ "#Now resolving Forces at pt C & D \n",
+ "F_C1=F_D1=F_C*sin(30*pi*180**-1) #N\n",
+ "F_C2=F_D2=F_D*cos(30*pi*180**-1) #N\n",
+ "\n",
+ "#Now taking Moment at pt A\n",
+ "#But In triangle BDA,\n",
+ "#cos(30*pi*180**-1)=L_AD*L_AB**-1\n",
+ "#After Further simplifying we get\n",
+ "L_AB=L_AD*(cos(30*pi*180**-1))**-1 #m\n",
+ "\n",
+ "R_B=(F_C*L_AC+F_D*L_AD)*L_AB**-1 #N\n",
+ "\n",
+ "#Now sum of components parallel to inclined surface AB\n",
+ "R_AH=F_C1+F_D1 #N\n",
+ "\n",
+ "#Now sum of forces perpendicular to inclined surface AB\n",
+ "R_AV=F_C2+F_D2-R_B #N\n",
+ "\n",
+ "#Reaction At A\n",
+ "R=(R_AV**2+R_AH**2)**0.5 #N\n",
+ "\n",
+ "#Result\n",
+ "print\"Reaction at A is\",round(R,2),\"KN\"\n",
+ "print\"Reaction at B is\",round(R_B,2),\"KN\""
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "Reaction at A is 544.86 KN\n",
+ "Reaction at B is 649.52 KN\n"
+ ]
+ }
+ ],
+ "prompt_number": 11
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 5.12,Page No.113 "
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "from math import sin, cos, tan, radians, pi\n",
+ "\n",
+ "#Declaration Of Variables\n",
+ "\n",
+ "#Lengths\n",
+ "L_AD=80*10**-2 #m\n",
+ "L_AE=L_EF=L_FB=60*10**-2 #m\n",
+ "L_AC=L_CD=40*10**-2 #cm\n",
+ "\n",
+ "#Forces\n",
+ "\n",
+ "#At pt D\n",
+ "F_D1=100*sin(pi*180**-1*30) #N\n",
+ "F_D2=100*cos(pi*180**-1*30) #N\n",
+ "\n",
+ "#At pt C\n",
+ "F_C1=70*sin(pi*180**-1*45) #N\n",
+ "F_C2=70*cos(pi*180**-1*45) #N\n",
+ "\n",
+ "w=250 #N/m #u.d.l\n",
+ "\n",
+ "#Calculations\n",
+ "\n",
+ "#Let R_A and R_B be the reactions at A & B respectively\n",
+ "#Resolving R_B into R_B1 & R_B2\n",
+ "#Taking Moment at pt A\n",
+ "R_B=-(-F_D2*L_AD+F_C2*L_AC-w*L_EF*(L_EF*2**-1+L_AE))*(cos(20*pi*180**-1)*(L_AE+L_EF+L_FB))**-1 #N\n",
+ "\n",
+ "#Vertical component of A\n",
+ "R_AX=(-F_D2+F_C1+R_B*sin(20*pi*180**-1)) #N\n",
+ "\n",
+ "#Now horizontal component of A\n",
+ "R_AY=(-F_D1-F_C2-R_B*cos(20*pi*180**-1)+w*L_EF) #KN\n",
+ "\n",
+ "##Reaction At A\n",
+ "R=(R_AY**2+R_AX**2)**0.5 #KN\n",
+ "\n",
+ "\n",
+ "#Result\n",
+ "print\"The Reaction at supports of an L-bent is\",round(R,3),\"KN\""
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "The Reaction at supports of an L-bent is 51.988 KN\n"
+ ]
+ }
+ ],
+ "prompt_number": 12
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 5.13,Page No.115 "
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "\n",
+ "#Declaration Of Variables\n",
+ "\n",
+ "#lengths\n",
+ "L_AC=2 #m\n",
+ "L_CD=3 #m\n",
+ "L_DB=2 #m\n",
+ "L=7 #m\n",
+ "\n",
+ "#Loads\n",
+ "w=4 #KN/m\n",
+ "m1=4 #KN/m #moment at pt C\n",
+ "m2=8 #KN/m #moment at pt D\n",
+ "\n",
+ "#Calculations\n",
+ "\n",
+ "#Let R_A & R_B be the reactions at pt a nd B respectively\n",
+ "#R_A+R_B=w*L_CD*2**-1\n",
+ "#Taking moment at pt A\n",
+ "R_B=(w*L_CD*2**-1*(2*3**-1*L_CD+L_AC)+m1-m2)*L**-1\n",
+ "R_A=w*L_CD*2**-1-R_B\n",
+ "\n",
+ "#Result\n",
+ "print\"Reaction at A is\",round(R_A,2),\"KN\"\n",
+ "print\"Reaction at B is\",round(R_B,2),\"KN\""
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "Reaction at A is 3.14 KN\n",
+ "Reaction at B is 2.86 KN\n"
+ ]
+ }
+ ],
+ "prompt_number": 13
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 5.14,Page No.116 "
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "from math import sin, cos, tan, radians, pi\n",
+ "\n",
+ "#Declaration Of Variables\n",
+ "\n",
+ "#Lengths\n",
+ "L_AC=L_CD=L_DE=L_EB=2 #m\n",
+ "L=8 #M\n",
+ "\n",
+ "#Forces\n",
+ "#At pt C\n",
+ "F_C1=40*sin(pi*180**-1*60) #KN\n",
+ "F_C2=40*cos(pi*180**-1*60) #KN\n",
+ "\n",
+ "#At pt E\n",
+ "F_E1=50*sin(pi*180**-1*60) #KN\n",
+ "F_E2=50*cos(pi*180**-1*60) #KN\n",
+ "\n",
+ "F_D=80 #KN\n",
+ "w=20 #KN/m\n",
+ "\n",
+ "#Calculations\n",
+ "\n",
+ "#LEt R_A and R_B be the reactions at A & B respectively\n",
+ "#Taking Moment at pt A\n",
+ "R_B=(F_C1*L_AC+w*L_CD*(L_CD*2**-1+L_AC)+F_D*(L_AC+L_CD)+F_E1*(L_AC+L_CD+L_DE))*(L*cos(30*pi*180**-1))**-1\n",
+ "R_B2=R_B*sin(30*pi*180**-1)\n",
+ "\n",
+ "#Vertical component of A\n",
+ "R_AY=(F_C1+w*L_CD+F_D+F_E1-R_B*cos(30*pi*180**-1)) #KN\n",
+ "\n",
+ "#Now horizontal component of A\n",
+ "R_AX=(-F_C2+F_E2+R_B2) #KN\n",
+ "#the direction of R_AX will be towards left of A\n",
+ "\n",
+ "#Reaction At A\n",
+ "R=(R_AY**2+R_AX**2)**0.5 #KN\n",
+ "\n",
+ "\n",
+ "#Result\n",
+ "print\"Reaction at A is:R\",round(R,2),\"KN\"\n",
+ "print\"Reaction at B is\",round(R_B,2),\"KN\""
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "Reaction at A is:R 118.43 KN\n",
+ "Reaction at B is 111.01 KN\n"
+ ]
+ }
+ ],
+ "prompt_number": 14
+ }
+ ],
+ "metadata": {}
+ }
+ ]
+}
\ No newline at end of file diff --git a/Engineering_Mechanics/chapter_6.ipynb b/Engineering_Mechanics/chapter_6.ipynb new file mode 100644 index 00000000..5cd8e15f --- /dev/null +++ b/Engineering_Mechanics/chapter_6.ipynb @@ -0,0 +1,1118 @@ +{
+ "metadata": {
+ "name": "chapter_6.ipynb"
+ },
+ "nbformat": 3,
+ "nbformat_minor": 0,
+ "worksheets": [
+ {
+ "cells": [
+ {
+ "cell_type": "heading",
+ "level": 1,
+ "metadata": {},
+ "source": [
+ "Chapter 6:Analysis Of Perfect Frames"
+ ]
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 6.1,Page No.124"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "from math import sin, cos, tan, radians, pi\n",
+ "\n",
+ "#Initilization of Variables\n",
+ "\n",
+ "F_A=20 #KN #Force at A\n",
+ "theta=60 #Degrees\n",
+ "alpha=30 #Degrees\n",
+ "L_BC=5 #m\n",
+ "\n",
+ "#Calculations\n",
+ "\n",
+ "#Length AB\n",
+ "L_AB=L_BC*cos(theta*pi*180**-1) #m\n",
+ " \n",
+ "#Distance of line of action \n",
+ "x=1.25 #m\n",
+ "\n",
+ "#Reactions\n",
+ "R_C=F_A*x*L_BC**-1 #KN\n",
+ "R_B=F_A-R_C #KN\n",
+ "\n",
+ "#Force in AB & BC\n",
+ "F_AB=R_B*(sin(theta*pi*180**-1))**-1 #KN\n",
+ "F_BC=F_AB*cos(theta*pi*180**-1) #KN\n",
+ "\n",
+ "#Force in AC & BC\n",
+ "F_AC=R_C*(sin(alpha*pi*180**-1))**-1 #KN\n",
+ "\n",
+ "#Result\n",
+ "print\"FOrces in members are:F_AB\",round(F_AB,2),\"KN\"\n",
+ "print\" :F_BC\",round(F_BC,2),\"KN\"\n",
+ "print\" :F_AC\",round(F_AC,2),\"KN\"\n",
+ "print\" :F_BC\",round(F_BC,2),\"KN\""
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "FOrces in members are:F_AB 17.32 KN\n",
+ " :F_BC 8.66 KN\n",
+ " :F_AC 10.0 KN\n",
+ " :F_BC 8.66 KN\n"
+ ]
+ }
+ ],
+ "prompt_number": 18
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 6.2,Page No.125"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "from math import sin, cos, tan, radians, pi\n",
+ "\n",
+ "#Initilization of Variables\n",
+ "\n",
+ "F_D=1 #KN\n",
+ "L_AD=5 #m #Length AD\n",
+ "L_AB=7.5 #m #Length AB\n",
+ "theta=60 #degrees\n",
+ "alpha=30 #Degrees\n",
+ "\n",
+ "#Calculations\n",
+ "\n",
+ "#REactions\n",
+ "R_B=L_AD*L_AB**-1 #KN\n",
+ "R_A=F_D-R_B #KN\n",
+ "\n",
+ "#Forces\n",
+ "\n",
+ "F_AC=R_A*(sin(alpha*pi*180**-1))**-1 #KN\n",
+ "F_AD=F_AC*cos(alpha*pi*180**-1) #KN\n",
+ "F_BC=R_B*(sin(alpha*pi*180**-1))**-1 #KN\n",
+ "F_BD=F_BC*(cos(alpha*pi*180**-1)) #KN\n",
+ "F_CD=1*(sin(theta*pi*180**-1))**-1\n",
+ "\n",
+ "#Result\n",
+ "print\"forces in members are:F_AC\",round(F_AC,2),\"KN\"\n",
+ "print\" :F_AD\",round(F_AD,2),\"KN\"\n",
+ "print\" :F_BC\",round(F_BC,2),\"KN\"\n",
+ "print\" :F_BD\",round(F_BD,2),\"KN\"\n",
+ "print\" :F_CD\",round(F_CD,2),\"KN\""
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "forces in members are:F_AC 0.67 KN\n",
+ " :F_AD 0.58 KN\n",
+ " :F_BC 1.33 KN\n",
+ " :F_BD 1.15 KN\n",
+ " :F_CD 1.15 KN\n"
+ ]
+ }
+ ],
+ "prompt_number": 19
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 6.3,Page No.127"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "from math import sin, cos, tan, radians, pi\n",
+ "\n",
+ "#Initilization of Variables\n",
+ "\n",
+ "L_AB=5 #m #Length AB\n",
+ "theta=60 #Degrees\n",
+ "alpha=30 #Degrees\n",
+ "F_D=10 #KN\n",
+ "F_E=12 #KN\n",
+ "\n",
+ "#Calculations\n",
+ "\n",
+ "#Length\n",
+ "L_AC=L_AD=L_AB*(cos(theta*pi*180**-1)) #m\n",
+ "\n",
+ "#Distance of line of action\n",
+ "x=1.25 #m\n",
+ "\n",
+ "L_BC=L_AB-L_AD #m\n",
+ "L_BE=L_BC*cos(alpha*pi*180**-1) #m\n",
+ "\n",
+ "#line of action \n",
+ "x2=1.875 #m\n",
+ "x3=3.125\n",
+ "\n",
+ "#Reactions\n",
+ "R_B=(F_D*x+F_E*x3)*L_AB**-1 #KN\n",
+ "R_A=(F_D+F_E)-R_B #KN\n",
+ "\n",
+ "#Forces\n",
+ "\n",
+ "F_AD=F_E*(sin(theta*pi*180**-1))**-1 #KN\n",
+ "F_AC=F_AD*cos(theta*pi*180**-1) #KN\n",
+ "F_BE=F_D*(sin(alpha*pi*180**-1))**-1 #KN\n",
+ "F_BC=F_BE*cos(alpha*pi*180**-1) #KN\n",
+ "\n",
+ "#After simplifying joint C we get\n",
+ "#F_CD=-F_CE\n",
+ "#after further simplifying\n",
+ "F_CE=20.784*2**-1 #KN\n",
+ "F_CD=F_CE #KN\n",
+ "F_ED=F_BE-(F_E*cos(theta*pi*180**-1)) #KN\n",
+ "\n",
+ "#Result\n",
+ "print\"forces in members are:F_AC\",round(F_AC,2),\"KN\"\n",
+ "print\" :F_AD\",round(F_AD,2),\"KN\"\n",
+ "print\" :F_BC\",round(F_BC,2),\"KN\"\n",
+ "print\" :F_BE\",round(F_BE,2),\"KN\"\n",
+ "print\" :F_CD\",round(F_CD,2),\"KN\"\n",
+ "print\" :F_CE\",round(F_CE,2),\"KN\"\n",
+ "print\" :F_ED\",round(F_ED,2),\"KN\""
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "forces in members are:F_AC 6.93 KN\n",
+ " :F_AD 13.86 KN\n",
+ " :F_BC 17.32 KN\n",
+ " :F_BE 20.0 KN\n",
+ " :F_CD 10.39 KN\n",
+ " :F_CE 10.39 KN\n",
+ " :F_ED 14.0 KN\n"
+ ]
+ }
+ ],
+ "prompt_number": 20
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 6.4,Page No.129"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "from math import sin, cos, tan, radians, pi\n",
+ "\n",
+ "#Initilization of Variables\n",
+ "\n",
+ "L_GH=L_AG=L_HB=3 #m\n",
+ "L_FB=L_EH=L_DG=L_AC=4 #m\n",
+ "L_AB=9 #m \n",
+ "F_G=9 #KN\n",
+ "F_H=12 #KN\n",
+ "\n",
+ "#Calculations\n",
+ "\n",
+ "#Reactions\n",
+ "R_B=(F_G*L_AG+F_H*(L_AG+L_GH))*L_AB**-1 #KN\n",
+ "R_A=(F_G+F_H)-R_B #KN\n",
+ "\n",
+ "#Joint C\n",
+ "#After resolving and simplifying we get\n",
+ "#cos(theta)=4*5**-1\n",
+ "#sin(theta)=3*4**-1\n",
+ "#Let cos(theta)=X\n",
+ "X=4*5**-1\n",
+ "Y=3*5**-1\n",
+ "\n",
+ "#Forces\n",
+ "\n",
+ "F_AC=R_A #KN\n",
+ "F_CG=R_A*X**-1 #KN\n",
+ "F_CD=F_CG*Y #KN\n",
+ "F_GD=-(F_G-F_CG*X)\n",
+ "F_GH=F_CG*Y \n",
+ "F_DH=1*X**-1 #KN\n",
+ "F_DE=F_GH+F_DH*Y\n",
+ "F_EF=F_DE #KN\n",
+ "F_HF=(F_H-F_GD)*X**-1\n",
+ "\n",
+ "\n",
+ "#Result\n",
+ "print\"Forces in members are:F_AC\",round(F_AC,2),\"KN\"\n",
+ "print\" :F_CG\",round(F_CG,2),\"KN\"\n",
+ "print\" :F_CD\",round(F_CD,2),\"KN\"\n",
+ "print\" :F_GD\",round(F_GD,2),\"KN\"\n",
+ "print\" :F_GH\",round(F_GH,2),\"KN\"\n",
+ "print\" :F_DH\",round(F_DH,2),\"KN\"\n",
+ "print\" :F_DE\",round(F_DE,2),\"KN\"\n",
+ "print\" :F_EF\",round(F_EF,2),\"KN\"\n",
+ "print\" :F_HF\",round(F_HF,2),\"KN\""
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "Forces in members are:F_AC 10.0 KN\n",
+ " :F_CG 12.5 KN\n",
+ " :F_CD 7.5 KN\n",
+ " :F_GD 1.0 KN\n",
+ " :F_GH 7.5 KN\n",
+ " :F_DH 1.25 KN\n",
+ " :F_DE 8.25 KN\n",
+ " :F_EF 8.25 KN\n",
+ " :F_HF 13.75 KN\n"
+ ]
+ }
+ ],
+ "prompt_number": 21
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 6.5,Page No.133"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "from math import sin, cos, tan, radians, pi\n",
+ "\n",
+ "#Initilization of Variables\n",
+ "\n",
+ "F_D=1000 #N \n",
+ "L_AE=L_EF=L_FH=L_BH=1 #m\n",
+ "L_CH=2.25 #m\n",
+ "L=4 #m\n",
+ "\n",
+ "#Calculations\n",
+ "\n",
+ "#Reactions\n",
+ "\n",
+ "#Let sin(theta)=0.6\n",
+ "#cos(theta)=0.8\n",
+ "#tan(theta)=0.75 \n",
+ "#sin(theta)=X\n",
+ "#Cos(theta)=Y\n",
+ "#tan(theta)=Z\n",
+ "X=0.6\n",
+ "Y=0.8\n",
+ "Z=0.75 \n",
+ "\n",
+ "R_B=F_D*L**-1 #KN\n",
+ "R_A=F_D-R_B #KN\n",
+ "\n",
+ "#Forces\n",
+ "\n",
+ "F_AD=R_A*X**-1 #KN\n",
+ "F_AE=F_AD*Y #KN\n",
+ "F_EF=F_AE #KN\n",
+ "\n",
+ "#After dimplifying And further resolving we get\n",
+ "F_DG=833.34*2**-1 #KN\n",
+ "F_DF=416.66+416.67 \n",
+ "F_FG=F_DF*X #KN\n",
+ "F_FH=F_D-F_DF*Y\n",
+ "\n",
+ "#Result\n",
+ "print\"Forces in the members are:F_DG\",round(F_DG,2),\"KN\"\n",
+ "print\" :F_DF\",round(F_DF,2),\"KN\"\n",
+ "print\" :F_FG\",round(F_FG,2),\"KN\"\n",
+ "print\" :F_FH\",round(F_FH,2),\"KN\"\n",
+ "print\" :F_AD\",round(F_AD,2),\"KN\"\n",
+ "print\" :F_AE\",round(F_AE,2),\"KN\"\n",
+ "print\" :F_EF\",round(F_EF,2),\"KN\""
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "Forces in the members are:F_DG 416.67 KN\n",
+ " :F_DF 833.33 KN\n",
+ " :F_FG 500.0 KN\n",
+ " :F_FH 333.34 KN\n",
+ " :F_AD 1250.0 KN\n",
+ " :F_AE 1000.0 KN\n",
+ " :F_EF 1000.0 KN\n"
+ ]
+ }
+ ],
+ "prompt_number": 22
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 6.6,Page No.135"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "from math import sin, cos, tan, radians, pi\n",
+ "\n",
+ "#Initilization of Variables\n",
+ "\n",
+ "theta=60\n",
+ "alpha=30\n",
+ "F_C=1000 #N \n",
+ "\n",
+ "#Calculations\n",
+ "\n",
+ "#Force CD\n",
+ "F_CD=F_C*(sin(theta*pi*180**-1))**-1 #N\n",
+ " \n",
+ "#Force CA\n",
+ "F_CA=F_CD*cos(theta*pi*180**-1) #N\n",
+ "\n",
+ "#FOrce AD\n",
+ "F_AD=F_CD*cos(alpha*pi*180**-1)*(cos(alpha*pi*180**-1))**-1 #N\n",
+ "\n",
+ "#Force BD\n",
