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diff --git a/Engineering_Physics_by_G_Aruldhas/8-SPECIAL_THEORY_OF_RELATIVITY.ipynb b/Engineering_Physics_by_G_Aruldhas/8-SPECIAL_THEORY_OF_RELATIVITY.ipynb new file mode 100644 index 0000000..07c28ec --- /dev/null +++ b/Engineering_Physics_by_G_Aruldhas/8-SPECIAL_THEORY_OF_RELATIVITY.ipynb @@ -0,0 +1,440 @@ +{ +"cells": [ + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# Chapter 8: SPECIAL THEORY OF RELATIVITY" + ] + }, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 8.10: Rate_of_decreasing_mass_of_sun.sci" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"// Scilab Code Ex8.10: Page-175 (2010)\n", +"c = 3e+008; // Speed of light in vacuum, m/s\n", +"dE = 4e+026; // Energy radiated per second my the sun, J/s\n", +"dm = dE/c^2; // Rate of decrease of mass of sun, kg/s\n", +"printf('\nThe rate of decrease of mass of sun = %4.2e kg/s', dm);\n", +"\n", +"// Result\n", +"// The rate of decrease of mass of sun = 4.44e+009 kg/s" + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 8.11: Relativistic_mass_energy_relation.sci" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"// Scilab Code Ex8.11: Page-175 (2010)\n", +"c = 1; // For simplicity assume speed of light to be unity, m/s\n", +"m0 = 9.1e-031; // Mass of the electron, kg\n", +"E0 = 0.512; // Rest energy of electron, MeV\n", +"T = 10; // Kinetic energy of electron, MeV\n", +"E = T + E0; // Total energy of electron, MeV\n", +"// From Relativistic mass-energy relation\n", +"// E^2 = c^2*p^2 + m0^2*c^4, solving for p\n", +"p = sqrt(E^2-m0^2*c^4)/c; // Momentum of the electron, MeV\n", +"// As E = E0/sqrt(1-(u/c)^2), solving for u\n", +"u = sqrt(1-(E0/E)^2)*c; // Velocity of the electron, m/s\n", +"printf('\nThe momentum of the electron = %4.1f/c MeV', p);\n", +"printf('\nThe velocity of the electron = %6.4fc', u);\n", +"\n", +"// Result\n", +"// The momentum of the electron = 10.5/c MeV\n", +"// The velocity of the electron = 0.9988c " + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 8.13: Mass_from_relativistic_energy.sci" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"// Scilab Code Ex8.13: Page-176 (2010)\n", +"c = 3e+008; // Speed of light in vacuum, m/s\n", +"E = 4.5e+017; // Total energy of object, J\n", +"px = 3.8e+008; // X-component of momentum, kg-m/s\n", +"py = 3e+008; // Y-component of momentum, kg-m/s\n", +"pz = 3e+008; // Z-component of momentum, kg-m/s\n", +"p = sqrt(px^2+py^2+px^2); // Total momentum of the object, kg-m/s\n", +"// From Relativistic mass-energy relation\n", +"// E^2 = c^2*p^2 + m0^2*c^4, solving for m0\n", +"m0 = sqrt(E^2/c^4 - p^2/c^2); // Rest mass of the body, kg\n", +"printf('\nThe rest mass of the body = %4.2f kg', m0);\n", +"\n", +"// Result\n", +"// The rest mass of the body = 4.56 kg " + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 8.14: Relativistic_momentum_of_high_speed_probe.sci" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"// Scilab Code Ex8.14: Page-176 (2010)\n", +"c = 3e+008; // Speed of light in vacuum, m/s\n", +"m = 50000; // Mass of high speed probe, kg\n", +"u = 0.8*c; // Speed of the probe, m/s\n", +"p = m*u/sqrt(1-(u/c)^2); // Momentum of the probe, kg-m/s\n", +"printf('\nThe momentum of the high speed probe = %1g kg-m/s', p);\n", +"\n", +"// Result\n", +"// The momentum of the high speed probe = 2e+013 kg-m/s " + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 8.15: Moving_electron_subjected_to_the_electric_field.sci" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"// Scilab Code Ex8.15: Page-177 (2010)\n", +"e = 1.6e-019; // Electronic charge, C = Energy equivalent of 1 eV, J/eV\n", +"m0 = 9.11e-031; // Rest mass of electron, kg\n", +"c = 3e+008; // Speed of light in vacuum, m/s\n", +"u1 = 0.98*c; // Inital speed of electron, m/s\n", +"u2 = 0.99*c; // Final speed of electron, m/s\n", +"m1 = m0/sqrt(1-(u1/c)^2); // Initial relativistic mass of electron, kg\n", +"m2 = m0/sqrt(1-(u2/c)^2); // Final relativistic mass of electron, kg\n", +"dm = m2 - m1; // Change in relativistic mass of the electron, kg\n", +"W = dm*c^2; // Work