{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Chapter 1 - Physics and Engineering"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Example 1 - pg 11"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Percentage Error (percentage) =  4.0\n"
     ]
    }
   ],
   "source": [
    "#calculate the percentage error\n",
    "#Given:\n",
    "l=9.3; # length in cm\n",
    "b=8.5;# breadth in cm\n",
    "h=5.4;# height in cm\n",
    "#calculations\n",
    "V= l*b*h; # Volume in cm**3\n",
    "delta_l = 0.1; delta_b = 0.1; delta_h = 0.1; # scale has a least count = 0.1 cm\n",
    "# absolute error \n",
    "delta_V = (b*h*delta_l + l*h*delta_b +l*b*delta_h); # in cm**3\n",
    "#relative error \n",
    "re = delta_V/V;\n",
    "p= re*100; # Evaluating percentage error\n",
    "#results\n",
    "print \"Percentage Error (percentage) = \",round(p,0)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Example 2 - pg 12"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Percentage error (percentage) =  2.86\n",
      "Result obtained differs from that in textbook, because delta_M walue is taken 0.1 g , instead of 0.2 g as mentioned in the problem statement.\n"
     ]
    }
   ],
   "source": [
    "#calculate the percentage error\n",
    "#Given :\n",
    "M= 10.0; #weight in g\n",
    "V= 5.80;#volume in cm**3\n",
    "#calculations\n",
    "Rho = M/V; # Density in g/cm**3\n",
    "delta_M= 0.2 #  apparatus has a least count of 0.2 g\n",
    "delta_V= 0.05# apparatus has a least count of 0.05 cm**3\n",
    "delta_Rho = (delta_M/V) +((M*delta_V)/V**2);# absolute error in g/cm**3\n",
    "re = delta_Rho/Rho ; #Evaluating Relative Error\n",
    "p = re*100;# Evaluating Percentage Error\n",
    "#results\n",
    "print \"Percentage error (percentage) = \",round(p,2)\n",
    "print'Result obtained differs from that in textbook, because delta_M walue is taken 0.1 g , instead of 0.2 g as mentioned in the problem statement.'\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Example 3 - pg 16"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "(a)Actual Value of c/r ranges between 5.9 - 6.6  and Percentage error = 5.3  percentage. \n",
      "(b)Actual Value of c/r ranges between 6.281 - 6.288 and Percentage error = 0.06  percentage.\n"
     ]
    }
   ],
   "source": [
    "#calculate the Actual val of c/r ranges and percentage error\n",
    "#Given:\n",
    "#(a) \n",
    "import math\n",
    "lc = 0.1# least count in cm\n",
    "c = 6.9 #Circumference c in cm\n",
    "r= 1.1 # radius of circle in cm\n",
    "val =2*math.pi;\n",
    "# Circumference,c= 2*pi*r or  c/r = 2*pi\n",
    "# Error in c/r is , delta(c/r)= [(c/r**2)+(1/r)](LC/2) , LC is Least Count .\n",
    "E= ((c/r**2)+(1./r))*(lc/2.);#Error in c/r is delta(c/r)\n",
    "ob = c/r; # Observed Value\n",
    "#Actual Value of c/r ranges between\n",
    "ac1 = ob-E;# Evaluating Minimum value for c/r \n",
    "ac2 = ob+E;# Evaluating Maximum value for c/r\n",
    "p = (E/ob)*100.; #Evaluating percentage error\n",
    "#results\n",
    "print \"(a)Actual Value of c/r ranges between\",round(ac1,1), \"-\",round(ac2,1),\" and Percentage error =\",round(p,1),\" percentage. \"\n",
    "#(b)\n",
    "lc1 = 0.001;#Now the least count is 0.001 cm\n",
    "c1 = 6.316;#Circumference in cm\n",
    "r1=1.005;#Circle radius in cm \n",
    "E1 =((c1/r1**2) + (1/r1))*(lc1/2); # Error in c/r is delta(c/r)\n",
    "ob1= c1/r1; #Observed Value\n",
    "p1=(E1/ob1)*100.;#Evaluating percentage error\n",
    "#Actual Value of c/r ranges between\n",
    "a1= ob1-E1;#Evaluating Minimum value for c/r\n",
    "a2= ob1+E1;#Evaluating Maximum value for c/r\n",
    "print \"(b)Actual Value of c/r ranges between\",round(a1,3),\"-\",round(a2,3),\"and Percentage error =\",round(p1,2),\" percentage.\"\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Example 4 - pg 17"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "(a) It is is 15.0  percentage lower than the experimental value.\n",
      "(b) It is 0.6 percentage  higher than the experimental value.\n"
     ]
    }
   ],
   "source": [
    "#calculate the percentage lower or higher than experimental value\n",
    "#Given\n",
    "import math\n",
    "# (a) Newton's Theory\n",
    "# v= (P/rho)**2  , P= Pressure , rho = density\n",
    "P = 76.; # 76 cm of Hg pressure\n",
    "V= 330. ; # velocity of sound in m/s\n",
    "rho = 0.001293; # density for dry air at 0 degrees celsius in g/cm**3\n",
    "g = 980.;#gravitational acceleration in cm/s**2\n",
    "#Density of mercury at room temperature is 13.6 g/cm**3 \n",
    "# 1 cm**2 = 1.0*10**-4 m**2\n",
    "#calculations\n",
    "v = math.sqrt(((P*13.6*g)/rho)*10**-4); # velocity of sound in m/s\n",
    "p= ((V-v)/V)*100; # % lower than the experimental value\n",
    "#results\n",
    "print \"(a) It is is\",round(p,0),\" percentage lower than the experimental value.\"\n",
    "\n",
    "# (b) Laplace's Theory \n",
    "# v= ((gama*P)/rho)**2., gamma = adiabatic index Thus,\n",
    "#Given :\n",
    "gama = 1.41 # Adiabatic index\n",
    "#Density of mercury at room temperature is 13.6 g/cm**3 \n",
    "# 1 cm**2 = 1.0*10**-4 m**2\n",
    "v1 = math.sqrt(((gama*P*13.6*g)/rho)*10**-4);# velocity of sound in m/s\n",
    "p1 = ((V-round(v1))/V)*100;# % higher than the eperimental value\n",
    "#results\n",
    "print \"(b) It is\",round(abs(p1),1),\"percentage  higher than the experimental value.\""
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 2",
   "language": "python",
   "name": "python2"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 2
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython2",
   "version": "2.7.9"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 0
}