From f270f72badd9c61d48f290c3396004802841b9df Mon Sep 17 00:00:00 2001 From: kinitrupti Date: Fri, 12 May 2017 18:53:46 +0530 Subject: Removed duplicates --- .../AdityaAnand_version_backup/Chapter_8.ipynb | 14 +- .../AdityaAnand_version_backup/Chapter_8_-.ipynb | 390 --------------------- 2 files changed, 7 insertions(+), 397 deletions(-) delete mode 100755 sample_notebooks/AdityaAnand/AdityaAnand_version_backup/Chapter_8_-.ipynb (limited to 'sample_notebooks/AdityaAnand') diff --git a/sample_notebooks/AdityaAnand/AdityaAnand_version_backup/Chapter_8.ipynb b/sample_notebooks/AdityaAnand/AdityaAnand_version_backup/Chapter_8.ipynb index cbd1971a..c08a4250 100755 --- a/sample_notebooks/AdityaAnand/AdityaAnand_version_backup/Chapter_8.ipynb +++ b/sample_notebooks/AdityaAnand/AdityaAnand_version_backup/Chapter_8.ipynb @@ -4,7 +4,7 @@ "cell_type": "markdown", "metadata": {}, "source": [ - "###Example 8.2" + "## Example 8.2 , page : 187" ] }, { @@ -64,7 +64,7 @@ "cell_type": "markdown", "metadata": {}, "source": [ - "###Example 8.3 " + "## Example 8.3 , page : 192" ] }, { @@ -117,7 +117,7 @@ "cell_type": "markdown", "metadata": {}, "source": [ - "###Example 8.4" + "## Example 8.4 , page : 193" ] }, { @@ -170,7 +170,7 @@ "cell_type": "markdown", "metadata": {}, "source": [ - "###Example 8.5 " + "## Example 8.5 , page : 195" ] }, { @@ -225,7 +225,7 @@ "cell_type": "markdown", "metadata": {}, "source": [ - "###Example 8.6" + "## Example 8.6 , page : 195" ] }, { @@ -279,7 +279,7 @@ "cell_type": "markdown", "metadata": {}, "source": [ - "###Example 8.7 " + "## Example 8.7 , page : 195 " ] }, { @@ -322,7 +322,7 @@ "cell_type": "markdown", "metadata": {}, "source": [ - "###Example 8.8 " + "## Example 8.8 , page : 196 " ] }, { diff --git a/sample_notebooks/AdityaAnand/AdityaAnand_version_backup/Chapter_8_-.ipynb b/sample_notebooks/AdityaAnand/AdityaAnand_version_backup/Chapter_8_-.ipynb deleted file mode 100755 index c08a4250..00000000 --- a/sample_notebooks/AdityaAnand/AdityaAnand_version_backup/Chapter_8_-.ipynb +++ /dev/null @@ -1,390 +0,0 @@ -{ - "cells": [ - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "## Example 8.2 , page : 187" - ] - }, - { - "cell_type": "code", - "execution_count": 37, - "metadata": { - "collapsed": false - }, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "(a) The force acting = [0.0, 2.5849394142282115e-26, 0.0] ≈ 0\n", - "(b) The force acting = 2 Gm²\n" - ] - } - ], - "source": [ - "# Importing module\n", - "\n", - "import math\n", - "\n", - "# Variable declaration\n", - "\n", - "G=6.67*pow(10,-11) # Gravitational constant\n", - "m=1 # For convenience,mass is assumed to be unity \n", - "x=30 # The angle between GC and the positive x-axis is 30° and so is the angle between GB and the negative x-axis\n", - "y=math.radians(x) # The angle in radians\n", - "a=math.cos(y)\n", - "b=math.sin(y)\n", - "v1=(0,1,0)\n", - "v2=(-a,-b,0)\n", - "v3=(a,-b,0)\n", - "c=(2*G*pow(m,2))/1 # 2Gm²/1\n", - "\n", - "# Calculation\n", - "\n", - "#(a)\n", - "F1=[y * c for y in v1] # F(GA)\n", - "F2=[y * c for y in v2] # F(GB)\n", - "F3=[y * c for y in v3] # F(GC)\n", - "# From the principle of superposition and the law of vector addition, the resultant gravitational force FR on (2m) is given by\n", - "Fa=[sum(x) for x in zip(F1,F2,F3)]\n", - "\n", - "#(b)\n", - "# By symmetry the x-component of the force cancels out and the y-component survives\n", - "Fb=4-2 # 4Gm² j - 2Gm² j\n", - "\n", - "# Result\n", - "\n", - "print(\"(a) The force acting =\",Fa,\"≈ 0\")\n", - "print(\"(b) The force acting =\",Fb,\"Gm²\")" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "## Example 8.3 , page : 192" - ] - }, - { - "cell_type": "code", - "execution_count": 