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diff --git a/Engineering_Mechanics_by_Tayal_A.K./chapter02_13.ipynb b/Engineering_Mechanics_by_Tayal_A.K./chapter02_13.ipynb new file mode 100644 index 00000000..d55d1267 --- /dev/null +++ b/Engineering_Mechanics_by_Tayal_A.K./chapter02_13.ipynb @@ -0,0 +1,794 @@ +{
+ "metadata": {
+ "name": "chapter02.ipynb"
+ },
+ "nbformat": 3,
+ "nbformat_minor": 0,
+ "worksheets": [
+ {
+ "cells": [
+ {
+ "cell_type": "heading",
+ "level": 1,
+ "metadata": {},
+ "source": [
+ "Chapter 2:Concurrent Forces in A Plane"
+ ]
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 2.2-1, Page No:10"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "\n",
+ "#Initilization of variables\n",
+ "\n",
+ "P=50 #N\n",
+ "Q=100 #N\n",
+ "beta=150 #degree # angle between P & the horizontal\n",
+ "\n",
+ "#Calculations\n",
+ "\n",
+ "R=(P**2+Q**2-(2*P*Q*cos(beta*(pi/180))))**0.5 # using the Trignometric solution\n",
+ "Alpha=(arcsin(((sin(beta*(pi/180))*Q)/R)))*(180/pi)+15 #Angle in degrees\n",
+ "\n",
+ "#Result\n",
+ "print \"The magnitude of resultant is\",round(R,2),\"N\"\n",
+ "print \"The direction of resultant is\",round(Alpha,2),\"degrees\"\n"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "The magnitude of resultant is 145.47 N\n",
+ "The direction of resultant is 35.1 degrees\n"
+ ]
+ }
+ ],
+ "prompt_number": 1
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 2.2-2,Page No:16"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "\n",
+ "#Initilization of variables\n",
+ "\n",
+ "P=50 #N\n",
+ "Q=100 #N\n",
+ "beta=15 #degree # angle between P& the horizontal\n",
+ "theta=45 #degree # angle between the resultant (R) & the horizontal\n",
+ "\n",
+ "#Calculations\n",
+ "\n",
+ "Rx=P*cos(beta*(pi/180))+Q*cos(theta*(pi/180)) #N\n",
+ "Ry=P*sin(beta*(pi/180))+Q*sin(theta*(pi/180)) #N\n",
+ "R=((Rx**2)+(Ry**2))**0.5 #N\n",
+ "alpha=arctan(Ry/Rx)*(180/pi) #degree\n",
+ "\n",
+ "#Results\n",
+ "\n",
+ "print\"The magnitude of the resultant is \",round(R,2),\"N\"\n",
+ "print\"The ange of the resultant with x-axis is\",round(alpha,2),\"degrees\""
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "The magnitude of the resultant is 145.47 N\n",
+ "The ange of the resultant with x-axis is 35.1 degrees\n"
+ ]
+ }
+ ],
+ "prompt_number": 13
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 2.2-4,Page No:19"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "\n",
+ "#Initilization of variables\n",
+ "\n",
+ "Tac=3.5 #kN\n",
+ "Tbc=3.5 #kN\n",
+ "alpha=20 #degree #angle made by Tac with -ve X axis\n",
+ "beta=50 #degree #angle made by Tbc with +ve X axis\n",
+ "\n",
+ "#Calculations\n",
+ "\n",
+ "theta=(arctan(((Tac*sin(alpha*(pi/180)))+(Tbc*sin(beta*(pi/180))))/((Tac*cos(alpha*(pi/180)))-(Tbc*cos(beta*(pi/180))))))*(180/pi) #degree\n",
+ "P=Tac*(cos(alpha*(pi/180))-cos(beta*(pi/180)))/(cos(theta*(pi/180))) #kN # from eq'n 1\n",
+ "\n",
+ "#Results\n",
+ "\n",
+ "print\"The maximum force that can be applied is \",round(P,1),\"kN\"\n",
+ "print\"The direction of applied force is \",round(theta,2),\"degrees\""
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "The maximum force that can be applied is 4.0 kN\n",
+ "The direction of applied force is 75.0 degrees\n"
+ ]