+ "F_BD=F_AD*sin(alpha*pi*180**-1)+F_CD*sin(alpha*pi*180**-1) #N\n",
+ "\n",
+ "#Result\n",
+ "print\"Forces in members are:F_CD\",round(F_CD,2),\"N\"\n",
+ "print\" :F_CA\",round(F_CA,2),\"N\"\n",
+ "print\" :F_AD\",round(F_AD,2),\"N\"\n",
+ "print\" :F_BD\",round(F_BD,2),\"N\""
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "Forces in members are:F_CD 1154.7 N\n",
+ " :F_CA 577.35 N\n",
+ " :F_AD 1154.7 N\n",
+ " :F_BD 1154.7 N\n"
+ ]
+ }
+ ],
+ "prompt_number": 23
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 6.7,Page No.136"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "\n",
+ "#Initilization of Variables\n",
+ "\n",
+ "#LEt tan(theta)=X\n",
+ "#cos(theta)=Y\n",
+ "#sin(theta)=Z\n",
+ "L_EC=5\n",
+ "F_B=F_C=1000 #N\n",
+ "X=3*4**-1 \n",
+ "Y=0.8\n",
+ "Z=0.6\n",
+ "\n",
+ "\n",
+ "#Calculations\n",
+ "\n",
+ "#Force CD\n",
+ "F_CD=F_B*Z**-1 #N\n",
+ "\n",
+ "#Force CB\n",
+ "F_CB=F_CD*Y\n",
+ "\n",
+ "#Force BD\n",
+ "F_BD=F_B #N\n",
+ "\n",
+ "#Force BA\n",
+ "F_BA=F_CB #N\n",
+ "\n",
+ "#in joint D,resolving forces we get\n",
+ "#F_AD+F_ED=3333.32 .........1\n",
+ "#After further simplifying we get\n",
+ "#F_ED-F_AD=1666.66 .............2\n",
+ "\n",
+ "#Froce ED\n",
+ "F_ED=4999.98*2**-1 #N\n",
+ "\n",
+ "#Force AD\n",
+ "F_AD=3333.32-F_ED #N\n",
+ "\n",
+ "\n",
+ "#Result\n",
+ "print\"Forces in the members are:F_CD\",round(F_CD,2),\"N\"\n",
+ "print\" :F_CB\",round(F_CB,2),\"N\"\n",
+ "print\" :F_BD\",round(F_BD,2),\"N\"\n",
+ "print\" :F_BA\",round(F_BA,2),\"N\"\n",
+ "print\" :F_AD\",round(F_AD,2),\"N\""
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "Forces in the members are:F_CD 1666.67 N\n",
+ " :F_CB 1333.33 N\n",
+ " :F_BD 1000.0 N\n",
+ " :F_BA 1333.33 N\n",
+ " :F_AD 833.33 N\n"
+ ]
+ }
+ ],
+ "prompt_number": 24
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 6.8,Page No.138"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "\n",
+ "#Initilization of Variables\n",
+ "\n",
+ "F_D=12 #KN #Force at D\n",
+ "F_C=18 #KN\n",
+ "L_AC=2 #m \n",
+ "L_CB=2 #m\n",
+ "L_DC=1.5 #m\n",
+ "L_AB=4 #m\n",
+ "\n",
+ "#Calculations\n",
+ "\n",
+ "#Reactions\n",
+ "\n",
+ "R_B=(F_C*L_AC+F_D*L_DC)*L_AB**-1 #KN\n",
+ "R_A=(F_C)-R_B #KN\n",
+ "\n",
+ "#Let cos(theta)=X\n",
+ "#sin(theta)=Y\n",
+ "\n",
+ "X=0.8 \n",
+ "Y=0.6 \n",
+ "\n",
+ "#Forces\n",
+ "\n",
+ "F_AD=R_A*Y**-1 #KN\n",
+ "F_AC=F_D+F_AD*X #KN\n",
+ "F_CD=F_AC\n",
+ "F_BC=F_AC #KN\n",
+ "F_BD=R_B*(Y)**-1 #KN\n",
+ "\n",
+ "#Result\n",
+ "print\"forces in members are:F_AC\",round(F_AC,2),\"KN\"\n",
+ "print\" :F_AD\",round(F_AD,2),\"KN\"\n",
+ "print\" :F_BC\",round(F_BC,2),\"KN\"\n",
+ "print\" :F_BD\",round(F_BD,2),\"KN\"\n",
+ "print\" :F_CD\",round(F_CD,2),\"KN\""
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "forces in members are:F_AC 18.0 KN\n",
+ " :F_AD 7.5 KN\n",
+ " :F_BC 18.0 KN\n",
+ " :F_BD 22.5 KN\n",
+ " :F_CD 18.0 KN\n"
+ ]
+ }
+ ],
+ "prompt_number": 25
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 6.9,Page No.139"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "\n",
+ "#Initilization of Variables\n",
+ "\n",
+ "L_AF=L_FG=L_BG=4 #m\n",
+ "L_AB=12 #m\n",
+ "F_F=3 #KN\n",
+ "F_G=6 #KN\n",
+ "F_E=8 #KN\n",
+ "V=1.5 #m #Vertical Distance\n",
+ "\n",
+ "#Calculations\n",
+ "\n",
+ "#Reactions\n",
+ "R_B=(F_E*V+F_F*L_AF+F_G*(L_AF+L_FG))*L_AB**-1\n",
+ "R_A=(F_F+F_G)-R_B\n",
+ "\n",
+ "#Let cos(theta)=X\n",
+ "#Sin(theta)=Y\n",
+ "X=0.8\n",
+ "Y=0.6 \n",
+ "\n",
+ "#Forces\n",
+ "F_CA=F_F*Y**-1 #KN\n",
+ "F_FA=F_CA*X+F_E #KN\n",
+ "F_CF=F_CA #KN\n",
+ "F_CD=(F_CA+F_CF)*X #KN\n",
+ "F_DF=(-F_CF*Y+F_F)*Y**-1 #KN\n",
+ "F_GF=F_FA+F_CF*X #KN\n",
+ "F_DE=F_CD #KN\n",
+ "F_GE=F_G*Y**-1 #KN\n",
+ "F_GB=F_GF-F_GE*X #KN\n",
+ "F_BE=F_GE #KN\n",
+ "\n",
+ "#Result\n",
+ "print\"Forces in the members are:F_CA\",round(F_CA,2),\"KN\"\n",
+ "print\" :F_FA\",round(F_FA,2),\"KN\"\n",
+ "print\" :F_CF\",round(F_CF,2),\"KN\"\n",
+ "print\" :F_CD\",round(F_CD,2),\"KN\"\n",
+ "print\" :F_DF\",round(F_DF,2),\"KN\"\n",
+ "print\" :F_GF\",round(F_GF,2),\"KN\"\n",
+ "print\" :F_DE\",round(F_DE,2),\"KN\"\n",
+ "print\" :F_GE\",round(F_GE,2),\"KN\"\n",
+ "print\" :F_GB\",round(F_GB,2),\"KN\"\n",
+ "print\" :F_BE\",round(F_BE,2),\"KN\""
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "Forces in the members are:F_CA 5.0 KN\n",
+ " :F_FA 12.0 KN\n",
+ " :F_CF 5.0 KN\n",
+ " :F_CD 8.0 KN\n",
+ " :F_DF 0.0 KN\n",
+ " :F_GF 16.0 KN\n",
+ " :F_DE 8.0 KN\n",
+ " :F_GE 10.0 KN\n",
+ " :F_GB 8.0 KN\n",
+ " :F_BE 10.0 KN\n"
+ ]
+ }
+ ],
+ "prompt_number": 26
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 6.10,Page No.142"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "from math import sin, cos, tan, radians, pi\n",
+ "\n",
+ "#Initilization of Variables\n",
+ "\n",
+ "theta=60 #DEgrees\n",
+ "alpha=30 #Degrees\n",
+ "L_AE=L_EF=L_FB=4 #m\n",
+ "L_AB=12 #m\n",
+ "F_A=1 #KN\n",
+ "F_C=2 #KN\n",
+ "F_D=1 #KN\n",
+ "\n",
+ "#Calculations\n",
+ "\n",
+ "L_AC=L_AE*cos(alpha*pi*180**-1) #m\n",
+ "L_AD=F_C*L_AC #m\n",
+ "\n",
+ "#Reactions\n",
+ "R_B=(F_C*L_AC+F_A*L_AD+F_D*L_AE)*L_AB**-1\n",
+ "V=(F_A+F_C+F_D)*sin(theta*pi*180**-1)+1 #KN\n",
+ "H=(F_A+F_C+F_D)*cos(theta*pi*180**-1) #KN\n",
+ "R_A=V-R_B #KN\n",
+ "\n",
+ "#Forces\n",
+ "F_AC=(R_A-(F_A*sin(theta*pi*180**-1)))*(sin(alpha*pi*180**-1))**-1\n",
+ "F_AE=F_C+F_AC*cos(alpha*pi*180**-1)-F_A*cos(theta*pi*180**-1) #KN\n",
+ "F_CD=F_AC\n",
+ "F_CE=F_C #KN\n",
+ "F_ED=F_C+(sin(theta*pi*180**-1))**-1 #KN\n",
+ "F_EF=F_AE-F_C*cos(theta*pi*180**-1)-F_ED*cos(theta*pi*180**-1)\n",
+ "F_FB=F_EF #KN\n",
+ "F_BG=R_B*(sin(alpha*pi*180**-1))**-1 #KN\n",
+ "F_GD=F_BG #KN\n",
+ "\n",
+ "#Result\n",
+ "print\"Forces in the members are:F_AC\",round(F_AC,2),\"KN\"\n",
+ "print\" :F_AE\",round(F_AE,2),\"KN\"\n",
+ "print\" :F_CD\",round(F_CD,2),\"KN\"\n",
+ "print\" :F_CE\",round(F_CE,2),\"KN\"\n",
+ "print\" :F_ED\",round(F_ED,2),\"KN\"\n",
+ "print\" :F_EF\",round(F_EF,2),\"KN\"\n",
+ "print\" :F_FB\",round(F_FB,2),\"KN\"\n",
+ "print\" :F_BG\",round(F_BG,2),\"KN\"\n",
+ "print\" :F_GD\",round(F_GD,2),\"KN\""
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "Forces in the members are:F_AC 4.22 KN\n",
+ " :F_AE 5.15 KN\n",
+ " :F_CD 4.22 KN\n",
+ " :F_CE 2.0 KN\n",
+ " :F_ED 3.15 KN\n",
+ " :F_EF 2.58 KN\n",
+ " :F_FB 2.58 KN\n",
+ " :F_BG 2.98 KN\n",
+ " :F_GD 2.98 KN\n"
+ ]
+ }
+ ],
+ "prompt_number": 27
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 6.11,Page No.145"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "from math import sin, cos, tan, radians, pi\n",
+ "\n",
+ "#Initilization of Variables\n",
+ "\n",
+ "theta=60 #degrees\n",
+ "alpha=30 #degrees\n",
+ "beta=90 #degrees\n",
+ "L_AB=2.5 #m\n",
+ "L_BC=5 #m\n",
+ "F_A=20 #KN\n",
+ "\n",
+ "#Calculations\n",
+ "\n",
+ "#Reactions\n",
+ "R_C=(F_A*L_AB*cos(theta*pi*180**-1))*L_BC**-1 #kn\n",
+ "R_B=F_A-R_C\n",
+ "\n",
+ "#Forces\n",
+ "\n",
+ "F_AB=(R_B*L_BC)*(R_C*cos(alpha*pi*180**-1))**-1 #KN\n",
+ "F_BC=(L_AB*sin(theta*pi*180**-1))**-1*(R_B*L_AB*cos(theta*pi*180**-1))\n",
+ "\n",
+ "\n",
+ "\n",
+ "#Result\n",
+ "print\"Force in Members are:F_BA\",round(F_AB,2),\"KN\"\n",
+ "print\" :F_BC\",round(F_BC,2),\"KN\""
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "Force in Members are:F_BA 17.32 KN\n",
+ " :F_BC 8.66 KN\n"
+ ]
+ }
+ ],
+ "prompt_number": 28
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 6.12,Page No.146"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "from math import sin, cos, tan, radians, pi\n",
+ "\n",
+ "#Initilization of Variables\n",
+ "\n",
+ "L_AC=L_AD=2.5 #m\n",
+ "L_BC=2.5 #m\n",
+ "L_AB=5 #m\n",
+ "theta=30 #Degrees\n",
+ "alpha=60 #degrees\n",
+ "F_D=10 #KN\n",
+ "F_E=12 #KN\n",
+ "\n",
+ "#Calculations\n",
+ "\n",
+ "L_BE=L_BC*cos(theta*pi*180**-1) #m\n",
+ "L_AD=L_AB*cos(alpha*pi*180**-1) #m\n",
+ "\n",
+ "#Distance of Line of action of load 12 KN\n",
+ "x=L_AB-1.875 #m\n",
+ "\n",
+ "#Reactions\n",
+ "R_B=(F_D*L_AC*2**-1+F_E*x)*L_AB**-1 #KN\n",
+ "R_A=(F_D+F_E)-R_B #KN\n",
+ "\n",
+ "#Forces\n",
+ "F_BC=(R_B*L_BE*cos(theta*pi*180**-1))*(L_BE*sin(theta*pi*180**-1))**-1\n",
+ "F_EC=F_E*cos(theta*pi*180**-1) #KN\n",
+ "F_DE=-((F_E*(L_AC-L_BE*cos(theta*pi*180**-1)))-R_B*L_BC)*(L_AC*sin(theta*pi*180**-1))**-1\n",
+ "\n",
+ "#Result\n",
+ "print\"Reactions are:R_A\",round(R_A,2),\"KN\"\n",
+ "print\" :R_B\",round(R_B,2),\"KN\"\n",
+ "print\"Forces in the members are:F_BC\",round(F_BC,2),\"KN\"\n",
+ "print\" :F_EC\",round(F_EC,2),\"KN\"\n",
+ "print\" :F_DE\",round(F_DE,2),\"KN\""
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "Reactions are:R_A 12.0 KN\n",
+ " :R_B 10.0 KN\n",
+ "Forces in the members are:F_BC 17.32 KN\n",
+ " :F_EC 10.39 KN\n",
+ " :F_DE 14.0 KN\n"
+ ]
+ }
+ ],
+ "prompt_number": 29
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 6.13,Page No.148"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "\n",
+ "#Initilization of Variables\n",
+ "\n",
+ "#Lengths\n",
+ "L_AG=L_GH=L_HB=3\n",
+ "L_AB=9 #m\n",
+ "L_FB=L_EH=L_DG=L_AC=4 #m\n",
+ "\n",
+ "#Forces\n",
+ "F_G=9 #KN\n",
+ "F_H=12 #KN\n",
+ "\n",
+ "#Calculations\n",
+ "\n",
+ "#Reactions\n",
+ "R_B=(F_G*L_AG+F_H*(L_AG+L_GH))*L_AB**-1\n",
+ "R_A=(F_G+F_H)-R_B #KN\n",
+ "\n",
+ "#Forces\n",
+ "F_3=(R_A*L_AG)*L_AC**-1 #KN\n",
+ "F_1=(R_A*L_AG)*L_AC**-1 #KN\n",
+ "F_2=(F_3*L_AC-F_G*L_AG)*L_AG**-1\n",
+ "\n",
+ "#Result\n",
+ "print\"Reactions are:R_A\",round(R_A,2),\"KN\"\n",
+ "print\" :R_B\",round(R_B,2),\"KN\"\n",
+ "print\"Forces in Members are:F_1\",round(F_1,2),\"KN\"\n",
+ "print\" :F_2\",round(F_2,2),\"KN\"\n",
+ "print\" :F_3\",round(F_3,2),\"KN\""
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "Reactions are:R_A 10.0 KN\n",
+ " :R_B 11.0 KN\n",
+ "Forces in Members are:F_1 7.5 KN\n",
+ " :F_2 1.0 KN\n",
+ " :F_3 7.5 KN\n"
+ ]
+ }
+ ],
+ "prompt_number": 30
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 6.14,Page No.149"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "from math import sin, cos, tan, radians, pi\n",
+ "import numpy as np\n",
+ "\n",
+ "#Initilization of Variables\n",
+ "\n",
+ "L_CH=5 #m\n",
+ "L_DE=4.5 #m\n",
+ "L_AE=L_EC=L_FB=4 #m\n",
+ "L_AB=16 #m\n",
+ "F=80 #KN\n",
+ "v=0.5 #m\n",
+ "\n",
+ "#Calculations\n",
+ "\n",
+ "#Reactions\n",
+ "R_B=F*(L_AE+L_EC+L_FB)*L_AB**-1 #m\n",
+ "R_A=F-R_B #KN\n",
+ "\n",
+ "#Forces\n",
+ "F1=R_A*L_AE*L_DE**-1 #KN\n",
+ "\n",
+ "theta=np.arctan(L_DE*L_EC**-1)*(180*pi**-1)\n",
+ "alpha=np.arctan(v*L_AE**-1)*(180*pi**-1) #Degrees\n",
+ "beta=alpha+theta #Degrees\n",
+ "\n",
+ "L_CD=(L_DE**2+L_EC**2)**0.5 #m\n",
+ "L_CL=L_CD*sin(beta*pi*180**-1) #m\n",
+ "\n",
+ "F3=R_A*(L_AE+L_EC)*L_CL**-1 #KN\n",
+ "F2=-(F3*sin(alpha*pi*180**-1)-R_A)*(sin(theta*pi*180**-1))**-1\n",
+ "\n",
+ "\n",
+ "#Result\n",
+ "print\"Forces in Members are:F1\",round(F1,2),\"KN\"\n",
+ "print\" :F2\",round(F2,2),\"KN\"\n",
+ "print\" :F3\",round(F3,2),\"KN\""
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "Forces in Members are:F1 17.78 KN\n",
+ " :F2 21.41 KN\n",
+ " :F3 32.25 KN\n"
+ ]
+ }
+ ],
+ "prompt_number": 31
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 6.15,Page No.151"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "from math import sin, cos, tan, radians, pi\n",
+ "\n",
+ "#Initilization of Variables\n",
+ "\n",
+ "L_EC=L_FD=L_BD=L_AC=L_OH=2 #m\n",
+ "L_AB=L_CD=L_EF=4 #m\n",
+ "F=20 #KN\n",
+ "H=20 #KN\n",
+ "theta=90\n",
+ "alpha=45\n",
+ "\n",
+ "#Calculations\n",
+ "\n",
+ "#Reactios\n",
+ "R_B=(H*L_EC+F*(L_FD+L_BD)+F*(L_AC+L_EC+L_OH))*L_AB**-1\n",
+ "R_A=0-R_B #KN\n",
+ "H_A=3*F #All horizontal Forces\n",
+ "\n",
+ "#Forces\n",
+ "F_BD=(F*L_FD+F*(L_FD+L_BD))*L_AB**-1 #KN\n",
+ "F_AC=(F*L_FD+H*(L_OH+L_EC))*L_AB**-1\n",
+ "F_BG=(R_B-F_BD)*(cos(alpha*pi*180**-1))**-1 #KN\n",
+ "F_BA=F_BG*sin(alpha*pi*180**-1)\n",
+ "F_AG=(H_A-F_BA)*(cos(alpha*pi*180**-1))**-1\n",
+ "\n",
+ "\n",
+ "#Result\n",
+ "print\"Forces in the Members are:F_BD\",round(F_BD,2),\"KN\"\n",
+ "print\" :F_AC\",round(F_AC,2),\"KN\"\n",
+ "print\" :F_BG\",round(F_BG,2),\"KN\"\n",
+ "print\" :F_BA\",round(F_BA,2),\"KN\"\n",
+ "print\" :F_AG\",round(F_AG,2),\"KN\""
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "Forces in the Members are:F_BD 30.0 KN\n",
+ " :F_AC 30.0 KN\n",
+ " :F_BG 42.43 KN\n",
+ " :F_BA 30.0 KN\n",
+ " :F_AG 42.43 KN\n"
+ ]
+ }
+ ],
+ "prompt_number": 32
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 6.16,Page No.153"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "from math import sin, cos, tan, radians, pi\n",
+ "\n",
+ "#Initilization of Variables\n",
+ "\n",
+ "F_E=F_A=F_D=1 #KN\n",
+ "F_C=2 #KN\n",
+ "L_AE=L_EF=L_FB=4 #m\n",
+ "L_AB=12 #m\n",
+ "theta=60 \n",
+ "alpha=30 #degrees\n",
+ "\n",
+ "#Calculations\n",
+ "\n",
+ "L_AC=L_AE*cos(alpha*pi*180**-1)\n",
+ "L_AD=F_C*L_AC #m\n",
+ "\n",
+ "#Reactions\n",
+ "R_B=(F_C*L_AC+F_A*L_AD+F_D*L_AE)*L_AB**-1\n",
+ "\n",
+ "#Forces\n",
+ "F_DG=(R_B*L_AE)*(L_FB*sin(alpha*pi*180**-1))**-1\n",
+ "F_FE=R_B*cos(alpha*pi*180**-1)*(sin(alpha*pi*180**-1))**-1\n",
