From 6279fa19ac6e2a4087df2e6fe985430ecc2c2d5d Mon Sep 17 00:00:00 2001 From: kinitrupti Date: Fri, 12 May 2017 18:53:46 +0530 Subject: Removed duplicates --- .../Chapter1.ipynb | 621 +++++++++++++++++++++ 1 file changed, 621 insertions(+) create mode 100755 Engineering_Physics_by_Shyam_Singh_and_Rajeev_Singh/Chapter1.ipynb (limited to 'Engineering_Physics_by_Shyam_Singh_and_Rajeev_Singh/Chapter1.ipynb') diff --git a/Engineering_Physics_by_Shyam_Singh_and_Rajeev_Singh/Chapter1.ipynb b/Engineering_Physics_by_Shyam_Singh_and_Rajeev_Singh/Chapter1.ipynb new file mode 100755 index 00000000..10f61da5 --- /dev/null +++ b/Engineering_Physics_by_Shyam_Singh_and_Rajeev_Singh/Chapter1.ipynb @@ -0,0 +1,621 @@ +{ + "metadata": { + "name": "", + "signature": "sha256:2f492bc2a6dad7cae3b696b117670d34888491ec5959ea22de590b83b18e09cd" + }, + "nbformat": 3, + "nbformat_minor": 0, + "worksheets": [ + { + "cells": [ + { + "cell_type": "heading", + "level": 1, + "metadata": {}, + "source": [ + "1: Theory of Relativity" + ] + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example number 1.1, Page number 29" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "#importing modules\n", + "import math\n", + "from __future__ import division\n", + "\n", + "#Variable declaration\n", + "l0 = 50 #length of rocket ship(m)\n", + "l = 49.5 #length observed on ground(m)\n", + "c = 3*10**8 #velocity of light(m/sec)\n", + "\n", + "#Calculation\n", + "#we know that l = l0*math.sqrt(1-((v**2)/(c**2)))\n", + "v = math.sqrt((c**2)*(1-((l/l0)**2))) #speed(m/sec)\n", + "v = v*10**-7;\n", + "v=math.ceil(v*10**3)/10**3; #rounding off to 3 decimals\n", + "\n", + "#Result\n", + "print \"speed of the rocket is\",v, \"*10**7 m/sec\"" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "speed of the rocket is 4.233 *10**7 m/sec\n" + ] + } + ], + "prompt_number": 3 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example number 1.2, Page number 30" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "#importing modules\n", + "import math\n", + "from __future__ import division\n", + "\n", + "#Variable declaration\n", + "l0 = 1; #assume length(m)\n", + "l = (99/100)*l0 #length observed on ground(m)\n", + "c = 1 #assume c = 1\n", + "\n", + "#Calculation\n", + "#we know that l = l0*math.sqrt(1-((v**2)/(c**2)))\n", + "v = math.sqrt((c**2)*(1-((l/l0)**2))) #speed(m/sec)\n", + "v=math.ceil(v*10**4)/10**4; #rounding off to 4 decimals\n", + "\n", + "#Result\n", + "print \"speed of the rocket is\",v,\"c\"\n", + "print \"answer given in the book is wrong\"" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "speed of the rocket is 0.1411 c\n", + "answer given in the book is wrong\n" + ] + } + ], + "prompt_number": 11 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example number 1.3, Page number 30" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "#importing modules\n", + "import math\n", + "from __future__ import division\n", + "\n", + "#Variable declaration\n", + "l0 = 120 #length of spaceship(m)\n", + "c = 1 #assume c = 1\n", + "v = 0.99*c; #speed of spaceship(m/sec)\n", + "\n", + "#Calculation\n", + "l = l0*math.sqrt(1-((v**2)/(c**2))); #length of the observer(m)\n", + "\n", + "#Result\n", + "print \"length of the observer is\",round(l),\"m\"" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "length of the observer is 17.0 m\n" + ] + } + ], + "prompt_number": 14 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example number 1.4, Page number 30 theoretical proof" + ] + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example number 1.5, Page number 31" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "#importing modules\n", + "import math\n", + "from __future__ import division\n", + "\n", + "#Variable declaration\n", + "#surface area of elliptical lamina = 1/2 (area of circular lamina)\n", + "\n", + "#Calculation\n", + "c = 3*10**8; #velocity of light(m/sec)\n", + "#((math.pi*D**2)/4)*math.sqrt(1-(v**2/c**2)) = 1/2*math.pi*D**2/4\n", + "#math.sqrt(1-(v**2/c**2)) = 1/2\n", + "v = c*math.sqrt(1-(1/4)); #velocity(m/sec)\n", + "v = v*10**-8;\n", + "v=math.ceil(v*10)/10; #rounding off to 1 decimal\n", + "\n", + "#Result\n", + "print \"velocity is\",v,\"*10**8 m/sec\"" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "velocity is 2.6 *10**8 m/sec\n" + ] + } + ], + "prompt_number": 18 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example number 1.6, Page number 32" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "#importing modules\n", + "import math\n", + "from __future__ import division\n", + "\n", + "#Variable declaration\n", + "t0 = 2*10**-8; #mean life of meson(sec)\n", + "c = 1; #assume c = 1\n", + "v = 0.8*c; #velocity of meson(m/sec)\n", + "\n", + "#Calculation\n", + "t = t0/math.sqrt(1-(v**2/c**2)); #mean life with a particular velocity\n", + "\n", + "#Result\n", + "print \"mean life of meson with a velocity is\",round(t/1e-8,3),\"*10**-8 sec\"" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "mean life of meson with a velocity is 3.333 *10**-8 sec\n" + ] + } + ], + "prompt_number": 22 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example number 1.7, Page number 32" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "#importing modules\n", + "import math\n", + "from __future__ import division\n", + "\n", + "#Variable declaration\n", + "t0 = 3; #time period of pendulum(sec)\n", + "c = 1; #assume c = 1\n", + "v = 0.95*c; #velocity of observer(m/sec)\n", + "\n", + "#Calculation\n", + "t = t0/math.sqrt(1-(v**2/c**2)); #time period measured by observer(sec)\n", + "t = math.ceil(t*100)/100; #rounding off to 2 decimals\n", + "\n", + "#Result\n", + "print \"time period measured by observer is\",t,\"sec\"" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "time period measured by observer is 9.61 sec\n" + ] + } + ], + "prompt_number": 3 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example number 1.8, Page number 33" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "#importing modules\n", + "import math\n", + "from __future__ import division\n", + "\n", + "#Variable declaration\n", + "t0 = 1; #life time of particle(micro sec)\n", + "v = 2.7*10**8; #velocity of particle(m/sec)\n", + "c = 3*10**8; #velocity of light(m/sec)\n", + "\n", + "#Calculation\n", + "t0 = t0*10**-6; #life time of particle(sec)\n", + "t = t0/math.sqrt(1-(v**2/c**2)); #life time(sec)\n", + "t = round(t/1e-6,1)*10**-6; \n", + "x = v*t; #distance travelled before disintegration(m)\n", + "\n", + "#Result\n", + "print \"life time is\",t,\"sec\"\n", + "print \"distance travelled before disintegration is\",x,\"m\"\n", + "print \"answer for distance given in the book is wrong\"" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "life time is 2.3e-06 sec\n", + "distance travelled before disintegration is 621.0 m\n", + "answer for distance given in the book is wrong\n" + ] + } + ], + "prompt_number": 9 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example number 1.9, Page number 33" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "#importing modules\n", + "import math\n", + "from __future__ import division\n", + "\n", + "#Variable declaration\n", + "c = 1; #assume c = 1\n", + "u = -0.85*c; #speed of B\n", + "v = 0.75*c; #speed of A\n", + "\n", + "#Calculation\n", + "u_dash = (u-v)/(1-(u*v/c**2)); #velocity of B with respect to A\n", + "u_dash = math.ceil(u_dash*10**3)/10**3; #rounding off to 3 decimals\n", + "\n", + "#Result\n", + "print \"velocity of B with respect to A is\",u_dash,\"c\"\n", + "print \"answer given in the book is wrong with respect to sign\"" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "velocity of B with respect to A is -0.977 c\n", + "answer given in the book is wrong with respect to sign\n" + ] + } + ], + "prompt_number": 3 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example number 1.10, Page number 34" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "#importing modules\n", + "import math\n", + "from __future__ import division\n", + "\n", + "#Variable declaration\n", + "c = 1; #assume c = 