+ }
+ ],
+ "prompt_number": 34
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 2.2-8,Page No:25"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "\n",
+ "#Initilization of variables\n",
+ "\n",
+ "lAB=0.4 #m\n",
+ "lBC=0.3 #m\n",
+ "\n",
+ "#Calculations\n",
+ "\n",
+ "alpha=arctan(lAB/lBC)*(180/pi) #degree\n",
+ "\n",
+ "#Results\n",
+ "\n",
+ "print\"The angle which the force should make with the horizontal to keep the edge AB of the body vertical is \",round(alpha,2),\"degrees\" #here alpha=theta"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "The angle which the force should make with the horizontal to keep the edge AB of the body vertical is 53.13 degrees\n"
+ ]
+ }
+ ],
+ "prompt_number": 37
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 2.2-9,Page No:28"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "\n",
+ "#Initilization of variables\n",
+ "\n",
+ "F=1000 #N\n",
+ "lAB=0.5 #m\n",
+ "lDC=0.25 #m #length of the perpendicular drawn from point C to AB\n",
+ "\n",
+ "#Calculations\n",
+ "\n",
+ "lAC=((0.3)**2+(0.25)**2)**0.5 #m\n",
+ "lBC=((0.20)**2+(0.25)**2)**0.5 #m\n",
+ "Sac=(lAC*F)*(lAB)**-1 #N #by law of concurrent forces\n",
+ "Sbc=(lBC*F)/(lAB) #N #by law of concurrent forces\n",
+ "\n",
+ "#Results\n",
+ "\n",
+ "print\"The axial force in the bar AC(by aw of concurrent forces) is \",round(Sac),\"N\" #the answer in textbook is wrong by 1 N \n",
+ "print\"The axial force in the bar BC(by aw of concurrent forces) is \",round(Sbc),\"N\""
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "The axial force in the bar AC(by aw of concurrent forces) is 781.0 N\n",
+ "The axial force in the bar BC(by aw of concurrent forces) is 640.0 N\n"
+ ]
+ }
+ ],
+ "prompt_number": 5
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 2.2-10,Page No:30"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "#Initilization of variables\n",
+ "\n",
+ "F3=500 #N\n",
+ "alpha=60 #degree #angle made by F3 with F2\n",
+ "beta=40 #degree #angle made by F1 with F3\n",
+ "theta=80 #degree #angle made by F1 with F2\n",
+ "\n",
+ "#Calculations\n",
+ "\n",
+ "# Solving by using law of sines\n",
+ "\n",
+ "F1=(F3*sin(alpha*(pi/180))/sin(theta*(pi/180))) #N #by law of sines\n",
+ "F2=(F3*sin(beta*(pi/180))/sin(theta*(pi/180))) #N #by law of sines\n",
+ "\n",
+ "#Resuts\n",
+ "\n",
+ "print\"The force F1 is \",round(F1,1),\"N\"\n",
+ "print\"The force F2 is \",round(F2,1),\"N\""
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "The force F1 is 439.7 N\n",
+ "The force F2 is 326.4 N\n"
+ ]
+ }
+ ],
+ "prompt_number": 44
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 2.2-11,Page No:31"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "\n",
+ "#Initilization of variables\n",
+ "\n",
+ "P=5000 #N\n",
+ "lAB=5 #m\n",
+ "lOB=1.443 # m\n",
+ "alpha=30 #degree #angle made by force P with the beam\n",
+ "\n",
+ "#Calculations\n",
+ "\n",
+ "theta=arctan(lOB/lAB)*(180/pi) #degree # eq'n 1\n",
+ "Xa=(P*cos(alpha*(pi/180))) #N #using eq'n 4\n",
+ "Ya=Xa*tan(theta*(pi/180)) #N #from eq'n 3 & 4\n",
+ "Rb=(P*sin(alpha*(pi/180)))-Ya # N # substuting value of Ya in eq'n 5\n",
+ "Ra=((Xa**2)+(Ya**2))**0.5 #N\n",
+ "\n",
+ "#Results\n",
+ "\n",
+ "print\"The reaction at support A is \",round(Ra,1),\"N\"\n",