done on the electron to change its velocity, J\n", +"// As W = eV, V = accelerating potential, solving for V\n", +"V = W/e; // Accelerating potential, volt\n", +"printf('\nThe change in relativistic mass of the electron = %4.1e kg', dm);\n", +"printf('\nThe work done on the electron to change its velocity = %4.2f MeV', W/(e*1e+006));\n", +"printf('\nThe accelerating potential = %4.2e volt', V);\n", +"\n", +"// Result\n", +"// The change in relativistic mass of the electron = 1.9e-030 kg\n", +"// The work done on the electron to change its velocity = 1.06 MeV\n", +"// The accelerating potential = 1.06e+006 volt" + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 8.1: Relativistic_length_contraction.sci" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"// Scilab Code Ex8.1: Page-171 (2010)\n", +"L_0 = 1; // For simplicity, we assume classical length to be unity, m\n", +"c = 1; // For simplicity assume speed of light to be unity, m/s\n", +"L = (1-1/100)*L_0; // Relativistic length, m\n", +"// Relativistic length contraction gives\n", +"// L = L_0*sqrt(1-v^2/c^2), solving for v\n", +"v = sqrt(1-(L/L_0)^2)*c; // Speed at which relativistic length is 1 percent of the classical length, m/s\n", +"printf('\nThe speed at which relativistic length is 1 percent of the classical length = %5.3fc', v);\n", +"\n", +"// Result\n", +"// The speed at which relativistic length is 1 percent of the classical length = 0.141c " + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 8.2: Time_Dilatio.sci" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"// Scilab Code Ex8.2: Page-171 (2010)\n", +"c = 1; // For simplicity assume speed of light to be unity, m/s\n", +"v = 0.9*c; // Speed at which beam of particles travel, m/s\n", +"delta_t = 5e-006; // Mean lifetime of particles as observed in the Lab. frame, s\n", +"delta_tau = delta_t*sqrt(1-(v/c)^2); // Proper lifetime of particle as per Time Dilation rule, s\n", +"printf('\nThe proper lifetime of particle = %4.2e s', delta_tau);\n", +"\n", +"// Result\n", +"// The proper lifetime of particle = 2.18e-006 s\n", +"" + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 8.4: Relativistic_velocity_additio.sci" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"// Scilab Code Ex8.4: Page-172 (2010)\n", +"c = 1; // For simplicity assume speed of light to be unity, m/s\n", +"v = 0.6*c; // Speed with which the rocket leaves the earth, m/s\n", +"u_prime = 0.9*c; // Relative speed of second rocket w.r.t. the first rocket, m/s\n", +"u = (u_prime+v)/(1+(u_prime*v)/c^2); // Speed of second rocket for same direction of firing as per Velocity Addition Rule, m/s\n", +"printf('\nThe speed of second rocket for same direction of firing = %5.3fc', u);\n", +"u = (-u_prime+v)/(1-(u_prime*v)/c^2); // Speed of second rocket for opposite direction of firing as per Velocity Addition Rule, m/s\n", +"printf('\nThe speed of second rocket for opposite direction of firing = %5.3fc', u);\n", +"\n", +"// Result\n", +"// The speed of second rocket for same direction of firing = 0.974c\n", +"// The speed of second rocket for opposite direction of firing = -0.652c" + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 8.5: Relativistic_effects_as_observed_for_spaceship.sci" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"// Scilab Code Ex8.5: Page-172 (2010)\n", +"c = 1; // For simplicity assume speed of light to be unity, m/s\n", +"L0 = 1; // For simplicity assume length in spaceship's frame to be unity, m\n", +"L = 1/2*L0; // Length as observed on earth, m\n", +"// Relativistic length contraction gives\n", +"// L = L_0*sqrt(1-v^2/c^2), solving for v\n", +"v = sqrt(1-(L/L0)^2)*c; // Speed at which length of spaceship is observed as half from the earth frame, m/s\n", +"tau = 1; // Unit time in the spaceship's frame, s\n", +"t = tau/sqrt(1-(v/c)^2); // Time dilation of the spaceship's unit time, s\n", +"printf('\nThe speed at which length of spaceship is observed as half from the earth frame = %5.3fc', v);\n", +"printf('\nThe time dilation of the spaceship unit time = %1g*tau', t);\n", +"\n", +"// Result\n", +"// The