1\n", + "u_dash = 0.9*c; #velocity of beta particle\n", + "v = 0.25*c; #speed of A\n", + "\n", + "#Calculation\n", + "u = (u_dash+v)/(1+(u_dash*v/c**2)); #speed of beta particle\n", + "u = math.ceil(u*10**2)/10**2; #rounding off to 2 decimals\n", + "\n", + "#Result\n", + "print \"speed of beta particle is\",u,\"c\"" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "speed of beta particle is 0.94 c\n" + ] + } + ], + "prompt_number": 6 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example number 1.11, Page number 34" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "#importing modules\n", + "import math\n", + "from __future__ import division\n", + "\n", + "#Variable declaration\n", + "mp = 1.6*10**-27; #mass of proton(kg)\n", + "me = 9.1*10**-31; #mass of electron(kg)\n", + "c = 3*10**8; #velocity of light(m/sec)\n", + "\n", + "#Calculation\n", + "m0 = me;\n", + "m = mp;\n", + "# we know that m = m0/math.sqrt(1-(v**2/c**2));\n", + "A = (m0/m)**2;\n", + "v_square = (1-A)*(c**2);\n", + "v = math.sqrt(v_square); #speed of electron(m/sec)\n", + "v = v*10**-8;\n", + "v = math.ceil(v*10**7)/10**7; #rounding off to 7 decimals\n", + "\n", + "#Result\n", + "print \"speed of electron is\",v,\"*10**8 m/sec\"" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "speed of electron is 2.9999996 *10**8 m/sec\n" + ] + } + ], + "prompt_number": 18 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example number 1.12, Page number 35" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "#importing modules\n", + "import math\n", + "from __future__ import division\n", + "\n", + "#Variable declaration\n", + "m0 = 1; #assume m0 = 1\n", + "m = 2.25*m0;\n", + "\n", + "#Calculation\n", + "A = (m0/m)**2;\n", + "v_square = (1-A)*(c**2);\n", + "v = math.sqrt(v_square); #speed of a body(m/sec)\n", + "v = v*10**-8;\n", + "v = math.ceil(v*10**3)/10**3; #rounding off to 3 decimals\n", + "\n", + "#Result\n", + "print \"speed of the body is\",v,\"*10**8 m/sec\"" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "speed of electron is 2.688 *10**8 m/sec\n" + ] + } + ], + "prompt_number": 22 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example number 1.13, Page number 35" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "#importing modules\n", + "import math\n", + "from __future__ import division\n", + "\n", + "#Variable declaration\n", + "c = 1; #assume c = 1\n", + "v = 0.99*c; #velocity of electron\n", + "m0 = 9.1*10**-31; #mass(kg)\n", + "\n", + "#Calculation\n", + "m = m0/math.sqrt(1-(v**2/c**2)); #mass of electron(kg)\n", + "m = m*10**31;\n", + "\n", + "#Result\n", + "print \"mass of the electron is\",int(m),\"*10**-31 kg\"" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "mass of the electron is 64 *10**-31 kg\n" + ] + } + ], + "prompt_number": 27 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example number 1.14, Page number 35" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "#importing modules\n", + "import math\n", + "from __future__ import division\n", + "\n", + "#Variable declaration\n" + ], + "language": "python", + "metadata": {}, + "outputs": [], + "prompt_number": 28 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example number 1.15, Page number 36" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "#importing modules\n", + "import math\n", + "from __future__ import division\n", + "\n", + "#Variable declaration" + ], + "language": "python", + "metadata": {}, + "outputs": [], + "prompt_number": 29 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example number 1.16, Page number 37" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "#importing modules\n", + "import math\n", + "from __future__ import division\n", + "\n", + "#Variable declaration" + ], + "language": "python", + "metadata": {}, + "outputs": [], + "prompt_number": 30 + }, + { + "cell_type": "code", + "collapsed": false, + "input": [], + "language": "python", + "metadata": {}, + "outputs": [] + } + ], + "metadata": {} + } + ] +} \ No newline at end of file -- cgit