+ "print\"The reaction at support B is \",round(Rb),\"N\""
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "The reaction at support A is 4506.8 N\n",
+ "The reaction at support B is 1250.0 N\n"
+ ]
+ }
+ ],
+ "prompt_number": 46
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 2.2-12,Page No:32"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "\n",
+ "#Initilization of variables\n",
+ "\n",
+ "W=1000 #N\n",
+ "OD=0.4 #m\n",
+ "AD=0.3 #m\n",
+ "AO=0.5 #m #AO=sqrt((0.4)^2+(0.3)^2)\n",
+ "\n",
+ "#Calculations\n",
+ "\n",
+ "Ra=W*AO/OD #N\n",
+ "Rc=W*AD/OD #N\n",
+ "alpha=arctan(OD/AD)*(180/pi) #degree\n",
+ "\n",
+ "#Results\n",
+ "\n",
+ "print\"The reaction at support A is \",round(Ra),\"N\" # answer in textbook is wrong by 50 N\n",
+ "print\"The reaction at support B is \",round(Rc),\"N\"\n",
+ "print\"The angle that Rc makes with horizontal \",round(alpha,1),\"degrees\""
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "The reaction at support A is 1250.0 N\n",
+ "The reaction at support B is 750.0 N\n",
+ "The angle that Rc makes with horizontal 53.1 degrees\n"
+ ]
+ }
+ ],
+ "prompt_number": 7
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 2.2-13,Page No:33"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "\n",
+ "#Initilization of variables\n",
+ "\n",
+ "W=2500 #N #This load acts at point B and C.\n",
+ "alpha=30 #degree # angle made by T1 with +ve y-axis & T2 with +ve x-axis\n",
+ "\n",
+ "#Calculations\n",
+ "\n",
+ "T2=W-(((cos(alpha*(pi/180)))**2/(sin(alpha*(pi/180))))-(sin(alpha*(pi/180)))) # N # substuting eq'n 1 in 2\n",
+ "T1=(T2*cos(30*(pi/180)))/(sin(30*(pi/180)))#N # using eq'n 1\n",
+ "T3=T2 #N # By equilibrium eq'n at point C(sumFx=0)\n",
+ "\n",
+ "#Results\n",
+ "\n",
+ "print\"Tension in portion AB is \",round(T1),\"N\" #due to decimal variance the answer varies by 2.0 N\n",
+ "print\"Tension in portion BC is \",round(T2),\"N\" #due to decimal variance the answer varies by 1.0 N\n",
+ "print\"Tension in portion CD is \",round(T3),\"N\" #due to decimal variance the answer varies by 1.0 N"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "Tension in portion AB is 4328.0 N\n",
+ "Tension in portion BC is 2499.0 N\n",
+ "Tension in portion CD is 2499.0 N\n"
+ ]
+ }
+ ],
+ "prompt_number": 10
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 2.2-15,Page No:35"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "\n",
+ "#Initilization of variables\n",
+ "\n",
+ "d=0.6 #m #diameter of the wheel\n",
+ "r=0.3 #m #radius of the wheel\n",
+ "W=1000 #N #weight of the wheel\n",
+ "h=0.15 #m #height of rectangular block\n",
+ "\n",
+ "#Calculations\n",
+ "\n",
+ "theta=arctan(((h)**0.5)/((d-h)**0.5))\n",
+ "P=(W*tan(theta)) #N # dividing eq'n 1 & 2\n",
+ "\n",
+ "#Resuts\n",
+ "\n",
+ "print\"The force P so that the wheel is just to roll over the block is \",round(P),\"N\""
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "The force P so that the wheel is just to roll over the block is 577.0 N\n"
+ ]
+ }
+ ],
+ "prompt_number": 56
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 2.2-16,Page No:36"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "\n",
+ "#Initilization of variables\n",
+ "\n",
+ "Soa=1000 #N (tension)\n",
+ "alpha=45 #degree #where alpha=(360/8)\n",
