{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "# Chapter 38: Relativity" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Example 38.1: Sample_Problem_1.sce" ] }, { "cell_type": "code", "execution_count": null, "metadata": { "collapsed": true }, "outputs": [], "source": [ "//Given that\n", "r = 0.9990\n", "t = 10 //in years\n", "\n", "//Sample Problem 38-1\n", "printf('**Sample Problem 38-1**\n')\n", "y = 1/sqrt(1-r^2)\n", "tEarth = t*y\n", "T = 2*tEarth\n", "printf('The time as measured from the earth is %1.2fy', T)" ] } , { "cell_type": "markdown", "metadata": {}, "source": [ "## Example 38.2: Sample_Problem_2.sce" ] }, { "cell_type": "code", "execution_count": null, "metadata": { "collapsed": true }, "outputs": [], "source": [ "//Given that\n", "Tl = 0.1237*10^-6 //in sec\n", "c = 3*10^8 //in m/s\n", "r = 0.990\n", "\n", "//Sample Problem 38-2\n", "printf('**Sample Problem 38-2**\n')\n", "y = 1/sqrt(1-r^2)\n", "Tb = Tl*y //in laboratory frame\n", "v = r*c\n", "d = v*Tb\n", "printf('The kaon can go till %dm', d)" ] } , { "cell_type": "markdown", "metadata": {}, "source": [ "## Example 38.3: Sample_Problem_3.sce" ] }, { "cell_type": "code", "execution_count": null, "metadata": { "collapsed": true }, "outputs": [], "source": [ "//Given that\n", "Lp = 230 ///in meter\n", "t = 3.57*10^-6 //in meter\n", "c = 3*10^8 //in m/s\n", "\n", "//Sample Problem 38-3\n", "printf('**Sample Problem 38-3**\n')\n", "//y = 1/sqrt(1-r^2)\n", "//L = Lp/y\n", "//L = r*c*t\n", "//solving -\n", "r = Lp/sqrt((c*t)^2 + Lp^2)\n", "printf('The relative velocoty is equal to %.3fc m/s', r)" ] } , { "cell_type": "markdown", "metadata": {}, "source": [ "## Example 38.4: Sample_Problem_4.sce" ] }, { "cell_type": "code", "execution_count": null, "metadata": { "collapsed": true }, "outputs": [], "source": [ "//Given that\n", "deltaT = 1.10 //in sec\n", "x = 4.00*10^8 //in meter\n", "c = 3*10^8 //in m/s\n", "r = 0.980\n", "\n", "//Sample Problem 38-4\n", "printf('**Sample Problem 38-4**\n')\n", "y = 1/sqrt(1-r^2)\n", "Xe = y*(x - r*c*deltaT)\n", "printf('The distance in earth frame is %1.2em\n', Xe)\n", "Te = y*(deltaT - r*x/c)\n", "printf('The time interval in earth frame is %1.2f', Te)" ] } , { "cell_type": "markdown", "metadata": {}, "source": [ "## Example 38.5: Sample_Problem_5.sce" ] }, { "cell_type": "code", "execution_count": null, "metadata": { "collapsed": true }, "outputs": [], "source": [ "//Given that\n", "lp1 = 499.8*10^-9 //in meter\n", "lp2 = 501.6*10^-9 //in meter\n", "c = 3*10^8 //in m/s\n", "Ms = 1.99*10^30 //in kg\n", "G = 6.67*10^-11 //in SI unit\n", "R = 100 //in light year\n", "conv = 9.46*10^15 //conversion factor from light year to sec\n", "\n", "//Sample Problem 38-5a\n", "printf('**Sample Problem 38-5a**\n')\n", "lo = lp1 + lp2\n", "lo = lo/2\n", "deltaL = abs(lp1 - lo)\n", "v = deltaL/lo * c\n", "printf('The speed of gas relative to us is %1.2em/s\n', v)\n", "\n", "//Sample Problem 38-5b\n", "printf('\n**Sample Problem 38-5b**\n')\n", "//G*M*m/r^2 = m*v^2/r\n", "r = R*conv\n", "M = v^2*r/G\n", "ratio = M/Ms\n", "printf('The mass of galaxy is %1.2e*Ms', ratio)" ] } , { "cell_type": "markdown", "metadata": {}, "source": [ "## Example 38.6: Sample_Problem_6.sce" ] }, { "cell_type": "code", "execution_count": null, "metadata": { "collapsed": true }, "outputs": [], "source": [ "//Given that\n", "K = 2.53 //in Mev\n", "Me = 9.109*10^-31 //in kg\n", "c = 3*10^8 //in m/s\n", "conv = 1.6*10^-19*10^6 //Mev to joule conversion factor\n", "\n", "//Sample Problem 38-6a\n", "printf('**Sample Problem 38-6a**\n')\n", "Eactual = Me*c^2/conv + K\n", "printf('The actual energy of the elctron is %1.2fMev\n', Eactual)\n", "\n", "//Sample Problem 38-6b\n", "printf('\n**Sample Problem 38-6b**\n')\n", "p = sqrt(Eactual^2 - (Me*c^2))\n", "printf('The momentum of the electron is %1.2fMev/c', p)" ] } , { "cell_type": "markdown", "metadata": {}, "source": [ "## Example 38.7: Sample_Problem_7.sce" ] }, { "cell_type": "code", "execution_count": null, "metadata": { "collapsed": true }, "outputs": [], "source": [ "//Given that\n", "K = 3.0*10^20*1.6*10^-19 //in J\n", "Mp = 1.67*10^-27 //in kg\n", "c = 3*10^8 //in m/s\n", "conv = 9.46*10^15 //conversion factor from light year to sec\n", "D = 9.8*10^4 //in light year\n", "\n", "//Sample Problem 38-7a\n", "printf('**Sample Problem 38-7a**\n')\n", "Erm = (Mp*c^2)\n", "y = (K + Erm)/Erm\n", "r = sqrt(1 - (1/y)^2)\n", "printf('The velocity is approximately equal to %1.2f*c\n', r)\n", "\n", "//Sample Problem 38-7b\n", "printf('\n**Sample Problem 38-7b**\n')\n", "deltaT = D //in year\n", "printf('The time taken is %1.1ey\n', deltaT)\n", "\n", "//Sample Problem 38-7c\n", "printf('\n**Sample Problem 38-7c**\n')\n", "deltaTp = deltaT/y * 365*24*3600\n", "printf('The time taken in reference frame of proton is %1.2fs', deltaTp)" ] } ], "metadata": { "kernelspec": { "display_name": "Scilab", "language": "scilab", "name": "scilab" }, "language_info": { "file_extension": ".sce", "help_links": [ { "text": "MetaKernel Magics", "url": "https://github.com/calysto/metakernel/blob/master/metakernel/magics/README.md" } ], "mimetype": "text/x-octave", "name": "scilab", "version": "0.7.1" } }, "nbformat": 4, "nbformat_minor": 0 }