speed at which length of spaceship is observed as half from the earth frame = 0.866c\n", +"// The time dilation of the spaceship unit time = 2*tau" + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 8.6: Time_difference_and_distance_between_the_events.sci" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"// Scilab Code Ex8.6: Page-172 (2010)\n", +"c = 3e+008; // Speed of light in vacuum, m/s\n", +"v = 0.6*c; // Velocity with which S2 frame moves relative to S1 frame, m/s\n", +"L_factor = 1/sqrt(1-(v/c)^2); // Lorentz factor\n", +"t1 = 2e-007; // Time for which first event occurs, s\n", +"t2 = 3e-007; // Time for which second event occurs, s\n", +"x1 = 10; // Position at which first event occurs, m\n", +"x2 = 40; // Position at which second event occurs, m\n", +"delta_t = L_factor*(t2 - t1)+L_factor*v/c^2*(x1 - x2); // Time difference between the events, s\n", +"delta_x = L_factor*(x2 - x1)-L_factor*v*(t2 - t1); // Distance between the events, m\n", +"printf('\nThe time difference between the events = %3.1e s', delta_t);\n", +"printf('\nThe distance between the events = %2d m', delta_x);\n", +"\n", +"// Result\n", +"// The time difference between the events = 5.0e-008 s\n", +"// The distance between the events = 15 m" + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 8.7: Speed_of_unstable_particle_in_the_Laboratory_frame.sci" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"// Scilab Code Ex8.7: Page-173 (2010)\n", +"c = 3e+008; // Speed of light in vacuum, m/s\n", +"tau = 2.6e-008; // Mean lifetime the particle in its own frame, s\n", +"d = 20; // Distance which the unstable particle travels before decaying, m\n", +"// As t = d/v and also t = tau/sqrt(1-(v/c)^2), so that\n", +"// d/v = tau/sqrt(1-(v/c)^2), solving for v\n", +"v = sqrt(d^2/(tau^2+(d/c)^2)); // Speed of the unstable particle in Lab. frame, m/s\n", +"printf('\nThe speed of the unstable particle in Lab. frame = %3.1e m/s', v)\n", +"\n", +"// Result\n", +"// The speed of the unstable particle in Lab. frame = 2.8e+008 m/s" + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 8.8: Relativistic_effects_applied_to_mu_meso.sci" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"// Scilab Code Ex8.8: Page-174 (2010)\n", +"c = 1; // For simplicity assume speed of light to be unity, m/s\n", +"me = 1; // For simplicity assume mass of electron to be unity, kg\n", +"tau = 2.3e-006; // Average lifetime of mu-meson in rest frame, s\n", +"t = 6.9e-006; // Average lifetime of mu-meson in laboratory frame, s\n", +"// Fromm Time Dilation Rule, tau = t*sqrt(1-(v/c)^2), solving for v\n", +"v = sqrt(1-(tau/t)^2)*c; // Speed of mu-meson in the laboratory frame, m/s\n", +"c\n", +"m0 = 207*me; // Rest mass of mu-meson, kg\n", +"m = m0/sqrt(1-(v/c)^2); // Relativistic variation of mass with velocity, kg\n", +"me = 9.1e-031; // Mass of an electron, kg\n", +"c = 3e+008; // Speed of light in vacuum, m/s\n", +"e = 1.6e-019; // Energy equivalent of 1 eV, J/eV\n", +"T = (m*me*c^2 - m0*me*c^2)/e; // Kinetic energy of mu-meson, J \n", +"printf('\nThe speed of mu-meson in the laboratory frame = %6.4fc', v);\n", +"printf('\nThe effective mass of mu-meson = %3d me', m);\n", +"printf('\nThe kinetic energy of mu-meson = %5.1f MeV', T/1e+006);\n", +"\n", +"// Result\n", +"// The speed of mu-meson in the laboratory frame = 0.9428c\n", +"// The effective mass of mu-meson = 620 me\n", +"// The kinetic energy of mu-meson = 211.9 MeV " + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 8.9: Speed_of_moving_mass.sci" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"// Scilab Code Ex8.9: Page-174 (2010)\n", +"c = 1; // For simplicity assume speed of light to be unity, m/s\n", +"m0 = 1; // For simplicity assume rest mass to be unity, kg\n", +"m = (20/100+1)*m0; // Mass in motion, kg\n", +"// As m = m0/sqrt(1-(u/c)^2), solving for u\n", +"u = sqrt(1-(m0/m)^2)*c; // Speed of moving mass, m/s \n", +"printf('\nThe speed of moving body, u = %5.3fc', u);\n", +"\n", +"// Result\n", +"// The speed of moving body, u = 0.553c " + ] + } +], +"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 +} |