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diff --git a/Engineering_Mechanics,_Schaum_Series_by_McLean/chapter14_4.ipynb b/Engineering_Mechanics,_Schaum_Series_by_McLean/chapter14_4.ipynb new file mode 100755 index 00000000..c04236af --- /dev/null +++ b/Engineering_Mechanics,_Schaum_Series_by_McLean/chapter14_4.ipynb @@ -0,0 +1,772 @@ +{
+ "metadata": {
+ "name": "chapter14.ipynb"
+ },
+ "nbformat": 3,
+ "nbformat_minor": 0,
+ "worksheets": [
+ {
+ "cells": [
+ {
+ "cell_type": "heading",
+ "level": 1,
+ "metadata": {},
+ "source": [
+ "Chapter 14: Kinematics of a Rigid Body in Plane Motion"
+ ]
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 14.14-2, Page no 265"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "\n",
+ "#Initilization of variables\n",
+ "d=500 #mm\n",
+ "wo=0 #rpm\n",
+ "w=300 #rpm\n",
+ "t=20 #s\n",
+ "t1=2 #s\n",
+ "\n",
+ "#Calculations\n",
+ "alpha=(2*pi*(60**-1)*(w-wo))/t #rad/s**2\n",
+ "w1=wo+alpha*t1 #rad/s\n",
+ "v=(d*(2*1000)**-1)*w1 #m/s\n",
+ "a_n=(d*(2*1000)**-1)*w1**2 #m/s**2\n",
+ "a_t=(d*(2*1000)**-1)*alpha #m/s**2\n",
+ "a=(a_n**2+a_t**2)**0.5 #m/s**2\n",
+ "theta=arccos(a_n/a)*(180/pi) #degrees\n",
+ "\n",
+ "#Result\n",
+ "print'The computed values are:'\n",
+ "print'alpha=',round(alpha,2),\"rad/s**2\"\n",
+ "print'w1=',round(w1,2),\"rad/s\"\n",
+ "print'v=',round(v,3),\"m/s\"\n",
+ "print'a=',round(a,2),\"m/s**2\"\n",
+ "print'theta=',round(theta,1),\"degrees\"\n",
+ "\n",
+ "# The answers may wary in decimal points."
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "The computed values are:\n",
+ "alpha= 1.57 rad/s**2\n",
+ "w1= 3.14 rad/s\n",
+ "v= 0.785 m/s\n",
+ "a= 2.5 m/s**2\n",
+ "theta= 9.0 degrees\n"
+ ]
+ }
+ ],
+ "prompt_number": 9
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 14.14-3, Page no 266"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "\n",
+ "#Initilization of variables\n",
+ "s_BC=2 #m\n",
+ "s_C=2.5 #m\n",
+ "\n",
+ "#Calculations\n",
+ "s_B=(s_BC**2+s_C**2)**0.5 #m\n",
+ "theta=arctan(s_BC*s_C**-1)*(180/pi) #degrees\n",
+ "\n",
+ "#Result\n",
+ "print'The absolute displacement is',round(s_B,1),\"m\",'and the angle made by the vector is',round(theta,1),\"degrees.\" \n"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "The absolute displacement is 3.2 m and the angle made by the vector is 38.7 degrees.\n"
+ ]
+ }
+ ],
+ "prompt_number": 10
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 14.14-4, Page no 266"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "import numpy as np\n",
+ "\n",
+ "#Initilization of variables\n",
+ "V_A=20 #mi/h\n",
+ "V_B=70 #mi/h\n",
+ "# as theta1=60 degrees,\n",
+ "sintheta1=sqrt(3)*2**-1\n",
+ "costheta1=2**-1\n",
+ "# also phi=45 degrees, thus\n",
+ "sinphi=sqrt(2)**-1\n",
+ "cosphi=sqrt(2)**-1\n",
+ "\n",
+ "#Result\n",
+ "#Vector's in matrix form\n",
+ "v_A=np.array([-V_A*cosphi,V_A*sinphi]) #mi/h\n",
+ "v_B=np.array([V_B*costheta1,V_B*sintheta1]) #mi/h\n",
+ "a=v_A[0]+v_B[0] #mi/h\n",
+ "b=v_A[1]+v_B[1] #mi/h\n",
+ "v_ab=(a**2+b**2)**0.5 #mi/h\n",
+ "theta=arctan(b/a)*(180/pi) #degrees\n",
+ "#The relative velocity v_ba is just different in sign while the magnitude stays the same\n",
+ "\n",
+ "#Resul\n",
+ "print'The relative velocity is',round(v_ab,1),\"mi/h\",'making an angle',round(theta,1),\"degrees\"\n",
+ "\n",
+ "# The ans may wary due to decimal point descrepancy."
