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Diffstat (limited to 'Engineering_Mechanics,_Schaum_Series_by_McLean/chapter2_3.ipynb')
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diff --git a/Engineering_Mechanics,_Schaum_Series_by_McLean/chapter2_3.ipynb b/Engineering_Mechanics,_Schaum_Series_by_McLean/chapter2_3.ipynb new file mode 100755 index 00000000..9a6ee7f9 --- /dev/null +++ b/Engineering_Mechanics,_Schaum_Series_by_McLean/chapter2_3.ipynb @@ -0,0 +1,562 @@ +{
+ "metadata": {
+ "name": "chapter 2.ipynb"
+ },
+ "nbformat": 3,
+ "nbformat_minor": 0,
+ "worksheets": [
+ {
+ "cells": [
+ {
+ "cell_type": "heading",
+ "level": 1,
+ "metadata": {},
+ "source": [
+ "Chapter 2: Operations with Forces"
+ ]
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 2.2-1, Page No: 21"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "\n",
+ "#Initilization of variables\n",
+ "\n",
+ "F=20 #lb\n",
+ "L=4.33 #ft\n",
+ "#Calculation\n",
+ "M=-F*L #lb-ft\n",
+ "\n",
+ "#Result\n",
+ "\n",
+ "print'The moment of force F about O is',round(M,1),\"lb-ft\"\n",
+ "\n"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "The moment of force F about O is -86.6 lb-ft\n"
+ ]
+ }
+ ],
+ "prompt_number": 1
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 2.2-2, Page no: 22"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "\n",
+ "#Initilization of variables\n",
+ "\n",
+ "F=20 #lb\n",
+ "theta=((60*pi)/180) #radians\n",
+ "L=5 #ft\n",
+ "\n",
+ "#Calculations\n",
+ "\n",
+ "F_x=F*cos(theta) #Resloving the vector\n",
+ "F_y=F*sin(theta) #Resloving the vector\n",
+ "M=-F_y*L #Appling Varignon's theorem\n",
+ "#Negative sign tells that moment is clockwise\n",
+ "\n",
+ "#Result\n",
+ "\n",
+ "print'The moment of the force about O is',round(M,1),\"lb-ft\"\n",
+ " "
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "The moment of the force about O is -86.6 lb-ft\n"
+ ]
+ }
+ ],
+ "prompt_number": 2
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 2.2-3,Page No: 22"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "\n",
+ "#Initilization of variables\n",
+ "\n",
+ "F=100 #N\n",
+ "x1=2 #m\n",
+ "x2=5 #m\n",
+ "y1=0 #m\n",
+ "y2=1 #m\n",
+ "z1=4 #m\n",
+ "z2=1 #m\n",
+ "\n",
+ "#Calculations\n",
+ "\n",
+ "xside=(x2-x1) #m\n",
+ "yside=(y2-y1) #m\n",
+ "zside=(z2-z1) #m\n",
+ "LD=sqrt(xside**2+yside**2+zside**2)\n",
+ "Fx=(xside/LD)*F #N\n",
+ "Fy=(yside/LD)*F #N\n",
+ "Fz=(zside/LD)*F #N\n",
+ "Mx=-Fy*z1 #N-m\n",
+ "My=Fx*x1-Fz*z1 #N-m\n",
+ "Mz=Fy*x1 #N-m\n",
+ "\n",
+ "#Result\n",
+ "\n",
+ "print'Fx is',round(Fx,1),\"N\"\n",
+ "print'Fy is',round(Fy,1),\"N\"\n",
+ "print'Fz is',round(Fz,1),\"N\"\n",
+ "print'Moment about X-Axis is',round(Mx,1),\"N.m\"\n",
+ "print'Moment about Y-Axis is +',round(My),\"N.m\"\n",
+ "print'Moment about Z-Axis is +',round(Mz,1),\"N.m\"\n",
+ "\n",
+ "# Decimal point error in calculation causes a small discrepancy in the resulting solutions."