+ "F_DF=0 #KN \n",
+ "\n",
+ "\n",
+ "#Result\n",
+ "print\"Force in members:DG\",round(F_DG,2),\"KN\"\n",
+ "print\" :FE\",round(F_FE,2),\"KN\"\n",
+ "print\" :DF\",round(F_DF,2),\"KN\""
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "Force in members:DG 2.98 KN\n",
+ " :FE 2.58 KN\n",
+ " :DF 0.0 KN\n"
+ ]
+ }
+ ],
+ "prompt_number": 33
+ }
+ ],
+ "metadata": {}
+ }
+ ]
+}
\ No newline at end of file diff --git a/Engineering_Mechanics/chapter_7.ipynb b/Engineering_Mechanics/chapter_7.ipynb new file mode 100644 index 00000000..4fdfee2a --- /dev/null +++ b/Engineering_Mechanics/chapter_7.ipynb @@ -0,0 +1,788 @@ +{
+ "metadata": {
+ "name": "chapter_7.ipynb"
+ },
+ "nbformat": 3,
+ "nbformat_minor": 0,
+ "worksheets": [
+ {
+ "cells": [
+ {
+ "cell_type": "heading",
+ "level": 1,
+ "metadata": {},
+ "source": [
+ "Chapter 7:Centre Of Gravity And Moment Of Inertia"
+ ]
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 7.1,Page No.165"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "\n",
+ "#Declaration Of Variables\n",
+ "\n",
+ "b1=12 #cm #width of flange\n",
+ "d1=3 #cm #depth\n",
+ "\n",
+ "#web\n",
+ "b2=3 #cm\n",
+ "d2=10 #cm \n",
+ "\n",
+ "#Calculations\n",
+ "\n",
+ "#area of flange\n",
+ "a1=b1*d1 #cm**2\n",
+ "\n",
+ "#area of web\n",
+ "a2=b2*d2 #cm**2\n",
+ "\n",
+ "#C.G of flange\n",
+ "y1=d1*2**-1+d2 #cm\n",
+ "\n",
+ "#C.G of web\n",
+ "y2=d2*2**-1 #cm\n",
+ "\n",
+ "#C.G of section\n",
+ "Y=(a1*y1+a2*y2)*(a1+a2)**-1\n",
+ "\n",
+ "#Result\n",
+ "print\"C.G of section is\",round(Y,2),\"cm\""
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "C.G of section is 8.55 cm\n"
+ ]
+ }
+ ],
+ "prompt_number": 1
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 7.2,Page No.166"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "\n",
+ "#Declaration Of Variables\n",
+ "\n",
+ "b1=10 #cm #width of top flange\n",
+ "d1=2 #cm #depth\n",
+ "\n",
+ "#web\n",
+ "b2=2 #cm\n",
+ "d2=15 #cm \n",
+ "\n",
+ "#bottom flange\n",
+ "b3=20 #cm \n",
+ "d3=2 #cm\n",
+ "\n",
+ "#Calculations\n",
+ "\n",
+ "#area of top flange\n",
+ "a1=b1*d1 #cm**2\n",
+ "\n",
+ "#area of web\n",
+ "a2=b2*d2 #cm**2\n",
+ "\n",
+ "#area of bottom flange\n",
+ "a3=b3*d3 #cm**2\n",
+ "\n",
+ "#C.G of flange\n",
+ "y1=d1*2**-1+d2+d3 #cm\n",
+ "\n",
+ "#C.G of web\n",
+ "y2=d2*2**-1+d3 #cm\n",
+ "\n",
+ "#C.G of bottom flange\n",
+ "y3=d3*2**-1 #cm\n",
+ "\n",
+ "#C.G of section\n",
+ "Y=(a1*y1+a2*y2+a2*y3)*(a1+a2+a3)**-1\n",
+ "\n",
+ "#Result\n",
+ "print\"C.G of section is\",round(Y,3),\"cm\""
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "C.G of section is 7.5 cm\n"
+ ]
+ }
+ ],
+ "prompt_number": 1
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 7.3,Page No.167"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "\n",
+ "#Declaration Of Variables\n",
+ "\n",
+ "b2=8 #cm #width of flange\n",
+ "d2=2 #cm #depth\n",
+ "\n",
+ "#web\n",
+ "b1=2 #cm\n",
+ "d1=10 #cm \n",
+ "\n",
+ "#Calculations\n",
+ "\n",
+ "#area of flange\n",
+ "a1=b1*d1 #cm**2\n",
+ "\n",
+ "#area of web\n",
+ "a2=b2*d2 #cm**2\n",
+ "\n",
+ "#distance of C.G of flange(y-axis)\n",
+ "y1=d1*2**-1+d2 #cm\n",
+ "\n",
+ "#distance of C.G of web(y-axis)\n",
+ "y2=d2*2**-1 #cm\n",
+ "\n",
+ "#C.G of section(y-axis)\n",
+ "Y=(a1*y1+a2*y2)*(a1+a2)**-1 #cm\n",
+ "\n",
+ "#distance of C.G of flange(y-axis)\n",
+ "x1=b1*2**-1 #cm\n",
+ "\n",
+ "#distance of C.G of web(y-axis)\n",
+ "x2=b2*2**-1 #cm\n",
+ "\n",
+ "#C.G of section(y-axis)\n",
+ "X=(a1*x1+a2*x2)*(a1+a2)**-1 #cm\n",
+ "\n",
+ "\n",
+ "#Result\n",
+ "print\"C.G of section(X-axis) is\",round(X,2),\"cm\"\n",
+ "print\"C.G of section(Y-axis) is\",round(Y,2),\"cm\""
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "C.G of section(X-axis) is 2.33 cm\n",
+ "C.G of section(Y-axis) is 4.33 cm\n"
+ ]
+ }
+ ],
+ "prompt_number": 3
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 7.4,Page No.168"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "from math import sin, cos, tan, radians, pi\n",
+ "\n",
+ "#Declaration Of Variables\n",
+ "\n",
+ "b=2.5 #cm #width of triangle\n",
+ "h=5 #cm #height of triangle\n",
+ "b2=10 #cm #width of rectangle\n",
+ "h2=5 #cm #height of rectangle\n",
+ "r=2.5 #cm #radius of semicircle\n",
+ "\n",
+ "#Calculations\n",
+ "\n",
+ "#Area of semicircle\n",
+ "a1=pi*2**-1*r**2 #cm**2\n",
+ "\n",
+ "#C.G of semicircle\n",
+ "y1=h2*2**-1 #cm\n",
+ "x1=r-(4*r*(3*pi)**-1)\n",
+ "\n",
+ "#area of rectangle\n",
+ "a2=b2*h2 #cm**2\n",
+ "\n",
+ "#C.G of rectangle\n",
+ "y2=h*2**-1 #cm\n",
+ "x2=r+b2*2**-1 #cm\n",
+ "\n",
+ "#Area of triangle\n",
+ "a3=2*b*h*2**-1 #cm**2\n",
+ "\n",
+ "#c.G of triangle\n",
+ "y3=h2+h2*3**-1 #cm\n",
+ "x3=r+b2*2**-1+b #cm\n",
+ "\n",
+ "#C.G of section (y-axis)\n",
+ "Y=(a1*y1+a2*y2+a3*y3)*(a1+a2+a3)**-1 #cm\n",
+ "\n",
+ "#C.G of section (x-axis)\n",
+ "\n",
+ "X=(a1*x1+a2*x2+a3*x3)*(a1+a2+a3)**-1 #cm\n",
+ "\n",
+ "#Result\n",
+ "print\"C.G of uniform lamina is\",round(Y,2),\"cm\"\n",
+ "print\" \",round(X,2),\"cm\""
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "C.G of uniform lamina is 3.22 cm\n",
+ " 7.11 cm\n"
+ ]
+ }
+ ],
+ "prompt_number": 2
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 7.4(A),Page No.169"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "from math import sin, cos, tan, radians, pi\n",
+ "\n",
+ "#Declaration Of Variables\n",
+ "\n",
+ "r=6 #cm #radius\n",
+ "b1=12 #cm #width of rectangle angle and triangle\n",
+ "h=6 #cm #height of triangle and rectangle\n",
+ "\n",
+ "#Calculations\n",
+ "\n",
+ "#Semicircle\n",
+ "\n",
+ "#area\n",
+ "A1=pi*r**2*2**-1 #cm**2 \n",
+ "\n",
+ "#distance of C.G\n",
+ "x1=4*r*(3*pi)**-1 #cm\n",
+ "y1=r*2**-1*2 #cm\n",
+ "\n",
+ "#Triangle\n",
+ "\n",
+ "#Area\n",
+ "A2=h*b1*2**-1 #cm**2 \n",
+ "\n",
+ "#Distance of c.g\n",
+ "x2=-b1*3**-1 #cm\n",
+ "y2=h*3**-1+h #cm\n",
+ "\n",
+ "#rectangle\n",
+ "\n",
+ "#Area\n",
+ "A3=b1*h #cm**2\n",
+ "\n",
+ "#Distance of C.G\n",
+ "x3=-b1*2**-1 #cm\n",
+ "y3=h*2**-1 #cm \n",
+ "\n",
+ "#C.G of section\n",
+ "X=(A1*x1+A2*x2+A3*x3)*(A1+A2+A3)**-1\n",
+ "Y=(A1*y1+A2*y2+A3*y3)*(A1+A2+A3)**-1\n",
+ "\n",
+ "#Answer for Y is incorrect in textbook\n",
+ "\n",
+ "#Result\n",
+ "print\"Centroid of Area is\",round(X,2),\"cm\"\n",
+ "print\" \",round(Y,2),\"cm\""
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "Centroid of Area is -2.63 cm\n",
+ " 5.12 cm\n"
+ ]
+ }
+ ],
+ "prompt_number": 5
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 7.5,Page No.170"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "\n",
+ "#Declaration Of Variables\n",
+ "\n",
+ "b=10 #cm #width\n",
+ "h=12 #cm #Height\n",
+ "b1=3 #cm #Width of cut hole\n",
+ "h2=4 #cm #height\n",
+ "\n",
+ "#Calculations\n",
+ "\n",
+ "#Area of rectangle\n",
+ "A=b*h #cm**2 \n",
+ "\n",
+ "#Distance of C.G\n",
+ "y=h*2**-1 #cm\n",
+ "\n",
+ "#Area of hole cut\n",
+ "A2=h2*b1 #cm**2\n",
+ "\n",
+ "#Distance of C.G of cut hole\n",
+ "y2=2+h2*2**-1 #cm\n",
+ "\n",
+ "#Distance between C.G of section with a cut hole\n",
+ "y3=(A*y-A2*y2)*(A-A2)**-1 #cm\n",
+ "\n",
+ "#Distance of C.G with acut hole from left\n",
+ "x1=b*2**-1 #cm\n",
+ "\n",
+ "#Distance of C.G of cut hole from left lineAD\n",
+ "x2=b*2**-1+1+b1*2**-1\n",
+ "\n",
+ "#C.G of section\n",
+ "X=(A*x1-A2*x2)*(A-A2)**-1 #cm\n",
+ "\n",
+ "#Result\n",
+ "print\"C.G of section is\",round(X,2),\"cm\"\n",
+ "print\" \",round(y3,2),\"cm\""
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "C.G of section is 4.72 cm\n",
+ " 6.22 cm\n"
+ ]
+ }
+ ],
+ "prompt_number": 6
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 7.12(A),Page No.197"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "\n",
+ "#Declaration Of Variables\n",
+ "\n",
+ "b=100 #mm #Width of triangle\n",
+ "h=90 #mm #height of triangle\n",
+ "\n",
+ "#Calculations\n",
+ "\n",
+ "#M.I about BC\n",
+ "I_BC=b*h**3*12**-1 #cm**4 \n",
+ "\n",
+ "#Result\n",
+ "print\"M.I of section about an axispassing through base BC\",round(I_BC,2),\"cm\""
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "M.I of section about an axispassing through base BC 6075000.0 cm\n"
+ ]
+ }
+ ],
+ "prompt_number": 7
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 7.12(B),Page No.199"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "\n",
+ "#Declaration Of Variables\n",
+ "\n",
+ "#Rectangle ABCD\n",
+ "L1=10 #cm #Length of rectangle\n",
+ "D1=2 #cm #Depth\n",
+ "\n",
+ "#Rectangle HGEF\n",
+ "L2=2 #cm\n",
+ "D2=10-2 #cm \n",
+ "\n",
+ "D=10 #cm #Total Depth\n",
+ "L=10 #cm #Total Length\n",
+ "\n",
+ "#Calculations\n",
+ "\n",
+ "#Areas\n",
+ "\n",
+ "a1=L1*D1 #cm**2 #Area of rectangle ABCD\n",
+ "a2=L2*D2 #cm**2 #Area of Rectangle HGEF\n",
+ "\n",
+ "#Centre of gravity of respective bodies From Bottom\n",
+ "\n",
+ "y1=D1*2**-1+D2 #cm #C.G of rectangle ABCD from bottom\n",
+ "y2=D2*2**-1 #cm #C.G of rectangle HGEF from bottom\n",
+ "\n",
+ "#Centre of gravity of whole section From bottom\n",
+ "\n",
+ "y_bar=(a1*y1+a2*y2)*(a1+a2)**-1 #cm\n",
+ "\n",
+ "#Centre of gravity of whole section From top\n",
+ "\n",
+ "y_bar2=D-y_bar #cm\n",
+ "\n",
+ "#M.I of respective bodies\n",
+ "\n",
+ "i1=L1*D1**3*12**-1 #cm**4 #M.I of ABCD about an axis passing through it's C.G\n",
+ "i2=L2*D2**3*12**-1 #cm**4 #M.I of HGEF about an axis passing through it's C.G\n",
+ " \n",
+ "h1=y_bar2-D1*2**-1 #cm #Distance of C.G of ABCD from C.G of whole section\n",
+ "h2=y_bar-D2*2**-1 #cm #Distance of C.G of HGEF from C.G of whole section\n",
+ "\n",
+ "I1=i1+a1*h1**2 #cm**4 #M.I of ABCD about an axis passing through C.G of section\n",
+ "I2=i2+a2*h2**2 #cm**4 #M.I of ABCD about an axis passing through C.G of section\n",
+ "\n",
+ "#Moment of Inertia of section about horizontal axis passing through C.G of given section\n",
+ "I_xx=I1+I2 #cm**4\n",
+ "\n",
+ "#Moment of Inertia of section about vertical axis passing through C.G of given section\n",
+ "I_yy=D1*L1**3*12**-1+D2*L2**3*12**-1 #cm**4\n",
+ "\n",
+ "#Result\n",
+ "print\"Moment of Inertia of section about horizontal axis passing through C.G of given section\",round(I_xx,2),\"cm**4\"\n",
+ "print\"Moment of Inertia of section about vertical axis passing through C.G of given section\",round(I_yy,2),\"cm**4\""
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "Moment of Inertia of section about horizontal axis passing through C.G of given section 314.22 cm**4\n",
+ "Moment of Inertia of section about vertical axis passing through C.G of given section 172.0 cm**4\n"
+ ]
+ }
+ ],
+ "prompt_number": 8
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 7.13,Page No.201"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "\n",
+ "#Declaration Of Variables\n",
+ "\n",
+ "#Rectangle ABCD\n",
+ "\n",
+ "L1=10 #cm #Length\n",
+ "d1=2 #cm #depth\n",
+ "\n",
+ "#Rectangle EHGF\n",
+ "\n",
+ "L2=2 #cm #Length\n",
+ "d2=10 #cm #depth\n",
+ "\n",
+ "#Rectangle JKLM\n",
+ "\n",
+ "L3=20 #cm #Length\n",
+ "d3=2 #cm #depth\n",
+ "\n",
+ "D=14 #cm #Overall Depth\n",
+ "\n",
+ "#Calculations\n",
+ "\n",
+ "a1=L1*d1 #cm**2 #Area of rectangle 1\n",
+ "a2=L2*d2 #cm**2 #Area of Rectangle 2\n",
+ "a3=L3*d3 #cm**2 #Area of rectangle 3\n",
+ "\n",
+ "#Centre of gravity of respective bodies From Bottom\n",
+ "\n",
+ "y1=D-d1*2**-1 #cm #C.G of rectangle 1 from bottom\n",
+ "y2=d2*2**-1+d3 #cm #C.G of rectangle 2from bottom\n",
+ "y3=d3*2**-1 #cm #C.G of rectangle 3from bottom\n",
+ "\n",
+ "#Centre of gravity of whole section From bottom\n",
+ "\n",
+ "y_bar=(a1*y1+a2*y2+a3*y3)*(a1+a2+a3)**-1 #cm\n",
+ "\n",
+ "#Centre of gravity of whole section From top\n",
+ "\n",
+ "y_bar2=D-y_bar #cm\n",
+ "\n",
+ "\n",
+ "#M.I of respective bodies\n",
+ "\n",
+ "i1=L1*d1**3*12**-1 #cm**4 #M.I of ABCD about an axis passing through it's C.G\n",
+ "i2=L2*d2**3*12**-1 #cm**4 #M.I of HGEF about an axis passing through it's C.G\n",
+ "i3=L3*d3**3*12**-1 #cm**4 #M.I of JKLM about an axis passing through it's C.G\n",
+ "\n",
+ "h1=y_bar2-d1*2**-1 #cm #Distance of C.G of ABCD from C.G of whole section\n",
+ "h2=y_bar2-(d2*2**-1+d1) #cm #Distance of C.G of HGEF from C.G of whole section\n",
+ "h3=y_bar-d3*2**-1 #cm #Distance of C.G of JKLM from C.G of whole section\n",
+ "\n",
+ "I1=i1+a1*h1**2 #cm**4 #M.I of ABCD about an axis passing through C.G of section\n",
+ "I2=i2+a2*h2**2 #cm**4 #M.I of HGEF about an axis passing through C.G of section\n",
+ "I3=i3+a3*h3**2 #cm**4 #M.I of JKLM about an axis passing through C.G of section\n",
+ "\n",
+ "#Moment of Inertia of section about horizontal axis passing through C.G of given section\n",
+ "I_xx=I1+I2+I3 #cm**4\n",
+ "\n",
+ "\n",
+ "#Result\n",
+ "print\"Moment of Inertia of section about horizontal axis passing through C.G of given section\",round(I_xx,2),\"cm**4\""
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "Moment of Inertia of section about horizontal axis passing through C.G of given section 2166.67 cm**4\n"
+ ]
+ }
+ ],
+ "prompt_number": 9
