path: root/Engineering_Mechanics/chapter_18.ipynb

{
 "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": {}
  }
 ]
}