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "Fx is 68.8 N\n",
+ "Fy is 22.9 N\n",
+ "Fz is -68.8 N\n",
+ "Moment about X-Axis is -91.8 N.m\n",
+ "Moment about Y-Axis is + 413.0 N.m\n",
+ "Moment about Z-Axis is + 45.9 N.m\n"
+ ]
+ }
+ ],
+ "prompt_number": 3
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 2.2-4, Page No: 23"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "\n",
+ "#Initilization of variables\n",
+ "\n",
+ "Fx=68.7 #N\n",
+ "Fy=22.9 #N\n",
+ "Fz=-68.7 #N\n",
+ "rx=2 #m\n",
+ "ry=0 #m\n",
+ "rz=4 #m\n",
+ "rx1=5 #m\n",
+ "ry1=1 #m\n",
+ "rz1=1 #m\n",
+ "\n",
+ "#Calculation\n",
+ "\n",
+ "Mx=Fz*ry-Fy*rz #N-m\n",
+ "My=-(Fz*rx-Fx*rz) #N-m\n",
+ "Mz=Fy*rx-Fx*ry #N-m\n",
+ "Mx1=Fz*ry1-Fy*rz1 #N-m\n",
+ "My1=-(Fz*rx1-Fx*rz1) #N-m\n",
+ "Mz1=Fy*rx1-Fx*ry1 #N-m\n",
+ "\n",
+ "#Result\n",
+ "\n",
+ "print'Moment with respect to origin using point(2,0,4)is',round(Mx,1),\"i +\",round(My),\"j +\",round(Mz,1),\"k N.m\"\n",
+ "print'Moment with respect to origin using point (5,1,1) is',round(Mx1,1),\"i +\",round(My1),\"j +\",round(Mz1,1),\"k N.m\"\n"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "Moment with respect to origin using point(2,0,4)is -91.6 i + 412.0 j + 45.8 k N.m\n",
+ "Moment with respect to origin using point (5,1,1) is -91.6 i + 412.0 j + 45.8 k N.m\n"
+ ]
+ }
+ ],
+ "prompt_number": 6
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 2.2-5, Page no: 23"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "\n",
+ "#Initilization of variables\n",
+ "\n",
+ "Fx=2 #lb\n",
+ "Fy=3 #lb\n",
+ "Fz=-1 #lb\n",
+ "rx=1 #ft\n",
+ "ry=-4 #ft\n",
+ "rz=3 #ft\n",
+ "#Coordinates of points\n",
+ "ax=3 #ft\n",
+ "ay=1 #ft\n",
+ "az=1 #ft\n",
+ "bx=3 #ft\n",
+ "by=-1 #ft\n",
+ "bz=1 #ft\n",
+ "cx=2 #ft\n",
+ "cy=5 #ft\n",
+ "cz=-2 #ft\n",
+ "\n",
+ "#Calculations\n",
+ "\n",
+ "Rx=ax-cx #ft\n",
+ "Ry=ay-cy #ft\n",
+ "Rz=az-cz #ft\n",
+ "Mx=(Ry*Fz)-(Rz*Fy) #lb-ft\n",
+ "My=-((Rx*Fz)-(Rz*Fx)) #lb-ft\n",
+ "Mz=(Rx*Fy)-(Ry*Fx) #lb-ft\n",
+ "E_u=sqrt((bx-cx)**2+(by-cy)**2+(bz-cz)**2) #ft\n",
+ "ex=(bx-cx)/E_u #ft\n",
+ "ey=(by-cy)/E_u #ft\n",
+ "ez=(bz-cz)/E_u #ft\n",
+ "M_lx=Mx*ex #lb-ft\n",
+ "M_ly=My*ey #lb-ft\n",
+ "M_lz=Mz*ez #lb-ft\n",
+ "M_l=M_lx+M_ly+M_lz #lb-ft\n",
+ "\n",
+ "#Result\n",
+ "\n",
+ "print'Hence the moment about line is',round(M_l,2),\"lb-ft\"\n"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "Hence the moment about line is -2.06 lb-ft\n"
+ ]
+ }
+ ],
+ "prompt_number": 7
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 2.2-6, Page No: 24"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "\n",
+ "#Initilization of variables\n",
+ "\n",
+ "P_x=22 #N\n",
+ "P_y=23 #N\n",
+ "P_z=7 #N\n",
+ "p1=1 #m\n",
+ "p2=-1 #m\n",
+ "p3=-2 #m\n",
+ "\n",
+ "#Calculations\n",
+ "\n",
+ "Mx=(p2*P_z)-(p3*P_y) #N-m\n",
+ "My=-((p1*P_z)-(p3*P_x)) #N-m\n",
+ "Mz=(p1*P_y)-(p2*P_x) #N-m\n",
+ "\n",
+ "#Result\n",
+ "\n",
+ "print'The moment about the line from the origin is',round(Mx),\"i\",round(My),\"j +\",round(Mz),\"k N.m\"\n"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "The moment about the line from the origin is 39.0 i -51.0 j + 45.0 k N.m\n"
+ ]
+ }
+ ],
+ "prompt_number": 9
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 2.2-8, Page No: 24"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "\n",