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "The relative velocity is 77.6 mi/h making an angle 74.4 degrees\n"
+ ]
+ }
+ ],
+ "prompt_number": 11
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 14.14-9, Page no 271"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "\n",
+ "#Initilization of variables\n",
+ "l=2.5 #m\n",
+ "v_A=4 #m/s\n",
+ "a_A=5 #m/s**2\n",
+ "theta=30 #degrees\n",
+ "\n",
+ "#Calculations\n",
+ "#Vector triangle yields v_a.b=2.93 m/s\n",
+ "v_ab=2.93 #m/s\n",
+ "w=v_ab*l**-1 #rad/s (clockwise)\n",
+ "#Ploygon yields alpha_a/b=2.75 m/s**2\n",
+ "alpha_ab=2.75 #m/s**2\n",
+ "alpha=alpha_ab*l**-1 #rad/s**2 (counterclockwise)\n",
+ "\n",
+ "#Result\n",
+ "print'The value of angular velocity is',round(w,2),\"rad/s\"\n",
+ "print'The value of angular acceleration is',round(alpha,1),\"rad/s**2\"\n"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "The value of angular velocity is 1.17 rad/s\n",
+ "The value of angular acceleration is 1.1 rad/s**2\n"
+ ]
+ }
+ ],
+ "prompt_number": 14
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 14.14-10, Page no 272"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "\n",
+ "#Initilization of variables\n",
+ "w=(2*pi*120)/60 #rad/s\n",
+ "l=24 #in\n",
+ "l_c=4 #in\n",
+ "# as th=30 degrees,\n",
+ "sinth=2**-1\n",
+ "\n",
+ "#Calculations\n",
+ "v=(l_c*12**-1)*w #ft/s\n",
+ "betaa=arcsin((l_c*sinth)/l)*(180/pi) #degrees\n",
+ "# betaa yeilds 4.8 degrees, thus value of cosbetaa is,\n",
+ "cosbetaa=0.996\n",
+ "theta=60-betaa #degrees\n",
+ "# here theta yeilds 55.2 degrees, thus value of costheta is,\n",
+ "costheta=0.57\n",
+ "#Component of velocity along connecting rod is \n",
+ "v1=v*costheta #ft/s\n",
+ "v_p=v1/cosbetaa #ft/s\n",
+ "\n",
+ "#Result\n",
+ "print'The absoulte velocity is',round(v_p,2),\"ft/s\"\n"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "The absoulte velocity is 2.4 ft/s\n"
+ ]
+ }
+ ],
+ "prompt_number": 29
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 14.14-13, Page no 274"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "\n",
+ "#Initilization of variables\n",
+ "v_pc=3.68 #ft/s\n",
+ "l=2 #ft\n",
+ "\n",
+ "#Calculations\n",
+ "w=v_pc/l #rad/s counterclockwise\n",
+ "\n",
+ "#Result\n",
+ "print'The angular velocity is',round(w,2),\"rad/s\"\n"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "The angular velocity is 1.84 rad/s\n"
+ ]
+ }
+ ],
+ "prompt_number": 30
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 14.14-14, Page no 274"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "\n",
+ "#This problem is a combination of numerical and graphical solution\n",
+ "#The program only deals with the numerical solution parts the rest can be verified by graphical solution\n",
+ "#Initilization of variables\n",
+ "r=4*12**-1 #ft\n",
+ "w=4*pi #rad/s\n",
+ "l=2 #ft\n",
+ "w2=1.84 #rad/s\n",
+ "\n",
+ "#Calculations\n",
+ "ac_n=r*w**2 #ft/s**2\n",
+ "a_pc_n=l*w2**2 #ft/s**2\n",
+ "\n",
+ "#Result\n",
+ "print'The value of ac_n is',round(ac_n,1),\"ft/s**2\"\n",