38, - "metadata": { - "collapsed": false - }, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "Potential energy of a system of four particles = -5.414213562373095 Gm²/l\n", - "The gravitational potential at the centre of the square = -5.65685424949238 Gm²/l\n" - ] - } - ], - "source": [ - "# Importing module\n", - "\n", - "import math\n", - "\n", - "# Variable declaration\n", - "\n", - "G=6.67*pow(10,-11) # Gravitational constant\n", - "m=1 # For convenience,mass is assumed to be unity \n", - "l=1 # For convenience,side of the square is assumed to be unity \n", - "c=(G*pow(m,2))/l\n", - "n=4 # Number of particles\n", - "\n", - "# Calculation\n", - "\n", - "d=math.sqrt(2)\n", - "# If the side of a square is l then the diagonal distance is √2l\n", - "# We have four mass pairs at distance l and two diagonal pairs at distance √2l \n", - "# Since the Potential Energy of a system of four particles is -4Gm²/l) - 2Gm²/dl\n", - "w=(-n-(2/d)) \n", - "# If the side of a square is l then the diagonal distance from the centre to corner is \n", - "# Since the Gravitational Potential at the centre of the square\n", - "u=-n*(2/d)\n", - "\n", - "# Result\n", - "\n", - "print (\"Potential energy of a system of four particles =\",w,\"Gm²/l\")\n", - "print(\"The gravitational potential at the centre of the square =\",u,\"Gm²/l\")" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "## Example 8.4 , page : 193" - ] - }, - { - "cell_type": "code", - "execution_count": 33, - "metadata": { - "collapsed": false - }, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "Minimum speed of the projectile to reach the surface of the second sphere = ( 0.6 GM/R ) ^(1/2)\n" - ] - } - ], - "source": [ - "# Importing module\n", - "\n", - "import math\n", - "\n", - "# Variable declaration\n", - "\n", - "R=1 # For convenience,radii of both the spheres is assumed to be unity \n", - "M=1 # For convenience,mass is assumed to be unity \n", - "m1=M # Mass of the first sphere\n", - "m2=6*M # Mass of the second sphere\n", - "m=1 # Since the mass of the projectile is unknown,take it as unity\n", - "d=6*R # Distance between the centres of both the spheres\n", - "r=1 # The distance from the centre of first sphere to the neutral point N\n", - "\n", - "G=6.67*pow(10,-11) # Gravitational constant\n", - "\n", - "# Calculation\n", - "\n", - "# Since N is the neutral point; GMm/r² = 4GMm/(6R-r)² and we get\n", - "r=2*R\n", - "# The mechanical energy at the surface of M is; Et = m(v^2)/2 - GMm/R - 4GMm/5R\n", - "# The mechanical energy at N is; En = -GMm/2R - 4GMm/4R\n", - "# From the principle of conservation of mechanical energy; Et = En and we get\n", - "v_sqr=2*((4/5)-(1/2))\n", - "\n", - "# Result\n", - "\n", - "print(\"Minimum speed of the projectile to reach the surface of the second sphere =\",\"(\",round(v_sqr,5),\"GM/R\",\")\",\"^(1/2)\")" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "## Example 8.5 , page : 195" - ] - }, - { - "cell_type": "code", - "execution_count": 36, - "metadata": { - "collapsed": false - }, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "(i) Mass of Mars = 6.475139697520706e+23 kg\n", - "(ii) Period of revolution of Mars = 684.0033777694376 days\n" - ] - } - ], - "source": [ - "# Importing module\n", - "\n", - "import math\n", - "\n", - "# Variable declaration\n", - "\n", - "π=3.14 # Constant pi\n", - "G=6.67*pow(10,-11) # Gravitational constant\n", - "R=9.4*pow(10,3) # Orbital radius of Mars in km\n", - "T=459*60\n", - "Te=365 # Period of revolution of Earth\n", - "r=1.52 # Ratio of Rms/Res, where Rms is the mars-sun distance and Res is the earth-sun distance. \n", - "\n", - "# Calculation\n", - "\n", - "# (i) \n", - "R=R*pow(10,3)\n", - "# Using Kepler's 3rd