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diff --git a/Principles_of_physics/chapter3.ipynb b/Principles_of_physics/chapter3.ipynb new file mode 100755 index 00000000..e57500e1 --- /dev/null +++ b/Principles_of_physics/chapter3.ipynb @@ -0,0 +1,222 @@ +{
+ "metadata": {
+ "name": "",
+ "signature": "sha256:754c71c2e29646e743d2602122b6349e57c8b539ae4803d803ea41cdce275af3"
+ },
+ "nbformat": 3,
+ "nbformat_minor": 0,
+ "worksheets": [
+ {
+ "cells": [
+ {
+ "cell_type": "heading",
+ "level": 1,
+ "metadata": {},
+ "source": [
+ "Chapter 3 Potential energy"
+ ]
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 3.1 page no 35"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "#given\n",
+ "m=0.04 #Mass of stone in kg\n",
+ "vi=25 #Initial velocity in m/s\n",
+ "vf=0 #Final velocity in m/s\n",
+ "yi=0 #Initial height in m\n",
+ "\n",
+ "#Calculations\n",
+ "import math\n",
+ "Ui=(m*9.81*yi)\n",
+ "Ki=(1/2.0)*m*vi**2\n",
+ "Etotal=(Ui+Ki)\n",
+ "h=(Etotal/(m*9.8))\n",
+ "#when the stone is at (2/3)h, total energy is again same\n",
+ "v=math.sqrt((Etotal-(m*9.8*(2/3.0)*h))/((1/2.0)*m))\n",
+ "\n",
+ "#Output\n",
+ "print\"Maximum height it will reach is \",round(h,1),\"m\" \n",
+ "print\"velocity when it is at the two-third of its maximum height is \",round(v,2),\"m/s\"\n"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "Maximum height it will reach is 31.9 m\n",
+ "velocity when it is at the two-third of its maximum height is 14.43 m/s\n"
+ ]
+ }
+ ],
+ "prompt_number": 3
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 3.2 page no 36"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "#given\n",
+ "m=0.5 #Mass of the sphere in kg\n",
+ "vi=100 #Initial velocity in m/s\n",
+ "vf=20 #Final velocity in m/s\n",
+ "\n",
+ "#Calculations\n",
+ "h=(vi**2-vf**2)/(2.0*9.8)\n",
+ "PE=(m*9.8*h)\n",
+ "\n",
+ "#Calculations\n",
+ "print\"Potential energy of the sphere is \",PE,\"J\"\n"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "Potential energy of the sphere is 2400.0 J\n"
+ ]
+ }
+ ],
+ "prompt_number": 4
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 3.3 page no 36"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "#given\n",
+ "m=0.5 #Mass of the block in kg\n",
+ "x=0.05 #Distance to which block is pulled in m\n",
+ "k=300 #Force constant of the spring in N/m\n",
+ "\n",
+ "#Calculations\n",
+ "import math\n",
+ "U=(1/2.0)*k*x**2\n",
+ "v=x*math.sqrt(k/m)\n",
+ "\n",
+ "#Output\n",
+ "print\"Potential energy of the block when spring is in stretched position is \",U,\"J\" \n",
+ "print\"Velocity of the block when it passes through the equilibrium position is \",round(v,2),\" m/s\"\n"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "Potential energy of the block when spring is in stretched position is 0.375 J\n",
+ "Velocity of the block when it passes through the equilibrium position is 1.22 m/s\n"
+ ]
+ }
+ ],
+ "prompt_number": 5
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 3.4 page no 37"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "#given\n",
+ "l=0.8 #Length of a simple pendulum in m\n",
+ "q=30 #Angle with the vertical through which the bob is released in degrees\n",
+ "q1=10 #Required angle in degrees\n",
+ "\n",
+ "#Calculations\n",
+ "import math\n",
+ "v=math.sqrt(2*9.8*l*(math.cos(q1*3.14/180.0)-math.cos(q*3.14/180.0)))\n",
+ "\n",
+ "#Output\n",
+ "print\"Speed when the bob is at the angle of \",q1,\"degrees with the vertical is \",round(v,2),\"m/s\"\n"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "Speed when the bob is at the angle of 10 degrees with the vertical is 1.36 m/s\n"
+ ]
+ }
+ ],
+ "prompt_number": 7
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 3.5 page no 37"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "#given\n",
+ "m=(9.1*10**-31) #Mass of the electron in kg\n",
+ "v=(3*10**8) #Velocity of light in m/s\n",
+ "c=(1.6*10**-19) #Charge of the electron in coloumbs\n",
+ "\n",
+ "#Calculations\n",
+ "import math\n",
+ "Re=(m*v**2)/(c*10**6)\n",
+ "E=(Re/math.sqrt(1-0.9**2))\n",
+ "\n",
+ "#Output\n",
+ "print\"Rest energy of the electron is \",round(Re,3),\"MeV\" \n",
+ "print\"Total energy is \",round(E,2),\"MeV\"\n"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "Rest energy of the electron is 0.512 MeV\n",
+ "Total energy is 1.17 MeV\n"
+ ]
+ }
+ ],
+ "prompt_number": 8
+ }
+ ],
+ "metadata": {}
+ }
+ ]
+}
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