+ "#Initilization of variables\n",
+ "\n",
+ "F=10 #N Force couple\n",
+ "a=3 #m Moment arm\n",
+ "#Calculations\n",
+ "C=-F*a #N-m\n",
+ "\n",
+ "#Result\n",
+ "\n",
+ "print'The resultant couple is',round(C),\"N-m\" \n"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "The resultant couple is -30.0 N-m\n"
+ ]
+ }
+ ],
+ "prompt_number": 10
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 2.2-11, Page No: 26"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "\n",
+ "#Initilization of variables\n",
+ "\n",
+ "C1=20 #N-m\n",
+ "C2=40 #N-m\n",
+ "C3=-55 #N-m\n",
+ "\n",
+ "#Calculations\n",
+ "\n",
+ "C=sqrt(C1**2+C2**2+C3**2) #N-m\n",
+ "thetax=C2/C \n",
+ "thetay=C3/C\n",
+ "thetaz=C1/C\n",
+ "Cx=C*thetax #N-m\n",
+ "Cy=C*thetay #N-m\n",
+ "Cz=C*thetaz #N-m\n",
+ "\n",
+ "#Result\n",
+ "\n",
+ "print'Couple in vector notation is',round(Cx),\"i\",round(Cy),\"j +\",round(Cz),\"k N.m\"\n"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "Couple in vector notation is 40.0 i -55.0 j + 20.0 k N.m\n"
+ ]
+ }
+ ],
+ "prompt_number": 11
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 2.2-12,Page No: 26"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "\n",
+ "#Initilization of variables\n",
+ "\n",
+ "F1=25 #lb\n",
+ "F2=25 #lb\n",
+ "L1=14 #in\n",
+ "L2=20 #in\n",
+ "\n",
+ "#Calculations\n",
+ "\n",
+ "C=F1*L1 #lb-in\n",
+ "M=-F2*L2 #lb-in\n",
+ "\n",
+ "#Result\n",
+ "\n",
+ "print'The twisting couple is',round(C),\"lb-in\"\n",
+ "print'The bending moment is',round(M),\"lb-in\"\n"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "The twisting couple is 350.0 lb-in\n",
+ "The bending moment is -500.0 lb-in\n"
+ ]
+ }
+ ],
+ "prompt_number": 12
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 2.2-13, Page No: 27"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "\n",
+ "#Initilization of variables\n",
+ "\n",
+ "rx=20 #in\n",
+ "ry=0 #in\n",
+ "rz=14 #in\n",
+ "Fx=0 #lb\n",
+ "Fy=-25 #lb\n",
+ "Fz=0 #lb\n",
+ "\n",
+ "#Calculation\n",
+ "\n",
+ "Mx=ry*Fz-rz*Fy #lb-in\n",
+ "My=rx*Fz-rz*Fx #lb-in\n",
+ "Mz=rx*Fy-ry*Fx #lb-in\n",
+ "\n",
+ "#Result\n",
+ "\n",
+ "print'The moment of the 25-lb force is',round(Mx),\"i +\",round(My),\"j\",round(Mz),\"k lb-in\"\n",
+ "\n"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "The moment of the 25-lb force is 350.0 i + 0.0 j -500.0 k lb-in\n"
+ ]
+ }
+ ],
+ "prompt_number": 14
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 2.2-14,Page No: 27"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "\n",
+ "#Initilization of variables\n",
+ "\n",
+ "#Co-ordinates with respect to point O\n",
+ "x=17.9 #ft\n",
+ "y=6.91 #ft\n",
+ "z=46.3 #ft\n",
+ "Fz=-4000 #lb\n",
+ "Fy=0 #lb\n",
+ "\n",
+ "#Calculation\n",
+ "\n",
+ "Mx=y*Fz-z*Fy #lb-ft\n",
+ "\n",
+ "#Result\n",
+ "\n",
+ "print'The scalar coefficient of the i term is the moment about the X-Axis is',round(Mx,3),\"lb-ft\"\n",
+ "\n",
+ "# The answer given in the textbook is incorrect"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "The scalar coefficient of the i term is the moment about the X-Axis is -27640.0 lb-ft\n"
+ ]
+ }
+ ],
+ "prompt_number": 16
+ }
+ ],
+ "metadata": {}
+ }
+ ]
+}
\ No newline at end of file |