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 7.14,Page No.202"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "\n",
+ "#Declaration Of Variables\n",
+ "\n",
+ "#Rectangle 1\n",
+ "\n",
+ "L1=80 #cm #Length\n",
+ "d1=12 #cm #depth\n",
+ "\n",
+ "#Rectangle 2\n",
+ "\n",
+ "L2=12 #cm #Length\n",
+ "d2=128 #cm #depth\n",
+ "\n",
+ "#Rectangle 3\n",
+ "\n",
+ "L3=120 #cm #Length\n",
+ "d3=10 #cm #depth\n",
+ "\n",
+ "D=150 #cm #Overall Depth\n",
+ "\n",
+ "\n",
+ "#Calculations\n",
+ "\n",
+ "a1=L1*d1 #cm**2 #Area of rectangle ABCD\n",
+ "a2=L2*d2 #cm**2 #Area of Rectangle EHGF\n",
+ "a3=L3*d3 #cm**2 #Area of rectangle JKLM\n",
+ "\n",
+ "#Centre of gravity of respective bodies From Bottom\n",
+ "\n",
+ "y1=D-d1*2**-1 #cm #C.G of rectangle ABCD from bottom\n",
+ "y2=d2*2**-1+d3 #cm #C.G of rectangle HGEF from bottom\n",
+ "y3=d3*2**-1 #cm #C.G of rectangle JKLM from bottom\n",
+ "\n",
+ "#Centre of gravity of whole section From bottom\n",
+ "\n",
+ "y_bar=(a1*y1+a2*y2+a3*y3)*(a1+a2+a3)**-1 #cm\n",
+ "\n",
+ "#Centre of gravity of whole section From top\n",
+ "\n",
+ "y_bar2=D-y_bar #cm\n",
+ "\n",
+ "#M.I of respective bodies\n",
+ "\n",
+ "i1=L1*d1**3*12**-1 #cm**4 #M.I of 1 about an axis passing through it's C.G\n",
+ "i2=L2*d2**3*12**-1 #cm**4 #M.I of 2 about an axis passing through it's C.G\n",
+ "i3=L3*d3**3*12**-1 #cm**4 #M.I of 3 about an axis passing through it's C.G\n",
+ "\n",
+ "h1=y_bar2-d1*2**-1 #cm #Distance of C.G of 1 from C.G of whole section\n",
+ "h2=y_bar2-(d2*2**-1+d1) #cm #Distance of C.G of 2 from C.G of whole section\n",
+ "h3=y_bar-d3*2**-1 #cm #Distance of C.G of 3 from C.G of whole section\n",
+ "\n",
+ "I1=i1+a1*h1**2 #cm**4 #M.I of 1 about an axis passing through C.G of section\n",
+ "I2=i2+a2*h2**2 #cm**4 #M.I of 2 about an axis passing through C.G of section\n",
+ "I3=i3+a3*h3**2 #cm**4 #M.I of 3 about an axis passing through C.G of section\n",
+ "\n",
+ "#Moment of Inertia of section about x-x axis\n",
+ "I_xx=(I1+I2+I3)*10**-6 #cm**4\n",
+ "\n",
+ "#Moment of Inertia of section about y-y axis\n",
+ "I_yy=(d1*L1**3*12**-1+d2*L2**3*12**-1+d3*L3**3*12**-1)*10**-6 #cm**4\n",
+ "\n",
+ "#Polar Moment of Inertia\n",
+ "I_zz=I_xx+I_yy #mm**4\n",
+ "\n",
+ "\n",
+ "#Result\n",
+ "print\"Polar Moment of Inertia is\",round(I_zz,2),\"mm**4\""
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "Polar Moment of Inertia is 14.44 mm**4\n"
+ ]
+ }
+ ],
+ "prompt_number": 10
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 7.17,Page No.207"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "from math import sin, cos, tan, radians, pi\n",
+ "\n",
+ "#Declaration Of Variables\n",
+ "\n",
+ "b=12 #cm #width of culvert\n",
+ "d=6 #cm #Depth\n",
+ "x=1 #cm #distance between axis of rectangle and semicircle\n",
+ "\n",
+ "b1=3 #cm #width of triangles\n",
+ "h1=6 #cm #height\n",
+ "x1=0 #cm #distance between axis of rectangle and triangles\n",
+ "r=4 #cm #radius of semicircle\n",
+ "\n",
+ "#Calculations\n",
+ "\n",
+ "#area of rectangle\n",
+ "A=b*d #cm\n",
+ "\n",
+ "#M.I of rectangle about an axis A-A\n",
+ "M1=b*d**3*12**-1+A*x #cm**4 \n",
+ "\n",
+ "#Area of rectangle\n",
+ "A1=b1*h1*2**-1 #cm**4\n",
+ "\n",
+ "#M.I of triangles\n",
+ "M2=2*(b1*h1**3*36**-1+A1*x1) #cm**4\n",
+ "\n",
+ "#M.I of semicircle\n",
+ "M3=0.11*r**4+pi*r**2*2**-1*(r-4*r*(3*pi)**-1)**2 #cm**4\n",
+ "\n",
+ "#M.I of c/s of culvert\n",
+ "M4=M1-M2-M3 #cm**4\n",
+ "\n",
+ "#Result\n",
+ "print\"Cross-section of culvert is\",round(M4,2),\"cm**4\""
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "Cross-section of culvert is 90.62 cm**4\n"
+ ]
+ }
+ ],
+ "prompt_number": 3
+ }
+ ],
+ "metadata": {}
+ }
+ ]
+}
\ No newline at end of file diff --git a/Engineering_Mechanics/chapter_8.ipynb b/Engineering_Mechanics/chapter_8.ipynb new file mode 100644 index 00000000..ca4a69c1 --- /dev/null +++ b/Engineering_Mechanics/chapter_8.ipynb @@ -0,0 +1,1699 @@ +{
+ "metadata": {
+ "name": "chapter_8.ipynb"
+ },
+ "nbformat": 3,
+ "nbformat_minor": 0,
+ "worksheets": [
+ {
+ "cells": [
+ {
+ "cell_type": "heading",
+ "level": 1,
+ "metadata": {},
+ "source": [
+ "Chapter 8:Friction"
+ ]
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 8.1,Page No.235"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "\n",
+ "#Declaration Of Variables\n",
+ "\n",
+ "W=100 #N #Weight of Body\n",
+ "P=F=60 #N #Horizontal Force\n",
+ "\n",
+ "#Calculations\n",
+ "\n",
+ "#Normal Reaction Force \n",
+ "R=W=100 #N\n",
+ "\n",
+ "#Coefficient of Friction\n",
+ "mu=F*R**-1 \n",
+ "\n",
+ "#Result\n",
+ "print\"Coefficient of Friction is\",round(mu,2)"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "Coefficient of Friction is 0.6\n"
+ ]
+ }
+ ],
+ "prompt_number": 1
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 8.2,Page No.236"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "\n",
+ "#Declaration Of Variables\n",
+ "\n",
+ "W=200 #N #Weight of Body\n",
+ "mu=0.3 #Coefficient of Friction\n",
+ "\n",
+ "#Calculations\n",
+ "\n",
+ "#Normal Reaction\n",
+ "R=W=200 #N\n",
+ "\n",
+ "#Horizontal Force\n",
+ "F=mu*R #N\n",
+ "\n",
+ "#Result\n",
+ "print\"Horizontal Force is\",round(F,2),\"N\""
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "Horizontal Force is 60.0 N\n"
+ ]
+ }
+ ],
+ "prompt_number": 2
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 8.3,Page No.236"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "from math import sin, cos, tan, radians, pi\n",
+ "\n",
+ "#Declaration Of Variables\n",
+ "\n",
+ "W=50 #N #WEight \n",
+ "F=15 #N #Force required to pull\n",
+ "theta=15 #Degree #Angle made by Force\n",
+ "\n",
+ "#Calculations\n",
+ "\n",
+ "#Normal Reaction\n",
+ "R=W-F*sin(theta*pi*180**-1) #N\n",
+ "\n",
+ "#Coefficient of friction\n",
+ "mu=F*cos(theta*pi*180**-1)*R**-1 #N\n",
+ "\n",
+ "\n",
+ "#Result\n",
+ "print\"Coefficient of Friction is\",round(mu,2)"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "Coefficient of Friction is 0.31\n"
+ ]
+ }
+ ],
+ "prompt_number": 3
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 8.4,Page No.236"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "from math import sin, cos, tan, radians, pi\n",
+ "\n",
+ "#Declaration Of Variables\n",
+ "\n",
+ "W=70 #N #Weight of Body\n",
+ "F=20 #N #force applied\n",
+ "theta=20 #degrees #Angle made by Force\n",
+ "\n",
+ "#Calculations\n",
+ "\n",
+ "#resolving Forces Normal to plane\n",
+ "R=W+F*sin(20*pi*180**-1) #N\n",
+ "\n",
+ "#Resolving Forces along the plane\n",
+ "mu=F*cos(20*pi*180**-1)*R**-1 #N\n",
+ "\n",
+ "#Result\n",
+ "print\"coefficient of Friction is\",round(mu,2)"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "coefficient of Friction is 0.24\n"
+ ]
+ }
+ ],
+ "prompt_number": 4
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 8.5,Page No.237"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "\n",
+ "#Declaration Of Variables\n",
+ "\n",
+ "P1=20 #N #pull\n",
+ "P2=25 #N #Required push\n",
+ "theta2=25 #Inclination of push\n",
+ "\n",
+ "#Calculations\n",
+ "\n",
+ "#Case-1 (When body is pulled)\n",
+ "\n",
+ "#Resolving Forces along the plane\n",
+ "#mu*R1=P1*cos(theta*pi*180**-1) #N .........1\n",
+ "\n",
+ "#Resolving Force normal to plane\n",
+ "#R1=W-P1*sin(theta*pi*180**-1) #N \n",
+ "\n",
+ "#Sub value of mu*R1 in above Equation we get\n",
+ "#mu*(W-8.452)=18.126 ......................2\n",
+ "\n",
+ "#Case-2 (When body is pushed)\n",
+ "\n",
+ "#Resolving Forces along the plane\n",
+ "#mu*R2=P2*cos(theta2*pi*180**-1) #N .........3\n",
+ "\n",
+ "#Resolving Force normal to plane\n",
+ "#R2=W-P2*cos(theta*pi*180**-1) #N \n",
+ "\n",
+ "#Sub value of mu*R2 in above Equation we get\n",
+ "#mu*(W-10.565)=22.657 .................4\n",
+ "\n",
+ "\n",
+ "#dividing equation 2 by 4 and Further simplifying we get\n",
+ "\n",
+ "#Weight of body\n",
+ "W=383*4.53**-1\n",
+ "\n",
+ "#Sub value of W in Equation 2\n",
+ "mu=18.126*(W-8.452)**-1 \n",
+ "\n",
+ "\n",
+ "#Result\n",
+ "print\"Weight of Body is\",round(W,2),\"N\"\n",
+ "print\"Coefficient of Friction is\",round(mu,2)"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "Weight of Body is 84.55 N\n",
+ "Coefficient of Friction is 0.24\n"
+ ]
+ }
+ ],
+ "prompt_number": 5
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 8.7,Page No.239"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "from math import sin, cos, tan, radians, pi\n",
+ "import numpy as np\n",
+ "\n",
+ "#Declaration Of Variables\n",
+ "\n",
+ "W=1000 #N #Weight of stone Block\n",
+ "mu=0.6 #Coefficient of Friction\n",
+ "theta=20 #Degrees #Angle with Horizontal\n",
+ "\n",
+ "#Calculations\n",
+ "\n",
+ "#PArt-1\n",
+ "#resolving Horizontal Forces\n",
+ "#P*cos(theta)=mu*R ...........................1\n",
+ "\n",
+ "#Resolving Verticla Forces\n",
+ "#R+P*sin(theta)=W .............................2\n",
+ "\n",
+ "#Sub value of P from equation 2,we get\n",
+ "P=mu*W*(cos(theta*pi*180**-1)+mu*sin(theta*pi*180**-1))**-1 #N ........3\n",
+ "\n",
+ "#PArt-2\n",
+ "#Let phi=Angle of Friction\n",
+ "\n",
+ "#Form Equation 3 ,angle 20 is replaced by angle phi\n",
+ "#Force required to pull the body\n",
+ "#P2=mu*W*(cos(phi)+mu*sin(phi))**-1\n",
+ "\n",
+ "#The Force P will be min if Dericative of (cos(phi)+mu*sin(phi)) is equal to zero\n",
+ "phi=np.arctan(mu)*(180*pi**-1) #degrees\n",
+ "\n",
+ "#Force required to pull the body\n",
+ "P2=mu*W*(cos(phi*pi*180**-1)+mu*sin(phi*pi*180**-1))**-1 #N\n",
+ "\n",
+ "#Result\n",
+ "print\"Minimum Pull necessary is\",round(P,2),\"N\"\n",
+ "print\"Pull Required if inclination of rope is equal to angle of friction\",round(P,2),\"N\""
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "Minimum Pull necessary is 524.06 N\n",
+ "Pull Required if inclination of rope is equal to angle of friction 524.06 N\n"
+ ]
+ }
+ ],
+ "prompt_number": 1
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 8.11,Page No.241"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "from math import sin, cos, tan, radians, pi\n",
+ "\n",
+ "#Declaration Of Variables\n",
+ "\n",
+ "W=500 #N #weight of Body\n",
+ "P=350 #N #Force applied\n",
+ "alpha=30 #Degrees #Inclination\n",
+ "\n",
+ "#Calculations\n",
+ "\n",
+ "#Resolving Weights\n",
+ "W1=W*sin(30*pi*180**-1) #N\n",
+ "W2=W*cos(30*pi*180**-1) #N\n",
+ "\n",
+ "#Resolving Forces Vertically\n",
+ "#R=W*cos(30)\n",
+ "\n",
+ "#Resolving Forces Horizontally\n",
+ "mu=(P-W*sin(alpha*pi*180**-1))*(W*cos(alpha*pi*180**-1))**-1 \n",
+ "\n",
+ "\n",
+ "#Result\n",
+ "print\"Coefficient Of Friction\",round(mu,2)"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "Coefficient Of Friction 0.23\n"
+ ]
+ }
+ ],
+ "prompt_number": 7
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 8.12,Page No.246"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "from math import sin, cos, tan, radians, pi\n",
+ "\n",
+ "#Declaration Of Variables\n",
+ "\n",
+ "W=450 #N #Weight of Body\n",
+ "alpha=30 #Degrees #Inclination of plane\n",
+ "mu=0.25 #coefficient of friction\n",
+ "d=10 #m #Distance travelled by body\n",
+ "\n",
+ "#Calculations\n",
+ "\n",
+ "#Resolving Force normal to plane\n",
+ "R=W*cos(alpha*pi*180**-1)\n",
+ "\n",
+ "#Resolving Forces along the plane\n",
+ "P=W*sin(alpha*pi*180**-1)+mu*R #N\n",
+ "\n",
+ "#Work done on the body\n",
+ "W=P*d #J\n",
+ "\n",
+ "#Result\n",
+ "print\"Force required is\",round(P,2),\"N\"\n",
+ "print\"Work done is\",round(W,2),\"J\" "
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "Force required is 322.43 N\n",
+ "Work done is 3224.28 J\n"
+ ]
+ }
+ ],
+ "prompt_number": 8
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 8.13,Page No.246"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "from math import sin, cos, tan, radians, pi\n",
+ "\n",
+ "#Declaration Of Variables\n",
+ "\n",
+ "#Case-1\n",
+ "P1=200 #N #Force applied\n",
+ "theta1=15 #Degrees #Inclination\n",
+ "\n",
+ "P2=230 #N #Force applied\n",
+ "theta2=20 #Degrees #Inclination\n",
+ "\n",
+ "#Calculations\n",
+ "\n",
+ "#For Case-1,\n",
+ "\n",
+ "#W1=W*sin(theta1*pi*180**-1) #N\n",
+ "#W2=W*cos(theta1*pi*180**-1) #N\n",
+ "\n",
+ "#Resolving Forces Vertically\n",
+ "#R=W2\n",
+ "\n",
+ "#Resolving Foces Horizontally\n",
+ "#mu*W2+W1=P1 .......................1\n",
+ "\n",
+ "#For case-2\n",
+ "\n",
+ "#W3=W*sin(theta2*pi*180**-1) #N\n",
+ "#W4=W*cos(theta2*pi*180**-1) #N\n",
+ "\n",
+ "#Resolving Forces Vertically\n",
+ "#R=W3\n",
+ "\n",
+ "#Resolving Foces Horizontally\n",
+ "#mu*W3+W4=P2 .......................2\n",
+ "\n",
+ "#After sub values inequations 1 & 2 and dividing equations 2 by 1 we get\n",
+ "mu=mu=(P1*sin(20*pi*180**-1)-P2*sin(15*pi*180**-1))*(P2*cos(15*pi*180**-1)-P1*cos(20*pi*180**-1))**-1 \n",
+ "\n",
+ "#weight of Body\n",
+ "W=P2*(sin(theta2*pi*180**-1)+mu*cos(theta2*pi*180**-1))**-1 #N\n",
+ "\n",
+ "#Result\n",
+ "print\"Weight of Body is\",round(W,2),\"N\"\n",
+ "print\"Coefficient of Friction is\",round(mu,2)"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "Weight of Body is 392.68 N\n",