+ "theta=67.5 #degree #angle made by bar AO with AB &AH\n",
+ "\n",
+ "#Calcultions\n",
+ "\n",
+ "Sab=Soa*(sin(theta*(pi/180))/sin(alpha*(pi/180))) # N # Using law of sines\n",
+ "Sah=Sab #N\n",
+ "Sob=(Sab*sin((180-2*(theta))*(pi/180)))/sin(theta*(pi/180)) #N\n",
+ "\n",
+ "#Results\n",
+ "\n",
+ "print\"The axial force in the bar AB is \",round(Sab,1),\"N\" #Compression\n",
+ "print\"The axial force in the bar OB is \",round(Sob),\"N\" #Tension"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "The axial force in the bar AB is 1306.6 N\n",
+ "The axial force in the bar OB is 1000.0 N\n"
+ ]
+ }
+ ],
+ "prompt_number": 60
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 2.2-17,Page No:37"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "\n",
+ "#Initilization of variables\n",
+ "\n",
+ "W=500 #N #weight of cylinder\n",
+ "alpha=25 #degree #angle made by OA with horizontal\n",
+ "beta=65 #degree #angle made by OB with horizontal\n",
+ "theta=90 #degree # theta=(alpha+beta)\n",
+ "\n",
+ "#Calculations\n",
+ "\n",
+ "Ra=(W*sin(beta*(pi/180)))/sin(theta*(pi/180)) #N #from equilibrium eq'n\n",
+ "Rb=(W*sin(alpha*(pi/180)))/sin(theta*(pi/180)) #N #from equilibrium eqn's\n",
+ "\n",
+ "#Results\n",
+ "\n",
+ "print\"The reaction at A is \",round(Ra,1),\"N\"\n",
+ "print\"The reaction at B is \",round(Rb,1),\"N\""
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "The reaction at A is 453.2 N\n",
+ "The reaction at B is 211.3 N\n"
+ ]
+ }
+ ],
+ "prompt_number": 62
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 2.2-18,Page No:38"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "\n",
+ "#Initilization of variables\n",
+ "\n",
+ "Wa=1000 #N #weight of sphere A\n",
+ "Wb=400 #N #weight of sphere B\n",
+ "Ra=0.09 #m #radius of sphere A\n",
+ "Rb=0.05 #m #radius of sphere B\n",
+ "theta=33.86 #degree #angle made by Rq with Wb\n",
+ "alpha=60 #degree #angle made by Rl with horizontal\n",
+ "\n",
+ "#Calculations\n",
+ "\n",
+ "Rq=Wb/cos(theta*(pi/180)) #N #using sum Fy=0 for sphere B\n",
+ "Rp=Rq*sin(theta*(pi/180)) #N #using sum Fx=0 for sphere B\n",
+ "Rl=(Rq*sin(theta*(pi/180)))/sin(alpha*(pi/180)) #N #using sum Fx=0 for sphere A\n",
+ "Rn=((Wa)+(Rq*cos(theta*(pi/180)))-(Rl*cos(alpha*(pi/180)))) #N\n",
+ "\n",
+ "#Results\n",
+ "\n",
+ "print\"The reaction at point P is \",round(Rp,1),\"N\"\n",
+ "print\"The reaction at point L is \",round(Rl),\"N\"\n",
+ "print\"The reaction at point N is \",round(Rn,1),\"N\" # the answer in textbook is wrong by 3.2 N"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "The reaction at point P is 268.4 N\n",
+ "The reaction at point L is 310.0 N\n",
+ "The reaction at point N is 1245.0 N\n"
+ ]
+ }
+ ],
+ "prompt_number": 65
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 2.2-19,Page No:39"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "\n",
+ "#Initilization of variables\n",
+ "\n",
+ "P=50 #N\n",
+ "Q=100 #N\n",
+ "alpha=30 #degree #angle made by Rq with +ve Y-axis\n",
+ "\n",
+ "#Calculations\n",
+ "\n",
+ "theta_r=arctan((P*((cos(alpha*(pi/180)))/(sin(alpha*(pi/180))))-Q*tan(alpha*(pi/180)))/(P+Q)) #radians\n",
+ "theta=theta_r*(180/pi)\n",
+ "T=Q/(cos(theta*(pi/180))*(cos(alpha*(pi/180)))/(sin(alpha*(pi/180)))-sin(theta*(pi/180))) #N\n",
