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   "source": [
    "# Chapter 14 Kinetics of a Particle : Work and Energy"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Ex 14.1 Page No 569"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "UT =  504.7 J\n"
     ]
    }
   ],
   "source": [
    "# Ex 14.1\n",
    "import math\n",
    "from __future__ import division\n",
    "\n",
    "# Variable Declaration\n",
    "P = 400  #[Newtons]\n",
    "s = 2  #[meters]\n",
    "\n",
    "# Calculation\n",
    "# Horizontal Force P\n",
    "UP = round(P*s*math.cos(math.pi*30/180),1)  #[Joules]\n",
    "# Spring force Fs\n",
    "Us = round(-((1/2)*30*2.5**(2)-(1/2)*30*0.5**(2)),1)  #[Joules]\n",
    "# Weight W\n",
    "UW = round(-98.1*(2*math.sin(math.pi*30/180)),1)  #[Joules]\n",
    "# Total Work\n",
    "UT = UP+Us+UW  #[Joules]\n",
    "\n",
    "# Result\n",
    "print\"UT = \",(UT),\"J\""
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Ex 14.2 Page No 574"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "s =  4.0 m\n"
     ]
    }
   ],
   "source": [
    "# Ex 14.2\n",
    "from __future__ import division\n",
    "import math\n",
    "\n",
    "# Variable Declaration\n",
    "uk = 0.5\n",
    "m = 20  #[kilo Newton]\n",
    "\n",
    "# Calculation\n",
    "# Using +ΣFn = 0\n",
    "NA = round(m*math.cos(math.pi*10/180),2)  #[kilo Newtons]\n",
    "FA = uk*NA  #[kilo Newtons]\n",
    "# Principle of Work and Energys\n",
    "s = round((-(1/2)*(m/9.81)*(5**(2)))/(m*math.sin(math.pi*10/180)-9.85),1)  #[meters]\n",
    "           \n",
    "# Result\n",
    "print\"s = \",(s),\"m\""
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Ex 14.3 Page No 575"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "v =  5.47 m/s\n",
      "t =  1.79 s\n"
     ]
    }
   ],
   "source": [
    "# Ex 14.3\n",
    "from __future__ import division\n",
    "from scipy import integrate\n",
    "\n",
    "# Calculation\n",
    "v = round((2.78*3+0.8*3**(3))**(1/2),2)  #[meters per second]\n",
    "x = lambda s : 1/((2.78*s+0.8*s**(3))**(1/2))\n",
    "t = round(integrate.quad(x,0,3)[0],2)  #[seconds]\n",
    " \n",
    "# Result\n",
    "print\"v = \",(v),\"m/s\"\n",
    "print\"t = \",(t),\"s\""
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Ex 14.4 Page No 576"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "h =  0.963 m\n"
     ]
    }
   ],
   "source": [
    "# Ex 14.4\n",
    "from __future__ import division\n",
    "\n",
    "# Calculation\n",
    "# Using Principle of Work and Energy\n",
    "h = round(((-(1/2)*200*(0.6**(2))+(1/2)*200*(0.7**(2)))/(19.62))+0.3,3)  #[meters]\n",
    "\n",
    "# Result\n",
    "print\"h = \",(h),\"m\""
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Ex 14.5 Page No 577"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "thetamax =  42.7 degrees\n"
     ]
    }
   ],
   "source": [
    "# Ex 14.5\n",
    "import math\n",
    "\n",
    "# Calculation\n",
    "thetamax = round(math.degrees(math.acos((9.81+1)/(4.905+9.81))),1)  #[Degrees]\n",
    "\n",
    "# Result\n",
    "print\"thetamax = \",(thetamax),\"degrees\""
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Ex 14.6 Page No 578"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "delta_sB =  0.883 m\n"
     ]
    }
   ],
   "source": [
    "# EX 14.6\n",
    "from __future__ import division\n",
    "\n",
    "# Calculation\n",
    "vA = -4*2  #[meters per second]\n",
    "# Substituting delta_sA = -4*delta_sB\n",
    "delta_sB = round(((1/2)*10*(vA**(2))+(1/2)*100*(2**(2)))/(-4*98.1+981),3)  #[meters]\n",
    "\n",
    "# Result\n",
    "print\"delta_sB = \",(delta_sB),\"m\""
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Ex 14.8 Page No 586"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 39,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "P =  162.0 kW\n"
     ]
    }
   ],
   "source": [
    "# Ex 14.8\n",
    "import math\n",
    "from __future__ import division\n",
    "\n",
    "# Variable Declaration\n",
    "uk = 0.35\n",
    "\n",
    "# Calculation\n",
    "# Using +ΣFy(upward) = 0\n",
    "NC = 19.62  #[kilo Newtons]\n",
    "FC = uk*NC  #[kilo Newtons]\n",
    "v = round(math.sqrt(((1/2)*2000*(25**(2))-6.867*(10**(3))*10)/((1/2)*2000)),2)  #[meters per second]\n",
    "P = round(FC*v,1)  #[kilo Watts]\n",
    "\n",
    "# Result\n",
    "print\"P = \",(P),\"kW\"  # Correction in the answer"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Ex 14.9 Page No 595"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 44,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "T =  148.7 kN\n"
     ]
    }
   ],
   "source": [
    "# Ex 14.9\n",
    "import math\n",
    "\n",
    "# Calculation\n",
    "# Using Principle of Conservation of Energy\n",
    "vB = round(math.sqrt((8000*9.81*20*math.cos(math.pi*15/180)-8000*9.81*20*math.cos(math.pi*60/180))/((1/2)*8000)),1)  #[meters per second]\n",
    "# Using ΣFn = m*an\n",
    "T = 8000*9.81*math.cos(math.pi*15/180)+8000*(13.5**(2))/20  #[Newtons]\n",
    "\n",
    "# Result\n",
    "print\"T = \",round((T/1000),1),\"kN\""
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Ex 14.10 Page No 596"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 47,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "sA =  0.331 m\n"
     ]
    }
   ],
   "source": [
    "# Ex 14.10\n",
    "import numpy as np\n",
    "\n",
    "# Calculation\n",
    "coeff = [13500, -2481, -660.75]\n",
    "# Taking positive root\n",
    "sA = round(np.roots(coeff)[0],3)  #[meters]\n",
    "\n",
    "# Result\n",
    "print\"sA = \",(sA),\"m\""
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Ex 14.11 Page No 597"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 51,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Part(a)\n",
      "vC =  4.39 m/s\n",
      "\n",
      "Part(b)\n",
      "vC =  4.82 m/s\n"
     ]
    }
   ],
   "source": [
    "# Ex 14.11\n",
    "import math\n",
    "from __future__ import division\n",
    "\n",
    "# Calculation\n",
    "# Part(a) Potential Energy\n",
    "vC = round(math.sqrt((-(1/2)*3*(0.5**(2))+2*9.81*1)/((1/2)*2)),2)  #[meters per second]\n",
    "\n",
    "# Result Part(a)\n",
    "print\"Part(a)\"\n",
    "print\"vC = \",(vC),\"m/s\\n\"\n",
    "\n",
    "# Part(b) Conservation of Energy\n",
    "vC = round(math.sqrt(((1/2)*2*(2**(2))-(1/2)*3*(0.5**(2))+2*9.81*1)/((1/2)*2)),2)   #[meters per second]\n",
    "\n",
    "# Result Part(b)\n",
    "print\"Part(b)\"\n",
    "print\"vC = \",(vC),\"m/s\"\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": []
  }
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