+ "Coefficient of Friction is 0.26\n"
+ ]
+ }
+ ],
+ "prompt_number": 9
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 8.15,Page No.249"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "from math import sin, cos, tan, radians, pi\n",
+ "\n",
+ "#Declaration Of Variables\n",
+ "\n",
+ "W=15 #N #Weight of Block\n",
+ "T=5 #N #Tension in string\n",
+ "alpha=45 #Degrees #Inclination\n",
+ "\n",
+ "#Calculations\n",
+ "\n",
+ "#Frictional Foce on Block\n",
+ "F=-(T*cos(alpha*pi*180**-1)-W*sin(alpha*pi*180**-1)) #N\n",
+ "\n",
+ "#Normal Reaction of inclined plane\n",
+ "R=(W*cos(alpha*pi*180**-1)+T*sin(alpha*pi*180**-1)) #N\n",
+ "\n",
+ "#Coefficient of friction \n",
+ "mu=F*R**-1 \n",
+ "\n",
+ "#Result\n",
+ "print\"Frictional Force on Block is\",round(F,2),\"N\"\n",
+ "print\"Normal Reaction of inclined plane\",round(R,2),\"N\"\n",
+ "print\"Coefficient of friction\",round(mu,2)"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "Frictional Force on Block is 7.07 N\n",
+ "Normal Reaction of inclined plane 14.14 N\n",
+ "Coefficient of friction 0.5\n"
+ ]
+ }
+ ],
+ "prompt_number": 10
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 8.16,Page No.250"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "from math import sin, cos, tan, radians, pi\n",
+ "\n",
+ "#Declaration Of Variables\n",
+ "\n",
+ "mu_s=0.4 #Coefficient of static Friction\n",
+ "mu_k=0.3 #Coefficient of Kinetic friction\n",
+ "M=40 #Kg #MAss of body\n",
+ "g=9.81 #acceleration due to gravity\n",
+ "W=M*g #N\n",
+ "theta=40 \n",
+ "alpha=30 #Inclination\n",
+ "P=800 #N\n",
+ "\n",
+ "#Calculations\n",
+ "\n",
+ "#normal Reaction \n",
+ "R=P*sin(theta*pi*180**-1)+M*g*cos(alpha*pi*180**-1) #N\n",
+ "\n",
+ "#Max Frictional Force\n",
+ "F=mu_s*R #N\n",
+ "\n",
+ "#Total Force along plane\n",
+ "F=P*cos(theta*pi*180**-1)-M*g*sin(alpha*pi*180**-1) #N\n",
+ "\n",
+ "#Magntude of Frictional Force\n",
+ "F2=mu_k*R #N\n",
+ "\n",
+ "#Result\n",
+ "print\"Magnitude of Friction Force\",round(F2,2),\"N\""
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "Magnitude of Friction Force 256.22 N\n"
+ ]
+ }
+ ],
+ "prompt_number": 11
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 8.17,Page No.252"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "from math import sin, cos, tan, radians, pi\n",
+ "import numpy as np\n",
+ "\n",
+ "#Declaration Of Variables\n",
+ "\n",
+ "W=30 #N #Weight acting vertically downward\n",
+ "P2=6 #N #Force at angle of 30 with inclined plane\n",
+ "theta=30 #Degrees #Inclination of force with the inclined plane\n",
+ "mu=0.3 #Coefficient of friction\n",
+ "\n",
+ "#Calculations\n",
+ "\n",
+ "#Part-1\n",
+ "\n",
+ "#Reaction Force is given by\n",
+ "#R=W*cos(alpha)-P2*sin(theta)\n",
+ "\n",
+ "#Now resolving Force we get\n",
+ "alpha=np.arcsin(P2*cos(theta*pi*180**-1)*W**-1)\n",
+ "alpha2=180*pi**-1*alpha #degrees\n",
+ "\n",
+ "#PArt-2\n",
+ "\n",
+ "#resolving Forces normal to inclined plane\n",
+ "R=W*cos(round(alpha2,2)*pi*180**-1) #N\n",
+ "\n",
+ "#Resolving Forces normal to inclined plane\n",
+ "P1=W*sin(round(alpha2,2)*pi*180**-1)+mu*round(R,2)\n",
+ "\n",
+ "#Result\n",
+ "print\"Force required to move a load 30 N up a rough plane is\",round(P1,2),\"N\""
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "Force required to move a load 30 N up a rough plane is 14.06 N\n"
+ ]
+ }
+ ],
+ "prompt_number": 2
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 8.18,Page No.253"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "\n",
+ "#Declaration Of Variables\n",
+ "\n",
+ "W1=400 #N #Weight of first body\n",
+ "W2=800 #N #Weight of second body\n",
+ "mu1=0.15 #Coefficient of friction of first body\n",
+ "mu2=0.40 #Coefficient of friction of seconnd body\n",
+ "\n",
+ "#Calculations\n",
+ "\n",
+ "#Forces acting on the first body\n",
+ "\n",
+ "#Resolving force along plane\n",
+ "#W1*sin(alpha)=T+mu1*R1 ............................1\n",
+ "\n",
+ "#Resolving Forces normal to plane\n",
+ "#W1*cos(alpha)=R1\n",
+ "\n",
+ "#Sub value of R1 in equation1,we get\n",
+ "#T=400*sin(alpha)-60*cos(alpha) .......................2\n",
+ "\n",
+ "#Forces on second body\n",
+ "\n",
+ "#Resolving forces along the plane\n",
+ "#W2*sin(alpha)+T=mu2*R2 .........................3\n",
+ "\n",
+ "#Resolving forces normal to plane\n",
+ "#R2=W2*cos(alpha)\n",
+ "\n",
+ "#sub value of R2 in equation3\n",
+ "#T=320*cos(alpha)-W2*sin(alpha) ...............4\n",
+ "\n",
+ "#Equating values of T,given by equation 2 and 3\n",
+ "#W1*sin(alpha)-60*cos(alpha)=320*cos(alpha)-W2*sin(alpha)\n",
+ "#Further simplifying we get\n",
+ "alpha=arctan(380*1200**-1)*(180*pi**-1) #Degrees\n",
+ "\n",
+ "#Sub value of alpha in equation 2\n",
+ "T=W1*sin(round(alpha,2)*pi*180**-1)-60*cos(round(alpha,2)*pi*180**-1)\n",
+ "\n",
+ "#Result\n",
+ "print\"Inclination of the plane to the horizontal is\",round(alpha,2),\"Degrees\"\n",
+ "print\"Tension in the cord is\",round(T,2),\"N\""
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "Inclination of the plane to the horizontal is 17.57 Degrees\n",
+ "Tension in the cord is 63.55 N\n"
+ ]
+ }
+ ],
+ "prompt_number": 13
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 8.19,Page No.255"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "\n",
+ "#Declaration Of Variables\n",
+ "\n",
+ "W_B=1500 #N #Weight of block B\n",
+ "mu_A=0.25 #Coefficint of friction of block A\n",
+ "mu_B=0.35 #Coefficient of Friction of block B\n",
+ "alpha=60 #Degrees\n",
+ "\n",
+ "#Calculations\n",
+ "\n",
+ "#BLock A\n",
+ "#F_A=mu_A*W_A #Force of friction\n",
+ "\n",
+ "#Block B\n",
+ "#HOrizontal Force of friction of block A is transmitted through rod to block B\n",
+ "\n",
+ "#Force of friction of block B\n",
+ "#F_B=mu2*R_B\n",
+ "\n",
+ "#Resolving Horizontal Forces\n",
+ "#mu1*W_A+F_B*cos(alpha)=R_B*cos(30)\n",
+ "#After further simplifying we get\n",
+ "#mu_A*W_A=0.691*R_B ...........................1\n",
+ "\n",
+ "#Resolving Forces vertically\n",
+ "#R_B*sin(30)+F_B*sin(alpha)=W_B\n",
+ "#After further simplifying we get\n",
+ "R_B=W_B*0.803**-1 #N\n",
+ "\n",
+ "#Sub value of R_b in equation 1 we get\n",
+ "W_A=0.691*R_B*mu_A**-1\n",
+ "\n",
+ "#Result\n",
+ "print\"Smallest Weight of Block A is\",round(W_A,2),\"N\""
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "Smallest Weight of Block A is 5163.14 N\n"
+ ]
+ }
+ ],
+ "prompt_number": 14
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 8.20,Page No.257"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "from math import sin, cos, tan, radians, pi\n",
+ "\n",
+ "#Declaration Of Variables \n",
+ "\n",
+ "W_A=100 #N Weight of block A\n",
+ "W_B=300 #N #Weight of block B\n",
+ "alpha=45 #Degrees #Inclination of plane\n",
+ "phi=30 #Degrees #Inclination of rigid bar with horizontal \n",
+ "mu=tan(15*pi*180**-1) #Degrees\n",
+ "\n",
+ "#Calculations\n",
+ "\n",
+ "#LEt R_A and R_B be the reactions at A And B respectively and t be the thrust in rod\n",
+ "\n",
+ "#Equilibrium of bLoack A\n",
+ "#Resolving forces along plane\n",
+ "#W_A*sin(alpha)+F_A=T*cos(15)\n",
+ "#After further simplifying we get\n",
+ "#70.7+0.2679*R_A=0.969*T .................1\n",
+ "\n",
+ "#Resolving force snormal to plane\n",
+ "#R_A=W_A*cos(alpha)+T*sin(15)=R_A\n",
+ "\n",
+ "#Now sub value of R_A in equation 1 we get\n",
+ "#70.7+0.269*(100*0.707+T*0.2588)=0.9659*T\n",
+ "#After further simplifying we get\n",
+ "T=89.64*0.8966**-1 #N\n",
+ "\n",
+ "#Equilibrium of block B\n",
+ "#Resolving forces normal to plane\n",
+ "R_B=W_B+T*sin(phi*180**-1*pi)\n",
+ "#Resolving forces along plane\n",
+ "P=T*cos(phi*pi*180**-1)+mu*R_B\n",
+ "\n",
+ "#Result\n",
+ "print\"HOrizontal Force required to be apllied to block B to just move block A is\",round(P,2),\"N\""
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "HOrizontal Force required to be apllied to block B to just move block A is 180.36 N\n"
+ ]
+ }
+ ],
+ "prompt_number": 15
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 8.21,Page No.258"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "from math import sin, cos, tan, radians, pi\n",
+ "import numpy as np\n",
+ "\n",
+ "#Declaration Of Variables\n",
+ "\n",
+ "mu=0.2 #Coefficient of friction\n",
+ "W1=100 #N #weight of Block1\n",
+ "W2=150 #N #Weight of Block2\n",
+ "theta=60 #Degrees\n",
+ "\n",
+ "#Calculations\n",
+ "\n",
+ "#Case-1\n",
+ "\n",
+ "#Reaction Force \n",
+ "R=W2*cos(theta*pi*180**-1) #N\n",
+ "\n",
+ "#Tension in the string\n",
+ "T=W2*sin(theta*pi*180**-1)+mu*R #N\n",
+ "\n",
+ "#Case-2\n",
+ "\n",
+ "theta2=np.arctan(mu)*(pi**-1*180) #Angle made by Force with horizontal acting on block 1\n",
+ "\n",
+ "#Force on block with weight 100 N\n",
+ "P=164.9*((cos(theta2*pi*180**-1)+mu*sin(theta2*pi*180**-1))**-1)\n",
+ "\n",
+ "#Result\n",
+ "print\"Least Value of Force P to cause motion to impend rightwards is\",round(P,2),\"N\""
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "Least Value of Force P to cause motion to impend rightwards is 161.7 N\n"
+ ]
+ }
+ ],
+ "prompt_number": 16
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 8.22,Page No.260"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "from math import sin, cos, tan, radians, pi\n",
+ "import numpy as np\n",
+ "\n",
+ "#Declaration Of Variables\n",
+ "\n",
+ "W1=90 #N #Weight of Block 1\n",
+ "W2=30 #N #Weight of Block2\n",
+ "mu=1*3**-1 #Coefficient of friction\n",
+ "\n",
+ "#Calculations\n",
+ "\n",
+ "#Considering Equilibrium of weight W2\n",
+ "\n",
+ "#Tension in the string\n",
+ "#T=W2*sin(theta)+mu*R1 .....................................1\n",
+ "\n",
+ "#Normal reaction to the plane\n",
+ "#R1=W2*cos(theta) .......................................2\n",
+ "\n",
+ "#Sub value of R1 in equation 1 we get\n",
+ "#T=W2*sin(theta)+10*cos(theta) ........................3\n",
+ "\n",
+ "#Considering Equilibrium of weight W1\n",
+ "\n",
+ "#Resolving Forces along the plane\n",
+ "#W1*sin(theta)=10*cos(theta)+mu*R2 ..................4\n",
+ "\n",
+ "#Resolving Forces normal to plane\n",
+ "#R2=120*cos(theta) ...........5\n",
+ "\n",
+ "#Sub value of R2 in equation 4 we get\n",
+ "theta=np.arctan(0.5555)*(pi**-1*180) #Degrees\n",
+ "\n",
+ "#Result\n",
+ "print\"Value of angle theta should be\",round(theta,2),\"degrees\""
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "Value of angle theta should be 29.05 degrees\n"
+ ]
+ }
+ ],
+ "prompt_number": 17
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 8.23,Page No.262"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "\n",
+ "#Declaration Of Variables\n",
+ "\n",
+ "L_AC=10 #m #Length of AC\n",
+ "L_BC=8 #m #Length of BC\n",
+ "W=20 #N #weight \n",
+ "\n",
+ "#Calculations\n",
+ "\n",
+ "L_AB=(L_AC**2-L_BC**2)**0.5 #m #Length of AB\n",
+ "L_CD=L_BC*2**-1 #m\n",
+ "\n",
+ "#Now Resolving Forces\n",
+ "\n",
+ "#Vertically\n",
+ "#Reaction Force at C\n",
+ "R_C=W #N\n",
+ "\n",
+ "#Horizontally\n",
+ "#R_A=F_C=mu*R_C \n",
+ "\n",
+ "#Taking Moment at pt C\n",
+ "#Coefficient of friction \n",
+ "mu=W*L_CD*(R_C*L_AB)**-1 \n",
+ "\n",
+ "#Frictional Force acting at C\n",
+ "F_C=round(mu,2)*R_C #N\n",
+ "\n",
+ "#Result\n",
+ "print\"Coefficient of Friction\",round(mu,2)\n",
+ "print\"Frictional Force acting at pt C\",round(F_C,2),\"N\""
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "Coefficient of Friction 0.67\n",
+ "Frictional Force acting at pt C 13.4 N\n"
+ ]
+ }
+ ],
+ "prompt_number": 18
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 8.24,Page No.263"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "\n",
+ "#Declaration Of Variables\n",
+ "\n",
+ "L_AB=13 #m #Length of AB\n",
+ "W=25 #N #weight of Ladder\n",
+ "L_AC=5 #m #Distance of lower ladder from wall\n",
+ "mu=0.3 #Coefficient of friction\n",
+ "\n",
+ "#Calculations\n",
+ "\n",
+ "#Forces on the ladder \n",
+ "\n",
+ "#Vertical Forces\n",
+ "R_A=W #N\n",
+ "\n",
+ "#Horizontal Forces\n",
+ "R_B=F_A=mu*R_A #N\n",
+ "\n",
+ "#MAx amount of frictional Force availale at A\n",
+ "F_A #N\n",
+ "\n",
+ "L_AD=L_CD=2.5 #m #Length of AD and CD\n",
+ "L_BC=(L_AB**2-L_AC**2)**0.5 #m\n",
+ "\n",
+ "#Moment at pt A\n",
+ "R_B2=R_A*L_AD*L_BC**-1 #N\n",
+ "\n",
+ "#Horizontal Forces\n",
+ "F_A2=R_B2 #N\n",
+ "\n",
+ "#Result\n",
+ "print\"Frictional Force acting on ladder is\",round(F_A,2),\"N\""
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "Frictional Force acting on ladder is 7.5 N\n"
+ ]
+ }
+ ],
+ "prompt_number": 19
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 8.25,Page No.264"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "from math import sin, cos, tan, radians, pi\n",
+ "\n",
+ "#Declaration Of Variables\n",
+ "\n",
+ "L_AB=14 #m #Length of AB\n",
+ "W=600 #N #weight of Ladder\n",
+ "L_AD=8 #m #Distance of lower ladder from wall\n",
+ "L_BD=6 #m #LEngth of BD\n",
+ "mu=1*3**-1 #Coefficient of friction\n",
+ "CBA=60 #Degrees\n",
+ "\n",
+ "#Calculations\n",
+ "\n",
+ "#Resolving forces\n",