+ "print'The value of a_pc_n is',round(a_pc_n,2),\"ft/s**2\"\n"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "The value of ac_n is 52.6 ft/s**2\n",
+ "The value of a_pc_n is 6.77 ft/s**2\n"
+ ]
+ }
+ ],
+ "prompt_number": 31
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 14.14-15, Page no 275"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "\n",
+ "#Initilization of variables\n",
+ "w_bc=10 #rad/s\n",
+ "AB=250 #mm\n",
+ "BC=150 #mm\n",
+ "AC=179 #mm\n",
+ "AD=200 #mm\n",
+ "# as theta1=45 degrees,\n",
+ "sintheta1=(2**0.5)**-1\n",
+ "costheta1=(2**0.5)**-1\n",
+ "\n",
+ "#Calculations\n",
+ "v_c=(BC*1000**-1)*w_bc #m/s\n",
+ "AC=((AB**2+BC**2)-(2*AB*BC*costheta1))**0.5 #m\n",
+ "betaa=arcsin((BC*sintheta1)/AC)*(180/pi) #degrees\n",
+ "gammaa=arcsin((AB*sintheta1)/AC)*(180/pi)#degrees answer in the textbook is incorrect\n",
+ "ang=60-betaa #degrees\n",
+ "# ang yeilds 23.7 degrees, thus\n",
+ "sinang=0.40056\n",
+ "cosang=0.916\n",
+ "CD=sqrt(AD**2+AC**2-(2*AD*AC*cosang)) #mm\n",
+ "D=arcsin((AC*sinang)/CD)*(180/pi) #degrees\n",
+ "# D yeilds 63.2 degrees,thus\n",
+ "sinD=0.8925\n",
+ "theta=arcsin((AD*sinD)/AC)*(180/pi) #degrees\n",
+ "n=360-(theta+gammaa+90) #degrees\n",
+ "# n yeilds 101.8 degrees, thus \n",
+ "cosn=-0.2045\n",
+ "v_cd=v_c*cosn #m/s\n",
+ "delta=180-(90+D) #degrees\n",
+ "# Delts yeilds 26.8 degrees, thus\n",
+ "cosdelta=0.8925\n",
+ "v_D=v_cd/cosdelta #m/s\n",
+ "w_AD=v_D/(AD*1000**-1) #rad/s\n",
+ "\n",
+ "#Result\n",
+ "print'The angular Velocity of AD is',round(w_AD,2),\"rad/s clockwise.\" #Negative sign indicates clockwise orientation \n",
+ "#Answer in the textbook is incorrect\n"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "The angular Velocity of AD is -1.72 rad/s clockwise.\n"
+ ]
+ }
+ ],
+ "prompt_number": 47
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 14.14-18, Page No 277"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "\n",
+ "#Initilization of variables\n",
+ "# as theta1=73.9 degrees,theta2=60 degrees and theta3=46.1 degrees\n",
+ "sintheta1=0.96\n",
+ "sintheta2=sqrt(3)*2**-1\n",
+ "sintheta3=0.72\n",
+ "V=900 #mm/s\n",
+ "\n",
+ "#Calculations\n",
+ "BC=((350*350)+(86.6*86.6))**0.5 #mm\n",
+ "CD=400 #mm\n",
+ "v_cb=(V*sintheta2)/(sintheta1) #mm/s\n",
+ "v_c=((V*sintheta3))/(sintheta1) #mm/s\n",
+ "w_dc=v_c/CD #rad/s\n",
+ "w_bc=v_cb/BC #rad/s\n",
+ "\n",
+ "#Result\n",
+ "print'The angular velocities are: w_dc=',round(w_dc,2),\"rad/s\",'and w_bc=',round(w_bc,2),\"rad/s\"\n"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "The angular velocities are: w_dc= 1.69 rad/s and w_bc= 2.25 rad/s\n"
+ ]
+ }
+ ],
+ "prompt_number": 78
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 14.14-19, Page No 278"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "import numpy as np\n",
+ "\n",
+ "#Calculations\n",
+ "#After equating the i and j terms we obtain simplified equations\n",
+ "#Solving by matrix method\n",
+ "A=np.array([[346,86.7],[200,-350]])\n",