law:T²=4π²(R^3)/GMm\n", - "Mm=(4*pow(π,2)*pow(R,3))/(G*pow(T,2))\n", - "\n", - "# (ii)\n", - "# Using Kepler's 3rd law: Tm²/Te² = (Rms^3/Res^3)\n", - "Tm=pow(r,(3/2))*365\n", - "\n", - "\n", - "# Result\n", - "\n", - "print(\"(i) Mass of Mars =\",Mm,\"kg\")\n", - "print(\"(ii) Period of revolution of Mars =\",Tm,\"days\")" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "## Example 8.6 , page : 195" - ] - }, - { - "cell_type": "code", - "execution_count": 17, - "metadata": { - "collapsed": false - }, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "Mass of the Earth = 5.967906881559221e+24 kg\n", - "Mass of the Earth = 6.017752855396305e+24 kg\n" - ] - } - ], - "source": [ - "# Importing module\n", - "\n", - "import math\n", - "\n", - "# Variable declaration\n", - "\n", - "g=9.81 # Acceleration due to gravity\n", - "G=6.67*pow(10,-11) # Gravitational constant\n", - "Re=6.37*pow(10,6) # Radius of Earth in m\n", - "R=3.84*pow(10,8) # Distance of Moon from Earth in m\n", - "T=27.3 # Period of revolution of Moon in days\n", - "π=3.14 # Constant pi\n", - "\n", - "# Calculation\n", - "\n", - "# I Method\n", - "# Using Newton's 2nd law of motion:g = F/m = GMe/Re²\n", - "Me1=(g*pow(Re,2))/G\n", - "\n", - "# II Method\n", - "# Using Kepler's 3rd law: T²= 4π²(R^3)/GMe\n", - "T1=T*24*60*60\n", - "Me2=(4*pow(π,2)*pow(R,3))/(G*pow(T1,2))\n", - "\n", - "#Result\n", - "\n", - "print(\"Mass of the Earth =\",Me1,\"kg\")\n", - "print(\"Mass of the Earth =\",Me2,\"kg\")" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "## Example 8.7 , page : 195 " - ] - }, - { - "cell_type": "code", - "execution_count": 9, - "metadata": { - "collapsed": false - }, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "Period of revolution of Moon = 27.5 days\n" - ] - } - ], - "source": [ - "# Importing module\n", - "\n", - "import math\n", - "\n", - "# Variable declaration\n", - "\n", - "k=pow(10,-13) # A constant = 4π² / GME\n", - "Re=3.84*pow(10,5) # Distance of the Moon from the Earth in m\n", - "\n", - "# Calculation\n", - "\n", - "k=pow(10,-13)*(pow(1/(24*60*60),2))*(1/pow((1/1000),3))\n", - "T2=k*pow(Re,3)\n", - "T=math.sqrt(T2) # Period of revolution of Moon in days\n", - "\n", - "# Result\n", - "\n", - "print(\"Period of revolution of Moon =\",round(T,1),\"days\")" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "## Example 8.8 , page : 196 " - ] - }, - { - "cell_type": "code", - "execution_count": 1, - "metadata": { - "collapsed": false - }, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "Change in Kinetic Energy = 3124485000.0 J\n", - "Change in Potential Energy = 6248970000.0 J\n" - ] - } - ], - "source": [ - "# Importing module\n", - "\n", - "import math\n", - "\n", - "# Variable declaration\n", - "\n", - "m=400 # Mass of satellite in kg\n", - "Re=6.37*pow(10,6) # Radius of Earth in m\n", - "g=9.81 # Acceleration due to gravity\n", - "\n", - "# Calculation\n", - "\n", - "# Change in energy is E=Ef-Ei\n", - "ΔE=(g*m*Re)/8 # Change in Total energy\n", - "# Since Potential Energy is twice as the change in Total Energy (V = Vf - Vi)\n", - "ΔV=2*ΔE # Change in Potential Energy in J\n", - "\n", - "# Result\n", - "\n", - "print(\"Change in Kinetic Energy =\",round(ΔE,4),\"J\")\n", - "print(\"Change in Potential Energy =\",round(ΔV,4),\"J\")" - ] - } - ], - "metadata": { - "kernelspec": { - "display_name": "Python 3", - "language": "python", - "name": "python3" - }, - "language_info": { - "codemirror_mode": { - "name": "ipython", - "version": 3 - }, - "file_extension": ".py", - "mimetype": "text/x-python", - "name": "python", - "nbconvert_exporter": "python", - "pygments_lexer": "ipython3", - "version": "3.4.3" - } - }, - "nbformat": 4, - "nbformat_minor": 0 -} -- cgit