+ "\n",
+ "#Vertically\n",
+ "R_B=W #N\n",
+ "#Actual Force of friction at pt B\n",
+ "F_B=mu*R_B #N\n",
+ "\n",
+ "\n",
+ "#Horizontally\n",
+ "R_A=F_B #N\n",
+ "\n",
+ "\n",
+ "L_BE=L_BD*cos(CBA*pi*180**-1) #m\n",
+ "L_AC=L_AB*sin(CBA*pi*180**-1) #m\n",
+ "\n",
+ "R_A2=R_B*L_BE*L_AC**-1\n",
+ "F_B2=R_A2 #N\n",
+ "\n",
+ "\n",
+ "#Result\n",
+ "print\"Force available at B the force required force for equilibrium,the ladder will be stable:F_B is\",round(F_B,2),\"N\""
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "Force available at B the force required force for equilibrium,the ladder will be stable:F_B is 200.0 N\n"
+ ]
+ }
+ ],
+ "prompt_number": 20
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 8.26,Page No.265"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "from math import sin, cos, tan, radians, pi\n",
+ "\n",
+ "#Declaration Of Variables\n",
+ "\n",
+ "W=850 #N #Weight of ladder\n",
+ "L=L_AB=6 #m #Length of AB\n",
+ "alpha=65 #Degrees #Angle made by ladder with ladder\n",
+ "W1=750 #N #Weight of man\n",
+ "L1=4 #m #Distance of man from top of ladder\n",
+ "L2=L-L1 #m #Distance of man form foot of ladder\n",
+ "L_BE=4 #m #Length of BE\n",
+ "\n",
+ "#Calculations\n",
+ "\n",
+ "#Forces acting on the ladder\n",
+ "\n",
+ "#Resolving Forces Vertically\n",
+ "R_A=W+W1 #N\n",
+ "\n",
+ "#Horizontally\n",
+ "#R_B=F_A=mu*R_A #N\n",
+ "\n",
+ "L_BC=L_AB*sin(alpha*pi*180**-1) #m #Length of BC\n",
+ "L_AC=L_AB*cos(alpha*pi*180**-1) #m #Length of AC\n",
+ "\n",
+ "L_AD=L_AC*2**-1 #m #Length of AD\n",
+ "L_AH=(L_AB-L_BE)*cos(alpha*pi*180**-1) #m\n",
+ "\n",
+ "#Coefficient of friction\n",
+ "mu=(W1*L_AD+W*L_AH)*(L_BC*R_A)**-1\n",
+ "\n",
+ "#Result\n",
+ "print\"Coefficient of friction is\",round(mu,2)"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "Coefficient of friction is 0.19\n"
+ ]
+ }
+ ],
+ "prompt_number": 21
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 8.27,Page No.266"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "from math import sin, cos, tan, radians, pi\n",
+ "import numpy as np\n",
+ "\n",
+ "#Declaration Of Variables\n",
+ "\n",
+ "W=200 #N #Weight of ladder\n",
+ "L=L_AB=4.5 #m\n",
+ "mu=0.4 #Coefficient of friction between ladder and floor\n",
+ "mu2=0.2 #coefficient of frictionbetween LAdder and wall\n",
+ "W1=900 #N #Weight on ladder \n",
+ "L_BE=1.2 #m #distance\n",
+ "\n",
+ "#Calculations\n",
+ "\n",
+ "#FOrces acting on ladder\n",
+ "\n",
+ "#Resolving FOrces Vertically\n",
+ "#R_A+F_B=W1+W #N ................1\n",
+ "\n",
+ "#Horizontally\n",
+ "#R_B=mu*R_A .....................2\n",
+ "\n",
+ "#Resolving Force R_B in equation 1 we get\n",
+ "R_A=(W1+W)*1.08**-1 #N\n",
+ "\n",
+ "#Reaction at B\n",
+ "R_B=mu*R_A #N\n",
+ "\n",
+ "#Moment at pt A\n",
+ "#W*L_AD+W1*L_AH=R_B*L_BC+F_B*L_AC\n",
+ "#After further simplifying we get\n",
+ "alpha=np.arctan(1.665)*(180*pi**-1)\n",
+ "\n",
+ "#Result\n",
+ "print\"Angle made by ladder with Horizontal\",round(alpha,2),\"Degrees\"\n",
+ "print\"Reaction at the Foot of ladder\",round(R_A,2),\"N\"\n",
+ "print\"Reaction at the Foot top of ladder\",round(R_B,2),\"N\"\n",
+ "\n",
+ "#Value of alpha is incorrect in book i.e 59degree 65seconds"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "Angle made by ladder with Horizontal 59.01 Degrees\n",
+ "Reaction at the Foot of ladder 1018.52 N\n",
+ "Reaction at the Foot top of ladder 407.41 N\n"
+ ]
+ }
+ ],
+ "prompt_number": 4
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 8.28,Page No.267"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "from math import sin, cos, tan, radians, pi\n",
+ "\n",
+ "#Declaration Of Variables\n",
+ "\n",
+ "L=5 #m #Length of ladder\n",
+ "alpha=30 #Degrees #Angle made by ladder with horizontal\n",
+ "W1=250 #N #weight of ladder\n",
+ "W2=800 #N #weight of man\n",
+ "mu=0.2 #Coefficinet of friction \n",
+ "L_AG=5*2**-1 #m\n",
+ "\n",
+ "#Calculations\n",
+ "\n",
+ "#Let R_A and R_B be the reactions at A and b respectively\n",
+ "#F_B=mu*R_B\n",
+ "#F_A=mu*R_A\n",
+ "\n",
+ "#Resolving forces vertically\n",
+ "#R_A+F_B=W1+W2 .............1\n",
+ "\n",
+ "#Resolving forces horizontally\n",
+ "#R_B=0.2*R_A.....................2\n",
+ "\n",
+ "#After sub values and further simplifying we get\n",
+ "R_A=1050*1.04**-1 #N\n",
+ "\n",
+ "#Sub value of R_A in equation 2 we get\n",
+ "R_B=0.2*R_A\n",
+ "\n",
+ "#Triangle AGD\n",
+ "L_AD=L_AG*cos(60*pi*180**-1)\n",
+ "\n",
+ "#TRiangle AEH\n",
+ "#L_AH=x*cos(60) \n",
+ "\n",
+ "L_BC=L*cos(alpha*pi*180**-1)\n",
+ "L_AC=L*cos(60*pi*180**-1)\n",
+ "\n",
+ "F_B=mu*R_B\n",
+ "\n",
+ "#Taking moment at A\n",
+ "#W2*x*2**-1+W*L_AD=R_B*L_BC+F_B*L_AC\n",
+ "#After sub values and further simplifying we get\n",
+ "x=66.276*40**-1\n",
+ "\n",
+ "\n",
+ "#Result\n",
+ "print\"The slipping will be induced at\",round(x,2),\"m\""
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "The slipping will be induced at 1.66 m\n"
+ ]
+ }
+ ],
+ "prompt_number": 3
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 8.29,Page No.271"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "from math import sin, cos, tan, radians, pi\n",
+ "import numpy as np\n",
+ "\n",
+ "#Declaration Of Variables\n",
+ "\n",
+ "alpha=10 #Degrees #Angle of Wedge\n",
+ "W=1500 #N #weight of Block\n",
+ "mu=0.3 #Coefficient of friction\n",
+ "phi=np.arctan(mu)*(180*pi**-1)\n",
+ "\n",
+ "#Calculations\n",
+ "\n",
+ "#Applying Lamis theorem to the point O\n",
+ "#W*(sin(2*phi+90+alpha))**-1=R3*(sin(180-(alpha+phi)))**-1=R2*(sin(90-phi))**-1\n",
+ "#After further simplifying we get\n",
+ "Y=180-(alpha+phi)\n",
+ "Z=sin(Y*pi*180**-1)\n",
+ "Y1=2*phi+90+alpha\n",
+ "Z1=sin(Y1*pi*180**-1)\n",
+ "R3=W*(Z)*(Z1)**-1 #N\n",
+ "\n",
+ "Y2=90-phi\n",
+ "Z2=sin(Y2*pi*180**-1)\n",
+ "R2=W*Z2*Z1**-1 #N\n",
+ "\n",
+ "#Applying Lamis theorem to the point L\n",
+ "#R1*sin(90+alpha+phi)**-1=R2*sin(90+phi)**-1=P*sin(180-2*phi-alpha)**-1\n",
+ "#After further simplifying we get\n",
+ "Y3=180-(2*phi+alpha)\n",
+ "Z3=sin(Y3*pi*180**-1)\n",
+ "P=Z3*R2*Z2**-1 #N\n",
+ "\n",
+ "\n",
+ "#Result\n",
+ "print\"Minimum Horizontal force be applied on wedge to raise the block is\",round(P,2),\"N\""
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "Minimum Horizontal force be applied on wedge to raise the block is 1418.4 N\n"
+ ]
+ }
+ ],
+ "prompt_number": 24
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 8.30,Page No.277"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "from math import sin, cos, tan, radians, pi\n",
+ "\n",
+ "#Declaration Of Variables\n",
+ "\n",
+ "D=0.1 #m #Diameter\n",
+ "R=0.05 #m #Radius\n",
+ "N=150 #r.p.m \n",
+ "mu=0.05 #Coefficient of friction\n",
+ "W=15*10**3 #N #Load\n",
+ "\n",
+ "#Calculations\n",
+ "\n",
+ "#Power Loast in friction assuming uniform pressure\n",
+ "T=2*3**-1*mu*W*R #N*m\n",
+ "\n",
+ "#Power Lost in Friction\n",
+ "P=2*pi*N*T*60**-1 #W\n",
+ "\n",
+ "#Power Lost in friction assuming wear\n",
+ "T2=0.5*mu*W*R #W\n",
+ "\n",
+ "#Power Lost in friction\n",
+ "P2=2*pi*N*T2*60**-1 #W\n",
+ "\n",
+ "#Result\n",
+ "print\"Power Loast in friction assuming uniform pressure is\",round(P,2),\"W\"\n",
+ "print\"Power Lost in friction assuming wear is\",round(P2,2),\"W\""
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "Power Loast in friction assuming uniform pressure is 392.7 W\n",
+ "Power Lost in friction assuming wear is 294.52 W\n"
+ ]
+ }
+ ],
+ "prompt_number": 5
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 8.31,Page No.282"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "from math import sin, cos, tan, radians, pi\n",
+ "\n",
+ "#Declaration Of Variables\n",
+ "\n",
+ "alpha=60 #Degrees\n",
+ "mu=0.05 #m #coefficient of friction\n",
+ "R=0.15 #m #Radius of shaft\n",
+ "W=20*10**3 #N\n",
+ "N=210 #r.p.m\n",
+ "\n",
+ "\n",
+ "#Calculations\n",
+ "\n",
+ "#Frictional Torque\n",
+ "T=2*3**-1*mu*W*R*(sin(alpha*pi*180**-1))**-1 #N*m\n",
+ "\n",
+ "#Power Lost in Friction for uniform pressure\n",
+ "P=2*pi*N*T*60**-1*10**-3 #KW\n",
+ "\n",
+ "#frictional torque\n",
+ "T2=1*2**-1*mu*W*R*(sin(alpha*pi*180**-1))**-1 #N*m\n",
+ "\n",
+ "#Power Loast in friction for uniform wear\n",
+ "P2=2*pi*N*T2*60**-1*10**-3 #KW\n",
+ "\n",
+ "#Result\n",
+ "print\"Power Lost in Friction assuming:Uniforming pressure\",round(P,2),\"KW\"\n",
+ "print\" :Uniform wear\",round(P2,2),\"KW\""
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "Power Lost in Friction assuming:Uniforming pressure 2.54 KW\n",
+ " :Uniform wear 1.9 KW\n"
+ ]
+ }
+ ],
+ "prompt_number": 6
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 8.32,Page No.283"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "from math import sin, cos, tan, radians, pi\n",
+ "\n",
+ "#Declaration Of Variables\n",
+ "\n",
+ "W=25*10**3 #N #load\n",
+ "alpha=60 #degrees \n",
+ "p=350*10**3 #N/m**2 #pressure\n",
+ "N=180 #r.p.m\n",
+ "mu=0.05 \n",
+ "#r1*2*r2\n",
+ "\n",
+ "#Calculations\n",
+ "\n",
+ "#From Equation of uniform pressure\n",
+ "r2=(W*(pi*p*3)**-1)**0.5 #m\n",
+ "r1=2*r2 #m\n",
+ "\n",
+ "#Frictional Torque\n",
+ "T=2*3**-1*mu*W*(sin(alpha*pi*180**-1))**-1*(r1**3-r2**3)*(r1**2-r2**2)**-1 #m\n",
+ "\n",
+ "#Power absorbed in friction\n",
+ "P=2*pi*N*T*60**-1*10**-3 #KW\n",
+ "\n",
+ "#Result\n",
+ "print\"Power absorbed in friction\",round(P,2),\"KW\""
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "Power absorbed in friction 3.68 KW\n"
+ ]
+ }
+ ],
+ "prompt_number": 27
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 8.33,Page No.286"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "\n",
+ "#Declaration Of Variables\n",
+ "\n",
+ "r1=0.25 #m #External Radius\n",
+ "r2=0.15 #m #Internal Radius\n",
+ "W=50*10**3 #N #Total axial load\n",
+ "mu=0.05 #Coefficient of friction\n",
+ "N=150 #r.p.m\n",
+ "\n",
+ "#Calculations\n",
+ "\n",
+ "#Torque\n",
+ "T=2*3**-1*mu*W*((r1**3-r2**3)*(r1**2-r2**2)**-1) #N*m\n",
+ "\n",
+ "#Power lost in Frction\n",
+ "P=2*pi*N*T*60**-1*10**-3 #KW \n",
+ "\n",
+ "#Result\n",
+ "print\"Power lost in Frction is\",round(P,2),\"KN\""
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "Power lost in Frction is 8.02 KN\n"
+ ]
+ }
+ ],
+ "prompt_number": 28
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 8.34,Page No.287"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "from math import sin, cos, tan, radians, pi\n",
+ "\n",
+ "#Declaration Of Variables\n",
+ "\n",
+ "r1=0.21 #m #External Radius\n",
+ "r2=0.16 #m #Internal Radius\n",
+ "W=60*10**3 #N #Total axial load\n",
+ "mu=0.05 #Coefficient of friction\n",
+ "N=380 #r.p.m\n",
+ "p=350*10**3 #N/m**2 #Intensity of pressure\n",
+ "\n",
+ "#Calculations\n",
+ "\n",
+ "#Power Loast in Overcoming friction\n",
+ "\n",
+ "#Torque\n",
+ "T=2*3**-1*mu*W*((r1**3-r2**3)*(r1**2-r2**2)**-1) #N*m\n",
+ "\n",
+ "P=2*pi*N*T*60**-1*10**-3 #KW \n",
+ "\n",
+ "#Number of collars required\n",
+ "\n",
+ "#Load per collar\n",
+ "W2=p*pi*(r1**2-r2**2)\n",
+ "\n",
+ "n=W*W2**-1\n",
+ "\n",
+ "#Result\n",
+ "print\"Power Loast in Overcoming friction is\",round(P,2),\"KW\"\n",
+ "print\"Number of collars required for the thrust\",round(n,1)"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "Power Loast in Overcoming friction is 22.22 KW\n",
+ "Number of collars required for the thrust 2.9\n"
+ ]
+ }
+ ],
+ "prompt_number": 10
+ }
+ ],
+ "metadata": {}
+ }
+ ]
+}
\ No newline at end of file diff --git a/Engineering_Mechanics/chapter_9.ipynb b/Engineering_Mechanics/chapter_9.ipynb new file mode 100644 index 00000000..73d7ecff --- /dev/null +++ b/Engineering_Mechanics/chapter_9.ipynb @@ -0,0 +1,1623 @@ +{
+ "metadata": {
+ "name": "chapter_9.ipynb"
+ },
+ "nbformat": 3,
+ "nbformat_minor": 0,
+ "worksheets": [
+ {
+ "cells": [
+ {
+ "cell_type": "heading",
+ "level": 1,
+ "metadata": {},
+ "source": [
+ "Chapter 9:Lifting Machines"
+ ]
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 9.1,Page No.295"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "\n",
+ "#Initilization of Variables\n",
+ "\n",
+ "P=100 #N #effort applied\n",
+ "W=900 #N #Lad applied\n",
+ "y=100 #cm #Distance moved by effort\n",
+ "x=10 #cm #Distance moved by load\n",
+ "\n",
+ "#Calculations\n",
+ "\n",
+ "#Mechanical Advantage\n",
+ "MA=W*P**-1 \n",
+ "\n",
+ "#Velocity ratio \n",
+ "VR=y*x**-1 \n",
+ "\n",
+ "#Efficiency\n",
+ "rho=MA*VR**-1*100\n",
+ "\n",
+ "#Result\n",
+ "print\"Mechanical Advantage is\",round(MA,2)\n",
+ "print\"velocity ratio is\",round(VR,2)\n",
+ "print\"Efficiency is\",round(rho,2)"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "Mechanical Advantage is 9.0\n",
+ "velocity ratio is 10.0\n",
+ "Efficiency is 90.0\n"
+ ]
+ }
+ ],
+ "prompt_number": 1
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 9.2,Page No.296"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "\n",
+ "#Initilization of Variables\n",
+ "\n",
+ "P=500 #N #Effort applied\n",
+ "y=5 #m #Distance moved by effort\n",
+ "x=0.5 #cm #Distance moved by load\n",