+ "B=np.array([[-3700],[-1790]]) \n",
+ "C=np.linalg.solve(A,B)\n",
+ "\n",
+ "#Result\n",
+ "print'The angular accelerations are alpha_DC=',round(C[0],3),\"rad/s**2\",'and alpha_BC=',round(C[1],2),\"rad/s**2\" \n",
+ "#The signs only indicate that the originally assumed orientations are incorrect and are opposite to those assumed\n"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "The angular accelerations are alpha_DC= -10.475 rad/s**2 and alpha_BC= -0.87 rad/s**2\n"
+ ]
+ }
+ ],
+ "prompt_number": 80
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 14.14-20, Page No 279"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "\n",
+ "#Initilization of variables\n",
+ "d=3 #m\n",
+ "w=8 #rad/s (clockwise)\n",
+ "alpha=4 #rad/s**2 (counterclockwise)\n",
+ "r=d*2**-1 #m\n",
+ "\n",
+ "#Calculations\n",
+ "vo=r*w #m/s\n",
+ "ao=r*alpha #m/s**2\n",
+ "#Here OB is r\n",
+ "OB=r #m\n",
+ "v_bo=OB*w #m/s\n",
+ "v_B=v_bo+vo #m/s\n",
+ "#Also\n",
+ "a_bo=r*alpha #m/s**2 (directed left)\n",
+ "a_bo_n=r*w**2 #m/s**2\n",
+ "a_h=ao+a_bo #m/s**2\n",
+ "a_v=a_bo_n #m/s**2\n",
+ "a_B=((a_h**2)+(a_v**2))**0.5 #m/s**2\n",
+ "phi=arctan(a_h/a_v)*(180/pi) #degrees\n",
+ "\n",
+ "#Result\n",
+ "print'The linear velocity at B is',round(v_B),\"m/s\",'and the acceleration is',round(a_B,1),\"m/s**2\",'making an angle of',round(phi,2),\"degrees with horizontal\"\n"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "The linear velocity at B is 24.0 m/s and the acceleration is 96.7 m/s**2 making an angle of 7.13 degrees with horizontal\n"
+ ]
+ }
+ ],
+ "prompt_number": 96
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 14.14-21, Page No 281"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "\n",
+ "#Initilization of variables\n",
+ "OA=0.6 #m\n",
+ "w=8 #rad/s\n",
+ "# as theta=30 degrees,\n",
+ "sintheta=2**-1\n",
+ "costheta=(3**0.5)*2**-1\n",
+ "v_O=12 #m/s\n",
+ "alpha=4 #rad/s**2\n",
+ "a_O=6 #m/s**2\n",
+ "\n",
+ "#Calculations\n",
+ "#Velocity Calculations\n",
+ "v_AO=OA*w #m/s\n",
+ "v_Ah=v_AO*sintheta+v_O #m/s horizontal component\n",
+ "v_Av=v_AO*costheta #m/s\n",
+ "v_A=((v_Ah**2)+(v_Av**2))**0.5 #m/s\n",
+ "phi=arctan(v_Av/v_Ah)*(180/pi) #degrees\n",
+ "#Acceleration Calculations\n",
+ "a_AOt=OA*alpha #m/s**2\n",
+ "a_AOn=OA*w**2 #m/s**2\n",
+ "a_Ah=-a_O-a_AOn*costheta-a_AOt*sintheta #m/s**2\n",
+ "a_Av=-a_AOn*sintheta+a_AOt*costheta #m/s**2\n",
+ "a_A=((a_Ah**2)+(a_Av**2))**0.5 #m/s**2\n",
+ "phi2=arctan(a_Av*a_Ah**-1)*(180/pi) #degrees\n",
+ "\n",
+ "#Result\n",
+ "print'The velocity is',round(v_A),\"m/s\",'making an angle of',round(phi,1),\"degrees with horizontal.\"\n",
+ "print'The acceleration is',round(a_A),\"m/s**2\",'making an angle of',round(phi2,1),\"degrees with horizontal\"\n"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "The velocity is 15.0 m/s making an angle of 16.1 degrees with horizontal.\n",
+ "The acceleration is 44.0 m/s**2 making an angle of 22.9 degrees with horizontal\n"
+ ]
+ }
+ ],
+ "prompt_number": 100
