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 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Chapter 1-INTRODUCTION TO MECHANICS OF SOLIDS "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# example1.1 Page number 10\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      " The resultant velocity : 21.54 km/hour\n",
      "68.2 °\n"
     ]
    }
   ],
   "source": [
    "#downstream direction as x\n",
    "#direction across river as y\n",
    "\n",
    "from math import sqrt,atan,pi\n",
    "\n",
    "#variable declaration\n",
    "\n",
    "Vx= 8                       #velocity of stream, km/hour\n",
    "Vy=float(20)                       #velocity of boat,km/hour\n",
    "\n",
    "V=sqrt(pow(Vx,2)+pow(Vy,2)) #resultant velocity, km/hour\n",
    "theta=Vy/Vx\n",
    "\n",
    "alpha= atan(theta)*180/pi   #angle, degrees     \n",
    "\n",
    "print \" The resultant velocity :\",round(V,2),\"km/hour\"\n",
    "print round(alpha,2),\"°\"\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# example 1.2 Page number 10"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "10.0 KN (to the left)\n",
      "17.32 KN (downward)\n"
     ]
    }
   ],
   "source": [
    "\n",
    "\n",
    "\n",
    "#components of force in horizontal and vertical components. \n",
    "from math import cos,sin,pi\n",
    "#variable declaration\n",
    "\n",
    "F= 20                        #force in wire, KN\n",
    "\n",
    "#calculations\n",
    "Fx= F*cos(60*pi/180)          \n",
    "Fy= F*sin(60*pi/180)\n",
    "\n",
    "print round(Fx,2),\"KN\" ,\"(to the left)\"\n",
    "print round(Fy,2), \"KN\" ,\"(downward)\"\n",
    "\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# example 1.3 Page number 11"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Component normal to the plane : 9.4 KN\n",
      "Component parallel to the plane : 3.42 KN\n"
     ]
    }
   ],
   "source": [
    "\n",
    "\n",
    " #The plane makes an angle of 20° to the horizontal. Hence the normal to the plane makes an angles of 70° to the horizontal i.e., 20° to the vertical\n",
    "from math import cos,sin,pi\n",
    "#variable declaration\n",
    "W= 10                        # black weighing, KN\n",
    "\n",
    "#calculations\n",
    "\n",
    "Nor= W*cos(20*pi/180)             #Component normal to the plane\n",
    "para= W*sin(20*pi/180)            #Component parallel to the plane\n",
    "\n",
    "print \"Component normal to the plane :\",round(Nor,2),\"KN\"\n",
    "print \"Component parallel to the plane :\",round(para,2) , \"KN\"\n",
    "\n",
    "\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# example 1.4 Page number 11"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "F1= 100.0 N\n",
      "F2= 200.0 N\n",
      "theta= 63.9 °\n"
     ]
    }
   ],
   "source": [
    "\n",
    "\n",
    "#Let the magnitude of the smaller force be F. Hence the magnitude of the larger force is 2F\n",
    "\n",
    "from math import pi,sqrt, acos\n",
    "#variable declaration\n",
    "R1=260            #resultant of two forces,N\n",
    "R2=float(180)          #resultant of two forces if larger force is reversed,N\n",
    "\n",
    "\n",
    "\n",
    "#calculations\n",
    "\n",
    "F=sqrt((pow(R1,2)+pow(R2,2))/10)\n",
    "F1=F\n",
    "F2=2*F\n",
    "theta=acos((pow(R1,2)-pow(F1,2)-pow(F2,2))/(2*F1*F2))*180/pi\n",
    "\n",
    "print \"F1=\",F1,\"N\"\n",
    "print  \"F2=\",F2,\"N\"\n",
    "print \"theta=\",round(theta,1),\"°\"\n",
    "\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# example 1.5 Page number 12"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "F1= 326.35 N\n",
      "F2= 223.24 N\n"
     ]
    }
   ],
   "source": [
    "\n",
    "\n",
    "#Let ?ABC be the triangle of forces drawn to some scale\n",
    "#Two forces F1 and F2 are acting at point A\n",
    "#angle in degrees '°'\n",
    "\n",
    "from math import  sin,pi\n",
    "  \n",
    "#variabble declaration\n",
    "cnv=pi/180\n",
    "\n",
    "BAC = 20*cnv                           #Resultant R makes angle with F1    \n",
    " \n",
    "ABC = 130*cnv                    \n",
    "\n",
    "ACB = 30*cnv   \n",
    "\n",
    "R =  500                            #resultant force,N\n",
    "\n",
    "#calculations\n",
    "#sinerule\n",
    "\n",
    "F1=R*sin(ACB)/sin(ABC)\n",
    "F2=R*sin(BAC)/sin(ABC)\n",
    "\n",
    "print \"F1=\",round(F1,2),\"N\"\n",
    "print \"F2=\",round(F2,2),\"N\"\n",
    "\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# example 1.6 Page number 12"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "theta= 78.13 °\n",
      "alpha= 29.29 °\n"
     ]
    }
   ],
   "source": [
    "\n",
    "\n",
    "#Let ABC  be the triangle of forces,'theta' be the angle between F1 and F2, and 'alpha' be the angle between resultant and F1 \n",
    "\n",
    "from math import sin,acos,asin,pi\n",
    "\n",
    "#variable declaration\n",
    "cnv= 180/pi\n",
    "F1=float(400)                         #all forces are in newtons,'N'\n",
    "F2=float(260)\n",
    "R=float(520)\n",
    "\n",
    "#calculations\n",
    "\n",
    "theta=acos((pow(R,2)-pow(F1,2)-pow(F2,2))/(2*F1*F2))*cnv\n",
    "\n",
    "alpha=asin(F2*sin(theta*pi/180)/R)*cnv\n",
    "\n",
    "print\"theta=\",round(theta,2),\"°\"\n",
    "print \"alpha=\",round(alpha,2),\"°\"\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# example 1.7 Page number 13"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "horizontal component= 2814.2 N\n",
      "Vertical component =  1039.2 N\n",
      "Component along crank = 507.1 N\n",
      "Component normal to crank= 2956.8 N\n"
     ]
    }
   ],
   "source": [
    "\n",
    "\n",
    "#The force of 3000 N acts along line AB. Let AB make angle alpha with horizontal.\n",
    "\n",
    "from math import cos,sin,pi,asin,acos\n",
    "\n",
    "#variable declaration\n",
    "F=3000                        #force in newtons,'N'\n",
    "BC=80                         #length of crank BC, 'mm'\n",
    "AB=200                        #length of connecting rod AB ,'mm'\n",
    "theta=60*pi/180               #angle b/w BC & AC\n",
    "\n",
    "#calculations\n",
    "\n",
    "alpha=asin(BC*sin(theta)/200)*180/pi\n",
    "\n",
    "HC=F*cos(alpha*pi/180)                    #Horizontal component \n",
    "VC= F*sin(alpha*pi/180)                   #Vertical component \n",
    "\n",
    "#Components along and normal to crank\n",
    "#The force makes angle alpha + 60  with crank.\n",
    "alpha2=alpha+60\n",
    "CAC=F*cos(alpha2*pi/180)             # Component along crank \n",
    "CNC= F*sin(alpha2*pi/180)             #Component normal to crank \n",
    "\n",
    "\n",
    "print \"horizontal component=\",round(HC,1),\"N\"\n",
    "print \"Vertical component = \",round(VC,1),\"N\"\n",
    "print \"Component along crank =\",round(CAC,1),\"N\"\n",
    "print \"Component normal to crank=\",round(CNC,1),\"N\""
   ]
  }
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