+ "rho=0.8 #Efficiency\n",
+ "\n",
+ "#Calculations\n",
+ "\n",
+ "#Load Lifted by machine\n",
+ "W=P*y*rho*(x)**-1 #N\n",
+ "\n",
+ "#Mechanical Advantage\n",
+ "MA=W*P**-1 \n",
+ "\n",
+ "#Velocity ratio\n",
+ "VR=y*x**-1 \n",
+ "\n",
+ "#Result\n",
+ "print\"Load Lifted by the machine is\",round(W,2),\"N\"\n",
+ "print\"Mechanical Advantage is\",round(MA,2)\n",
+ "print\"Velocity ratio is\",round(VR,2)"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "Load Lifted by the machine is 4000.0 N\n",
+ "Mechanical Advantage is 8.0\n",
+ "Velocity ratio is 10.0\n"
+ ]
+ }
+ ],
+ "prompt_number": 2
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 9.3,Page No.297"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "\n",
+ "#Initilization of Variables\n",
+ "\n",
+ "P=20 #N #Actual Effort\n",
+ "W=900 #N #Load Lifted\n",
+ "y=2.40 #m #Distance moved by effort\n",
+ "x=0.04 #m #Distance moved by load\n",
+ "\n",
+ "#Calculations\n",
+ "\n",
+ "#Mechanical Advantage\n",
+ "MA=W*P**-1 \n",
+ "\n",
+ "#Velocity ratio\n",
+ "VR=y*x**-1 \n",
+ "\n",
+ "#Efficiency\n",
+ "rho=MA*VR**-1\n",
+ "\n",
+ "#Ideal Effort required\n",
+ "P1=rho*P \n",
+ "\n",
+ "#Result\n",
+ "print\"Mechanical Advantage is\",round(MA,2)\n",
+ "print\"Velocity ratio is\",round(VR,2)\n",
+ "print\"Efficiency is\",round(rho,2)\n",
+ "print\"Ideal Effort is\",round(P1,2)"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "Mechanical Advantage is 45.0\n",
+ "Velocity ratio is 60.0\n",
+ "Efficiency is 0.75\n",
+ "Ideal Effort is 15.0\n"
+ ]
+ }
+ ],
+ "prompt_number": 3
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 9.4,Page No.297"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "\n",
+ "#Initilization of Variables\n",
+ "\n",
+ "rho=0.7 #eifficiency\n",
+ "P=10 #N #Effort\n",
+ "W=500 #N #Load\n",
+ "\n",
+ "#Calculations\n",
+ "\n",
+ "#Mechanical Advantage\n",
+ "MA=W*P**-1 \n",
+ "\n",
+ "#Velocity ratio\n",
+ "VR=MA*rho**-1\n",
+ "\n",
+ "#Result\n",
+ "print\"Mechanical Advantage is\",round(MA,2)\n",
+ "print\"Velocity ratio is\",round(VR,2)"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "Mechanical Advantage is 50.0\n",
+ "Velocity ratio is 71.43\n"
+ ]
+ }
+ ],
+ "prompt_number": 4
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 9.5,Page No.299"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "\n",
+ "#Initilization of Variables\n",
+ "\n",
+ "P1=15 #N #Effort\n",
+ "W1=770 # #Load\n",
+ "rho=0.60 #Efficiency\n",
+ "\n",
+ "P2=25 #N \n",
+ "W2=1320\n",
+ "\n",
+ "P=15 #N \n",
+ "W=500 #N\n",
+ "\n",
+ "#Calculations\n",
+ "\n",
+ "#First Case\n",
+ "\n",
+ "#Mechanical Advantage\n",
+ "MA=W1*P1**-1 \n",
+ "\n",
+ "#Velocity ratio\n",
+ "VR=MA*rho**-1 \n",
+ "\n",
+ "#Second case\n",
+ "\n",
+ "#Mechanical Advantage\n",
+ "MA2=W2*P2**-1 \n",
+ "\n",
+ "#Efficiency\n",
+ "rho2=MA2*VR**-1*100\n",
+ "\n",
+ "#Third case\n",
+ "\n",
+ "#from LAw of machine\n",
+ "#P=m*W+C ................1\n",
+ "\n",
+ "#Equation 2\n",
+ "#P2=W2*m+C ...............2\n",
+ "\n",
+ "#Subtracting equation 2 from 1 we get\n",
+ "m=10*550**-1\n",
+ "\n",
+ "#Constacnt value \n",
+ "C=P2-W2*m\n",
+ "\n",
+ "#Sub value C in equation 1 we get\n",
+ "P3=m*W+C #N\n",
+ "\n",
+ "#MAx Mechanical advantage\n",
+ "MA_max=1*m**-1\n",
+ "\n",
+ "#MAx Efficiency \n",
+ "rho_max=1*(m*VR)**-1*100\n",
+ "\n",
+ "#Result\n",
+ "print\"Mechanical Advantage is\",round(MA,2)\n",
+ "print\"Velocity Ratio is\",round(VR,2)\n",
+ "print\"Efficiency is\",round(rho2,2),\"%\"\n",
+ "print\"Effort Required to raise the Load 500 N\",round(P3,2),\"N\"\n",
+ "print\"MAx Mechanical Advantage is\",round(MA_max,2)\n",
+ "print\"MAx Efficiency is\",round(rho_max,2)"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "Mechanical Advantage is 51.33\n",
+ "Velocity Ratio is 85.56\n",
+ "Efficiency is 61.71 %\n",
+ "Effort Required to raise the Load 500 N 10.09 N\n",
+ "MAx Mechanical Advantage is 55.0\n",
+ "MAx Efficiency is 64.29\n"
+ ]
+ }
+ ],
+ "prompt_number": 5
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 9.6,Page No.301"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "\n",
+ "#Initilization of Variables\n",
+ "\n",
+ "#Effort\n",
+ "P1=15.5 #N\n",
+ "P2=19.5 #N\n",
+ "\n",
+ "#Loads\n",
+ "W1=100 #N\n",
+ "W2=90 #N\n",
+ "\n",
+ "m=0.2\n",
+ "\n",
+ "#Calculations\n",
+ "\n",
+ "#Law of machine equation \n",
+ "#P=m*W+C \n",
+ "\n",
+ "#Equations\n",
+ "#P1=m*W1+C ................1\n",
+ "#P2=m*W2+C ....................2\n",
+ "\n",
+ "#sub value of m in equation 1 weget\n",
+ "C=P1-m*W1\n",
+ "\n",
+ "#Effort required to lift a Load\n",
+ "P1=m*W1+C\n",
+ "\n",
+ "#MEchanical advantage\n",
+ "MA=1*m**-1\n",
+ "\n",
+ "#Result\n",
+ "print\"Effort required to Lift a Load of 100 N\",round(P1,2),\"N\"\n",
+ "print\"MAx MEchanical Advantage is\",round(MA,2)"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "Effort required to Lift a Load of 100 N 15.5 N\n",
+ "MAx MEchanical Advantage is 5.0\n"
+ ]
+ }
+ ],
+ "prompt_number": 6
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 9.7,Page No.303"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "\n",
+ "#Initilization of Variables\n",
+ "\n",
+ "rho=0.8 #Efficiency\n",
+ "P=15 #N #Effort\n",
+ "W=130 #N #Load\n",
+ "\n",
+ "#Calculations\n",
+ "\n",
+ "#Velocity ratio\n",
+ "VR=W*(P*rho)**-1 \n",
+ "\n",
+ "#Frictional force in terms of machine in tems of effort\n",
+ "Fp=P-W*VR**-1 #N\n",
+ "\n",
+ "#Frictional Force of the machine in terms of Load\n",
+ "Fw=P*VR-W #N\n",
+ "\n",
+ "#Result\n",
+ "print\"Velocity ratio is\",round(VR,2)\n",
+ "print\"Frictional force in terms of machine in tems of effort\",round(Fp,2),\"N\"\n",
+ "print\"Frictional Force of the machine in terms of Load is\",round(Fw,2),\"N\""
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "Velocity ratio is 10.83\n",
+ "Frictional force in terms of machine in tems of effort 3.0 N\n",
+ "Frictional Force of the machine in terms of Load is 32.5 N\n"
+ ]
+ }
+ ],
+ "prompt_number": 7
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 9.8,Page No.303"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "\n",
+ "#Initilization of Variables\n",
+ "\n",
+ "VR=15 #Velocity ratio\n",
+ "rho=0.6 #Efficiency\n",
+ "W=100 #N #Load Lifted\n",
+ "\n",
+ "#Calculations\n",
+ "\n",
+ "#Power\n",
+ "P=W*(VR*rho)**-1 #N\n",
+ "\n",
+ "#Frictional Force\n",
+ "Fp=P-(W*VR**-1) #N\n",
+ "\n",
+ "#Let C=Fp\n",
+ "C=Fp\n",
+ "\n",
+ "#From law of machine,we get\n",
+ "#P=m*W+C\n",
+ "#After sub values and furter simplifying we get\n",
+ "m=(P-C)*W**-1\n",
+ "\n",
+ "#After sub values in above equaion we get law of machine as\n",
+ "#P2=m*W2+c #N\n",
+ "\n",
+ "#when W2=140 #N\n",
+ "W2=140 #N\n",
+ "P2=m*W2+C #N\n",
+ "\n",
+ "#When W3=0\n",
+ "W3=0 #N\n",
+ "P3=m*W3+C #N\n",
+ "\n",
+ "#Result\n",
+ "print\"Effort required to run the machine at Load:W2=140 is\",round(P2,2),\"N\"\n",
+ "print\"Effort required to run the machine at Load:W3=0 is\",round(P3,2),\"N\""
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "Effort required to run the machine at Load:W2=140 is 13.78 N\n",
+ "Effort required to run the machine at Load:W3=0 is 4.44 N\n"
+ ]
+ }
+ ],
+ "prompt_number": 8
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 9.9,Page No.304"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "\n",
+ "#Initilization of Variables\n",
+ "\n",
+ "P=12 #N #Effort\n",
+ "VR=18 #Velocity ratio\n",
+ "rho=0.6 #efficiency\n",
+ "\n",
+ "#Calculations\n",
+ "\n",
+ "#Load lifted\n",
+ "W=rho*P*VR #N\n",
+ "\n",
+ "#LEt C=Fp\n",
+ "Fp=P-(W*VR**-1) #N\n",
+ "C=Fp\n",
+ "\n",
+ "#From law of machine we get\n",
+ "m=(P-C)*W**-1 #N\n",
+ "\n",
+ "#Sub value of m in equation we get\n",
+ "#P2=1*18**-1*W2+C\n",
+ "\n",
+ "#Sub W2=90\n",
+ "W2=90 \n",
+ "P2=m*W2+C\n",
+ "\n",
+ "\n",
+ "#Result\n",
+ "print\"Effort required to run the machine is\",round(P2,2),\"N\""
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "Effort required to run the machine is 9.8 N\n"
+ ]
+ }
+ ],
+ "prompt_number": 9
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 9.10,Page No.305"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "\n",
+ "#Initilization of Variables\n",
+ "\n",
+ "VR=10 #Velocity ratio\n",
+ "P=100 #N #Effort applied\n",
+ "Fp=20 #N #effort lost in friction\n",
+ "\n",
+ "#Calculations\n",
+ "\n",
+ "#Load Lifted\n",
+ "W=(P-Fp)*VR #N\n",
+ "\n",
+ "#Efficiency\n",
+ "rho=W*P**-1*VR**-1*100 \n",
+ "\n",
+ "#Result\n",
+ "print\"Load Lifted is\",round(W,2),\"N\"\n",
+ "print\"Efficiency is\",round(rho,2),\"%\""
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "Load Lifted is 800.0 N\n",
+ "Efficiency is 80.0 %\n"
+ ]
+ }
+ ],
+ "prompt_number": 10
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 9.11,Page No.305"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "\n",
+ "#Initilization of Variables\n",
+ "P=40 #N #Effort applied\n",
+ "W=600 #N #Load Lifted\n",
+ "VR=20 #Velocity ratio\n",
+ "\n",
+ "#Calculations\n",
+ "\n",
+ "#MAchine Fiction in terms of effort\n",
+ "Fp=P-W*VR**-1 #N\n",
+ "\n",
+ "#M/c Friction in terms of Load\n",
+ "Fw=P*VR-W #N\n",
+ "\n",
+ "#efficiency\n",
+ "rho=W*P**-1*VR**-1*100\n",
+ "\n",
+ "#Result\n",
+ "print\"MAchine Fiction in terms of effort is\",round(Fp,2),\"N\"\n",
+ "print\"M/c Friction in terms of Load is\",round(Fw,2),\"N\"\n",
+ "print\"Ffficiency of the machine is\",round(rho,2),\"%\""
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "MAchine Fiction in terms of effort is 10.0 N\n",
+ "M/c Friction in terms of Load is 200.0 N\n",
+ "Ffficiency of the machine is 75.0 %\n"
+ ]
+ }
+ ],
+ "prompt_number": 11
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 9.12,Page No.306"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "\n",
+ "#Initilization of Variables\n",
+ "P=15 #N #Effort applied\n",
+ "W=200 #N #Load Lifted\n",
+ "VR=40 #Velocity ratio\n",
+ "\n",
+ "#Calculations\n",
+ "\n",
+ "#Efficiency\n",
+ "rho=W*P**-1*VR**-1 #%\n",
+ "\n",
+ "#Friction Load of m/c \n",
+ "Fw=P*VR-W #N\n",
+ "\n",
+ "#Result\n",
+ "print\"Friction Load of m/c is\",round(Fw,2),\"N\""
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "Friction Load of m/c is 400.0 N\n"
+ ]
+ }
+ ],
+ "prompt_number": 12
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 9.13,Page No.307"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "\n",
+ "#Initilization of Variables\n",
+ "\n",
+ "W=48 #N #Weight\n",
+ "P=16 #N #Force\n",
+ "D=400 #mm #Diameter of wheel\n",
+ "d=100 #mm #Diameter of axle\n",
+ "\n",
+ "#Calculations\n",
+ "\n",
+ "#Mechanical Advantage\n",
+ "MA=W*P**-1 \n",
+ "\n",
+ "#Velocity ratio\n",
+ "VR=D*d**-1 \n",
+ "\n",
+ "#Efficiency of the machine\n",
+ "rho=MA*VR**-1*100 #%\n",
+ "\n",
+ "#Result\n",
+ "print\"Mechanical Advantage is\",round(MA,2)\n",
+ "print\"Velocity ratio is\",round(VR,2)\n",
+ "print\"Efficiency of the machine is\",round(rho,2),\"%\""
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "Mechanical Advantage is 3.0\n",
+ "Velocity ratio is 4.0\n",
+ "Efficiency of the machine is 75.0 %\n"
+ ]
+ }
+ ],
+ "prompt_number": 13
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 9.14,Page No.309"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "\n",
+ "#Initilization of Variables\n",
+ "\n",
+ "D=25 #cm #Diameter of wheel\n",
+ "d1=10 #cm #LArge dia. of axle\n",
+ "d2=9 #cm #Small Dia. of axle\n",
+ "P=30 #N #Effort applied\n",
+ "W=900 #N #Load Lifted\n",
+ "\n",
+ "#Calculations\n",
+ "\n",
+ "#Velocity ratio\n",
+ "VR=2*D*(d1-d2)**-1 \n",
+ "\n",
+ "#Mechanical advantage\n",
+ "MA=W*P**-1 \n",
+ "\n",
+ "#Efficiency\n",
+ "rho=MA*VR**-1*100\n",
+ "\n",
+ "#Result\n",
+ "print\"Velocity ratio is\",round(VR,2)\n",
+ "print\"Mechanical advantage is\",round(MA,2)\n",
+ "print\"Efficiency is\",round(rho,2),\"%\""
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "Velocity ratio is 50.0\n",
+ "Mechanical advantage is 30.0\n",
+ "Efficiency is 60.0 %\n"
+ ]
+ }
+ ],
+ "prompt_number": 14
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 9.15,Page No.310"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "\n",
+ "#Initilization of Variables\n",
+ "\n",
+ "T=60 #No. of teeth on worm wheel\n",
+ "L=12.5 #cm #Radius of effort wheel\n",
+ "r=6.25 #cm #Radius of Load drum\n",
+ "P=20 #N #Effort\n",
+ "W=600 #N #Load\n",
+ "\n",
+ "#Calculations\n",
+ "\n",
+ "#Velocity ratio\n",
+ "VR=L*T*r**-1 \n",
+ "\n",
+ "#Efficiency\n",
+ "rho=W*P**-1*VR**-1*100\n",
+ "\n",
+ "#Result\n",
+ "print\"Velocity ratio for single threaded worm is\",round(VR,2)\n",
+ "print\"Efficiency of the worm is\",round(rho,2),\"%\""
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "Velocity ratio for single threaded worm is 120.0\n",
+ "Efficiency of the worm is 25.0 %\n"
+ ]
+ }
+ ],
+ "prompt_number": 15
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 9.16,Page No.312"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "\n",
+ "#Initilization of Variables\n",
+ "\n",