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 14.14-22, Page No 282"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "\n",
+ "#Initilization of variables\n",
+ "AL=5 #ft\n",
+ "d=10 #ft displacement\n",
+ "\n",
+ "#Calculations\n",
+ "theta=d/AL #radians\n",
+ "s_o=3*theta#ft\n",
+ "\n",
+ "#Result\n",
+ "print'The displacement So is',round(s_o),\"ft\"\n"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "The displacement So is 6.0 ft\n"
+ ]
+ }
+ ],
+ "prompt_number": 101
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 14.14-23, Page No 283"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "\n",
+ "#Initilization of variables\n",
+ "#Speed and acceleration at the center\n",
+ "v=12 #in/s\n",
+ "a=18 #in/s**2\n",
+ "\n",
+ "#Calculations\n",
+ "v_D=((a+v*0.5)*a**-1)*v #in/s\n",
+ "#Speed at point F\n",
+ "v_F=((v/2)*v**-1)*v_D #in/s\n",
+ "#Acceleration at D\n",
+ "a_D=(24/a)*a #in/s**2\n",
+ "#Acceleration at F\n",
+ "a_F=((v/2)*v**-1)*24 #in/s**2\n",
+ "\n",
+ "#Result\n",
+ "print'The velocity and acceleration of weight A are',round(v_F),\"in/s\",'and',round(a_F),\"in/s**2 respectively.\"\n"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "The velocity and acceleration of weight A are 8.0 in/s and 12.0 in/s**2 respectively.\n"
+ ]
+ }
+ ],
+ "prompt_number": 103
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 14.14-24, Page No 283"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "\n",
+ "#Calculations\n",
+ "#Speed and acceleration of D\n",
+ "sD=((18-6)*18**-1)*12 #in/s\n",
+ "aD=(12*18**-1)*18 #in/s**2\n",
+ "#Speed and acceleration of F\n",
+ "sF=(6*12**-1)*8 #in/s\n",
+ "aF=(6*12**-1)*12 #in/s^2\n",
+ "\n",
+ "#Result\n",
+ "print'The velocity and acceleration of weight A are',round(sF),\"in/s\",'and',round(aF),\"in/s**2 respectively.\"\n"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "The velocity and acceleration of weight A are 4.0 in/s and 6.0 in/s**2 respectively.\n"
+ ]
+ }
+ ],
+ "prompt_number": 104
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 14.14-26, Page No 284"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "\n",
+ "#Initilization of variables\n",
+ "v_BG=300 #mm/s\n",
+ "v_G=300 #mm/s\n",
+ "a_BGt=500 #mm/s**2\n",
+ "a_BGn=3600#mm/s**2\n",
+ "a_Gh=500 #mm/s**2\n",
+ "a_Bv=1800 #mm/s**2\n",
+ "\n",
+ "#Calculations\n",
+ "w=((75-25)/25)*6 #rad/s\n",
+ "alpha=((75-25)/25)*10 #rad/s**2\n",
+ "v_B=(v_BG**2+v_G**2)**0.5 #mm/s\n",
+ "a_v=a_Bv-a_BGt #mm/s**2\n",
+ "a_h=a_BGn-a_Gh #mm/s**2\n",
+ "a_B=(a_v**2+a_h**2)**0.5 #mm/s**2\n",
+ "\n",
+ "#Result \n",
+ "print'The velocity and acceleration of point B are',round(v_B),\"mm/s\",'and',round(a_B),\"mm/s**2 respectively.\"\n",
+ "\n",
+ "# The ans for a_B is incorrectin textbook."
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "The velocity and acceleration of point B are 424.0 mm/s and 3362.0 mm/s**2 respectively.\n"
+ ]
+ }
+ ],
+ "prompt_number": 106
+ }
+ ],
+ "metadata": {}
+ }
+ ]
+}
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