path: root/Engineering_Mechanics/chapter_17.ipynb

{
 "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": {}
  }
 ]
}