+ "T1=10 #No.of teeth on pinion\n",
+ "T2=100 #No.of teeth on spur wheel\n",
+ "D=30 #cm #Dia. of Load axle\n",
+ "L=30 #cm #Length of lever\n",
+ "P=20 #N #Effort applied\n",
+ "W=360 #N #Load Lifted\n",
+ "\n",
+ "#Calculations\n",
+ "\n",
+ "#Velocity ratio\n",
+ "VR=2*L*T2*(D*T1)**-1\n",
+ "\n",
+ "#Efficiency\n",
+ "rho=W*P**-1*VR**-1*100\n",
+ "\n",
+ "#Result\n",
+ "print\"Velocity ratio is\",round(VR,2)\n",
+ "print\"Efficinecy is\",round(rho,2),\"%\""
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "Velocity ratio is 20.0\n",
+ "Efficinecy is 90.0 %\n"
+ ]
+ }
+ ],
+ "prompt_number": 16
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 9.17,Page No.314"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "\n",
+ "#Initilization of Variables\n",
+ "\n",
+ "P=40 #N #Effort\n",
+ "rho=0.5 #Efficincy\n",
+ "D=20 #cm #Dia. of load axle\n",
+ "L=80 #cm #Length of Lever\n",
+ "T1=10 #No. of teeth om pinion of effort axle\n",
+ "T2=100 #No. of teeth on spur wheel of intermediate axle\n",
+ "T3=20 #No. of teeth om pinion of Load axle\n",
+ "T4=200 #No. of teeth on spur wheel of load axle\n",
+ "\n",
+ "#Calculations\n",
+ "\n",
+ "#Velocity ratio\n",
+ "VR=2*L*D**-1*T2*T1**-1*T4*T3**-1 \n",
+ "\n",
+ "#Mechanical Advatnage\n",
+ "MA=rho*VR\n",
+ "\n",
+ "#Load Which can be Lifted\n",
+ "W=MA*P*10**-3 #N\n",
+ "\n",
+ "#Result\n",
+ "print\"Velocity ratio is\",round(VR,2)\n",
+ "print\"Load Which can be Lifted is\",round(W,2),\"KN\""
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "Velocity ratio is 800.0\n",
+ "Load Which can be Lifted is 16.0 KN\n"
+ ]
+ }
+ ],
+ "prompt_number": 17
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 9.17(A),Page No.315"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "\n",
+ "#Initilization of Variables\n",
+ "\n",
+ "rho=0.4 #Efficincy\n",
+ "D=20 #cm #Dia. of load axle\n",
+ "L=40 #cm #Length of Lever\n",
+ "T1=15 #No. of teeth om pinion of effort axle\n",
+ "T2=45 #No. of teeth on spur wheel of intermediate axle\n",
+ "T3=20 #No. of teeth om pinion of Load axle\n",
+ "T4=40 #No. of teeth on spur wheel of load axle\n",
+ "W=250 #N #Load Lifted\n",
+ "\n",
+ "#Calculations\n",
+ "\n",
+ "#Velocity ratio\n",
+ "VR=VR=2*L*D**-1*T2*T1**-1*T4*T3**-1 \n",
+ "\n",
+ "#Effort applied\n",
+ "P=W*(rho*VR)**-1 #N\n",
+ "\n",
+ "#Result\n",
+ "print\"Effort applied at the end is\",round(P,2),\"N\""
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "Effort applied at the end is 26.04 N\n"
+ ]
+ }
+ ],
+ "prompt_number": 18
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 9.18,Page No.318"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "\n",
+ "#Initilization of Variables\n",
+ "\n",
+ "n=4 #No. of movable pulleys\n",
+ "W=1440 #N #Load\n",
+ "P=100 #N #effort\n",
+ "\n",
+ "#Calculations\n",
+ "\n",
+ "#Mechanical Advantage\n",
+ "MA=W*P**-1 \n",
+ "\n",
+ "#Velocity ratio\n",
+ "VR=2**4\n",
+ "\n",
+ "#Efficiency\n",
+ "rho=MA*VR**-1*100 #%\n",
+ "\n",
+ "#Ideal Effort\n",
+ "P2=W*VR**-1\n",
+ "\n",
+ "#Effort wsted in friction\n",
+ "P3=P-P2 #N\n",
+ "\n",
+ "#Load WAsted in friction\n",
+ "W2=VR*P\n",
+ "\n",
+ "W3=W2-W\n",
+ "\n",
+ "#Result\n",
+ "print\"Efficiency of the machine is,\",round(rho,2),\"%\"\n",
+ "print\"Effort Wasted in friction is\",round(P3,2),\"N\"\n",
+ "print\"Load Wasted in friction is\",round(W3,2),\"N\""
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "Efficiency of the machine is, 90.0 %\n",
+ "Effort Wasted in friction is 10.0 N\n",
+ "Load Wasted in friction is 160.0 N\n"
+ ]
+ }
+ ],
+ "prompt_number": 19
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 9.19,Page No.320"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "\n",
+ "#Initilization of Variables\n",
+ "\n",
+ "W=2000 #N #Weight\n",
+ "P=600 #Effort\n",
+ "n=5 #Total No. of pulleys\n",
+ "VR=n \n",
+ "\n",
+ "#Calculations\n",
+ "\n",
+ "#Mechanical advantage\n",
+ "MA=W*P**-1\n",
+ "\n",
+ "#efficiency\n",
+ "rho=MA*VR**-1*100\n",
+ "\n",
+ "#Result\n",
+ "print\"Efficiency of the system is\",round(rho,2),\"%\""
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "Efficiency of the system is 66.67 %\n"
+ ]
+ }
+ ],
+ "prompt_number": 20
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 9.20,Page No.321"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "\n",
+ "#Initilization of Variables\n",
+ "\n",
+ "n=4 #No. of pulleys\n",
+ "P=160 #N #Effort\n",
+ "rho=0.75 #efficiency\n",
+ "VR=15 #Velocity ratio\n",
+ "\n",
+ "#Calculations\n",
+ "\n",
+ "#weight Lifted\n",
+ "W=rho*P*VR \n",
+ "\n",
+ "#Result\n",
+ "print\"Weight Lifted is\",round(W,2),\"N\""
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "Weight Lifted is 1800.0 N\n"
+ ]
+ }
+ ],
+ "prompt_number": 21
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 9.21,Page No.323"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "\n",
+ "#Initilization of Variables\n",
+ "\n",
+ "rho=0.5 #Efficency\n",
+ "D=25 #cm #Diameter of Large pulley\n",
+ "d=20 #cm #Dia. of smaller pulley\n",
+ "P=20 #N #Effort applied\n",
+ "\n",
+ "#Calculations\n",
+ "\n",
+ "#Velocity ratio\n",
+ "VR=2*D*(D-d)**-1\n",
+ "\n",
+ "#Load Lifted\n",
+ "W=rho*d*VR #N\n",
+ "\n",
+ "#Result\n",
+ "print\"Load Lifted by the machine is\",round(W,2),\"N\""
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "Load Lifted by the machine is 100.0 N\n"
+ ]
+ }
+ ],
+ "prompt_number": 22
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 9.22,Page No.327"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "\n",
+ "#Initilization of Variables\n",
+ "\n",
+ "W=1500 #Load\n",
+ "L=0.7 #Length of handle\n",
+ "d=0.06 #m #Mean diaof screw jack\n",
+ "p=0.009 #pitch of the screw jack\n",
+ "mu=0.095 #co-efficient of friction\n",
+ "pi=3.14\n",
+ "\n",
+ "#Calculations\n",
+ "\n",
+ "#Effort required\n",
+ "X=(W*d*(2*L)**-1)*(p+mu*pi*d)*(pi*d-p*mu)**-1 #N\n",
+ "\n",
+ "#Effort required at the end of the handle for lowering the load\n",
+ "P2=W*d*(2*L)**-1*(mu*pi*d-p)*(pi*d+mu*p)**-1 #N\n",
+ "\n",
+ "#Result\n",
+ "print\"Effort required at the end of the handle for Lifting Load 1500 N\",round(X,2),\"N\"\n",
+ "print\"Effort required at the end of the handle for lowering the load is\",round(P2,2),\"N\""
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "Effort required at the end of the handle for Lifting Load 1500 N 9.22 N\n",
+ "Effort required at the end of the handle for lowering the load is 3.02 N\n"
+ ]
+ }
+ ],
+ "prompt_number": 23
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 9.23,Page No.328"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "from math import sin, cos, tan, radians, pi\n",
+ "\n",
+ "#Initilization of Variables\n",
+ "\n",
+ "W=3000 #N #Load Lifted\n",
+ "n=2 #No. of square thread\n",
+ "D1=6 #cm #Outer diameter\n",
+ "mu=0.09 #Coefficient offriction\n",
+ "L=0.6 #m #Length\n",
+ "\n",
+ "#Calculations\n",
+ "\n",
+ "#pitch of screw\n",
+ "p=1.2*n**-1*10**-2 #m\n",
+ "\n",
+ "#Thickness of thread\n",
+ "t=0.5*p #\n",
+ "\n",
+ "#Diameter at base of screw\n",
+ "D2=D1-2*t\n",
+ "\n",
+ "#Mean Diameter\n",
+ "d=(D1+D2)*2**-1*10**-2 #m\n",
+ "\n",
+ "#Force \n",
+ "P=W*d*(2*L)**-1*(p+mu*pi*d)*(pi*d-p*mu)**-1 #N\n",
+ "\n",
+ "#Result\n",
+ "print\"Force required at the end of handle is\",round(P,2),\"N\"\n",
+ "\n",
+ "#Answer in textbook is incorrect"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "Force required at the end of handle is 18.32 N\n"
+ ]
+ }
+ ],
+ "prompt_number": 1
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 9.23(A),Page No.328"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "from math import sin, cos, tan, radians, pi\n",
+ "\n",
+ "#Initilization of Variables\n",
+ "\n",
+ "W=5000 #N #Load\n",
+ "n=2\n",
+ "t=0.003 #m #Thickness\n",
+ "D1=0.06 #m #outer diameter\n",
+ "D2=0.054 #m #Inner diameter\n",
+ "d=0.057 #MEan diameter\n",
+ "mu=0.08 #Coefficient of friction\n",
+ "L=0.6 #m #Length\n",
+ "p=0.006 #m #pitch\n",
+ "\n",
+ "#Calculations\n",
+ "\n",
+ "#Let tan(alpha)=X\n",
+ "X=p*(pi*d)**-1\n",
+ "\n",
+ "#Let tan(phi)=Y\n",
+ "Y=mu\n",
+ "\n",
+ "#Force reuired at the end of handle \n",
+ "P=d*(2*L)**-1*W*(X+Y)*(1-X*Y)**-1\n",
+ "\n",
+ "#Result \n",
+ "print\"Force reuired at the end is\",round(P,2),\"N\""
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "Force reuired at the end is 27.03 N\n"
+ ]
+ }
+ ],
+ "prompt_number": 25
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 9.24,Page No.329"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "from math import sin, cos, tan, radians, pi\n",
+ "\n",
+ "#Initilization of Variables\n",
+ "\n",
+ "W=2000 #N #Load Lifted\n",
+ "p=1 #mm #pitch\n",
+ "rho=0.5 #efficiency\n",
+ "L=50 #cm #Length of handle\n",
+ "\n",
+ "#Calculations\n",
+ "\n",
+ "#Velocity ratio\n",
+ "VR=2*pi*L*p**-1\n",
+ "\n",
+ "#Effort applied\n",
+ "P=W*(rho*VR)**-1\n",
+ "\n",
+ "#Result\n",
+ "print\"Effort applied at the end of handle\",round(P,2),\"N\""
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "Effort applied at the end of handle 12.74 N\n"
+ ]
+ }
+ ],
+ "prompt_number": 26
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 9.25,Page No.332"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "from math import sin, cos, tan, radians, pi\n",
+ "\n",
+ "#Initilization of Variables\n",
+ "\n",
+ "rho=0.55 #efficiency\n",
+ "W=1500 #N #Load Lifted\n",
+ "L=0.5 #m #Length of handle\n",
+ "p=0.01 #m #Pitch of the screw\n",
+ "\n",
+ "#Calculations\n",
+ "\n",
+ "#Velocity ratio\n",
+ "VR=2*pi*L*p**-1 \n",
+ "\n",
+ "#Effort applied\n",
+ "P=W*(VR*rho)**-1 #N\n",
+ "\n",
+ "#Result\n",
+ "print\"Effort applied is\",round(P,2),\"N\""
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "Effort applied is 8.69 N\n"
+ ]
+ }
+ ],
+ "prompt_number": 27
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 9.26,Page No.333"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "from math import sin, cos, tan, radians, pi\n",
+ "\n",
+ "#Initilization of Variables\n",
+ "\n",
+ "d=0.075 #m #Mean diameter\n",
+ "p=0.015 #m #Pitch of threads\n",
+ "mu=0.05 #Coefficient of friction\n",
+ "W=600 #N\n",
+ "L=0.36 #m #LEngth\n",
+ "\n",
+ "#Calculations\n",
+ "\n",
+ "#Tangential Force\n",
+ "P=W*d*(2*L)**-1*(p+mu*pi*d)*(pi*d-p*mu)**-1 #N\n",
+ "\n",
+ "#Let Tan(alpha)=X\n",
+ "#tan(phi)=Y\n",
+ "#tan(alpha+phi)=Z\n",
+ "X=p*(pi*d)**-1\n",
+ "Y=mu\n",
+ "Z=(X+Y)*(1-X*Y)**-1\n",
+ "\n",
+ "#efficiency\n",
+ "rho=X*Z**-1 \n",
+ "\n",
+ "#Effort\n",
+ "P2=W*((X-Y)*(1+X*Y)**-1) #N\n",
+ "\n",
+ "#Torque required\n",
+ "T=P2*d*2**-1 #N*m\n",
+ "\n",
+ "#Result\n",
+ "print\"Tangential Force to be qpplied is\",round(P,2),\"N\"\n",
+ "print\"Torque necesscary to lower the load is\",round(T,2),\"Nm\""
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "Tangential Force to be qpplied is 7.13 N\n",
+ "Torque necesscary to lower the load is 0.31 Nm\n"
+ ]
+ }
+ ],
+ "prompt_number": 28
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 9.27,Page No.334"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "from math import sin, cos, tan, radians, pi\n",
+ "\n",
+ "#Initilization of Variables\n",
+ "\n",
+ "d=0.06 #m #Mean diameter\n",
+ "p=0.008 #m P#itch\n",
+ "mu=0.09\n",
+ "W=3 #Load Lifted\n",
+ "x=0.12 #m\n",
+ "n=15 #No. of turns\n",
+ "\n",
+ "#Calculations\n",
+ "\n",
+ "#Let Tan(alpha)=X\n",
+ "#tan(phi)=Y\n",
+ "X=p*(pi*d)**-1\n",
+ "Y=mu\n",
+ "P=W*((X+Y)*(1-X*Y)**-1) #N\n",
+ "\n",
+ "#Torque required\n",
+ "T=P*d*2**-1 #N*m\n",
+ "\n",
+ "#Total Angular displacement\n",
+ "omega=n*2*pi\n",
+ "\n",
+ "#Workk done\n",
+ "W2=omega*T #KNm\n",
+ "\n",
+ "#efficiency\n",
+ "rho=W*x*W2**-1*100 #%\n",
+ "\n",
+ "#Efficiency can also be determined as\n",
+ "rho2=X*(X+Y)**-1*(1-X*Y)*100\n",
+ "\n",
+ "#Result\n",
+ "print\"Torque required is\",round(T,2),\"Nm\"\n",
+ "print\"Work done in lifting the load is\",round(W2,3),\"KN\"\n",
+ "print\"Efficiency of the jack is\",round(rho2,1),\"%\""
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "Torque required is 0.01 Nm\n",
+ "Work done in lifting the load is 1.127 KN\n",
+ "Efficiency of the jack is 31.9 %\n"
+ ]
+ }
+ ],
+ "prompt_number": 29
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 9.28,Page No.336"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "from math import sin, cos, tan, radians, pi\n",
+ "\n",
+ "#Initilization of Variables\n",
+ "\n",
+ "p1=1 #cm #Pitch of Larger screw\n",
+ "p2=0.7 #cm #Pitch of smaller screw\n",
+ "l=36 #cm #Length of handle\n",
+ "rho=0.28 #efficiency\n",
+ "W=5000 #N #Weight\n",
+ "\n",
+ "#Calculations\n",
+ "\n",
+ "#Velocity ratio\n",
+ "VR=2*pi*l*(p1-p2)**-1\n",
+ "\n",
+ "#Effort applied\n",
+ "P=W*(rho*VR)**-1 #N\n",
+ "\n",
+ "#Result\n",
+ "print\"Effort required to Lift the Load\",round(P,2),\"N\" "
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "Effort required to Lift the Load 23.68 N\n"
+ ]
+ }
+ ],
+ "prompt_number": 3
+ }
+ ],
+ "metadata": {}
+ }
+ ]
+}
\ No newline at end of file |