+ "\n",
+ "#Results\n",
+ "print\"The tension in the string is \",round(T,1),\"N\"\n",
+ "print\"The angle wich the string makes with the horizontal when the system is in equilibrium is \",round(theta,1),\"degrees\" \n",
+ "#Note:The decimal accuracy in python causes discrepancy in answers"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "The tension in the string is 66.1 N\n",
+ "The angle wich the string makes with the horizontal when the system is in equilibrium is 10.9 degrees\n"
+ ]
+ }
+ ],
+ "prompt_number": 4
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 2.2-20,Page No:41"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "\n",
+ "#Initilization of variables\n",
+ "\n",
+ "theta1=50.5 #degree #is the angle made between BC & and BE\n",
+ "theta2=36.87 #degree #is te angle ade between BA &BE \n",
+ "g=9.81 #m/s^2\n",
+ "Wa=15*g #N\n",
+ "Wb=40*g #N\n",
+ "Wc=20*g #N\n",
+ "\n",
+ "#Calculations\n",
+ "\n",
+ "R2=Wc/(sin(theta1*(pi/180))) #N #from F.B.D of cylinder C(sum Fy=0)\n",
+ "R4=(Wb+R2*sin(theta1*(pi/180)))/sin(theta2*(pi/180)) #N #from F.B.D of cylinder B(sum Fy=0)\n",
+ "R6=R4*cos(theta2*(pi/180)) #N #from F.B.D of cylinder A(sum Fx=0)\n",
+ "\n",
+ "#Results\n",
+ "\n",
+ "print\"The reaction between the cylinder A and the wall of the channel is \",round(R6,2),\"N\""
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "The reaction between the cylinder A and the wall of the channel is 784.8 N\n"
+ ]
+ }
+ ],
+ "prompt_number": 70
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 2.2-21,Page No:50"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "\n",
+ "#Initilazation of variables\n",
+ "\n",
+ "F=1000 #N\n",
+ "theta=30 #degree #angle made by the force with the beam AB\n",
+ "Lab=3 #m\n",
+ "Lae=2 #m\n",
+ "Lce=1 #m\n",
+ "\n",
+ "#Calculations\n",
+ "\n",
+ "Re=(F*Lab*sin(theta*(pi/180)))/Lae #N #Taking moment at A\n",
+ "Rd=(Re*Lce)/(Lab*sin(theta*(pi/180))) #N #Taking moment about C\n",
+ "\n",
+ "#Results\n",
+ "\n",
+ "print\"The reaction at D due to force of 1000 N acting at B is \",round(Rd,2),\"N\""
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "The reaction at D due to force of 1000 N acting at B is 500.0 N\n"
+ ]
+ }
+ ],
+ "prompt_number": 71
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 2.2-23,Page No:51"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "\n",
+ "#Initilization of variables\n",
+ "\n",
+ "W=1000 #N\n",
+ "r=0.30 #m #radius of the wheel\n",
+ "h=0.15 #m #height of the obstacle\n",
+ "\n",
+ "#Calculations\n",
+ "\n",
+ "theta=arcsin(1)*(180/pi) #degree #P is mini when sin(theta)=1 from eq'n of P\n",
+ "Pmini=(W*((2*r*h)-(h**2))**0.5)/(r*sin(theta*(pi/180))) #N\n",
+ "\n",
+ "#Results\n",
+ "\n",
+ "print\"The least force required to just turn the wheel over the block is \",round(Pmini),\"N\"\n",
+ "print\"The angle wich should be made by Pmini with AC is \",round(theta,2),\"degrees\""
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "The least force required to just turn the wheel over the block is 866.0 N\n",
+ "The angle wich should be made by Pmini with AC is 90.0 degrees\n"
+ ]
+ }
+ ],
+ "prompt_number": 2
+ }
+ ],
+ "metadata": {}
+ }
+ ]
+}
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