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diff --git a/Concise_Physics_by_H_Matyaka/2-Mechanics.ipynb b/Concise_Physics_by_H_Matyaka/2-Mechanics.ipynb new file mode 100644 index 0000000..28799cc --- /dev/null +++ b/Concise_Physics_by_H_Matyaka/2-Mechanics.ipynb @@ -0,0 +1,886 @@ +{ +"cells": [ + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# Chapter 2: Mechanics" + ] + }, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 2.10: resultant_force.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"clc \n", +"clear\n", +"//input magnitude of forces\n", +"f1=40\n", +"f2=50\n", +"//calculation\n", +"d=50^2+40^2+2*50*40*cosd(50)//finding the diagonal\n", +"r=50^2+40^2+2*50*(40)*cosd(130)//reversing the side and finding diagonlprintf('the resultant is %3.3f',d1)\n", +"r1=sqrt(r)//resultant sum\n", +"d1=sqrt(d)// resultant when smaller force is subtracted from larger\n", +"//output\n", +"printf('1. the resultant sum is %3.3f N',d1)\n", +"printf('\n 2. the resultant when smaller force is subtracted from larger is %3.3f N',r1)" + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 2.11: components_of_velocity.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"clc\n", +"clear\n", +"//input\n", +"v=380//velocity\n", +"//calculation\n", +"vh=v*cosd(60)//horizontal component\n", +"vv=v*sind(60)//vertical component\n", +"//output\n", +"printf('the horizontal component is %3.3f ms^-1',vh)\n", +"printf('\nthe vertical component is %3.3f ms^-1',vv)" + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 2.12: components_of_force.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"clc\n", +"clear\n", +"//input\n", +"fc=50//force applied by magnet\n", +"x=90-20 //angle of force\n", +"//calculation\n", +"fb=fc*sind(70)//force due to b\n", +"fa=fc*cosd(70)//force due to a\n", +"//output\n", +"printf('the force due to b is %3.3f N',fb)\n", +"printf('\nthe force due to b is %3.3f N',fa)" + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 2.13: inelastic_collission.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"clc\n", +"clear\n", +"//input\n", +"m1=1\n", +"v1=25\n", +"m2=2\n", +"v2=0\n", +"//calculation\n", +"v=(m1*v1)+(m2*v2)//applying princilpe of conservation of linear momentum\n", +"v4=v/(m1+m2)\n", +"//output\n", +"printf('the velocity with which both will move is %3.3f ms^-1',v4)" + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 2.14: Inelastic_collission.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"clc\n", +"clear\n", +"//input\n", +"m1=1//mass of object 1\n", +"v1=25//velocity of object 1\n", +"m2=2//mass of object 2\n", +"v2=0//body at rest,velocity =0\n", +"v3=10\n", +"//caclulation\n", +"u=((m1*v1)+(m2*v2)-(m2*v3))/2//applying princilpe of conservation of linear momentum\n", +"//output\n", +"printf('\n the value of u is %3.3f ms^-1',-u)" + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 2.15: angularvelocity_and_centripetal_force.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"clc\n", +"clear\n", +"//input\n", +"m=2//mass\n", +"r=4//radius\n", +"v=6//uniform speed\n", +"//calculation\n", +"w=v/r//angular velocity\n", +"f=m*r*w*w//centripetal force\n", +"//output\n", +"printf('the angular velocity is %3.3f rads^-1',w)\n", +"printf('\n the centripetal force is %3.3f N',f)" + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 2.16: tension_in_arm.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"clc\n", +"clear\n", +"//input\n", +"m=140//mass\n", +"v=8//speed\n", +"r=5//radius\n", +"g=9.8//acceleration due to gravity\n", +"//calculation\n", +"t=((m*v^2/5)^2)+(140*9.8)^2 //applying parallelogram of vectors\n", +"t1=sqrt(t)\n", +"//output\n", +"printf('the tension in arm is %3.3f N',t1)" + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 2.17: inclination_and_reaction.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"clc\n", +"clear\n", +"//input\n", +"v=15//velocity\n", +"m=70//mass\n", +"r=50//radius\n", +"//calculation\n", +"x=v*v/(r*10)//applying parallelogram of vectors,then for equilibrium\n", +"y=atand(x)\n", +"r1=(m*10)/cosd(y)\n", +"//output\n", +"printf('the inclination is %3.3f deg',y)\n", +"printf('\n the reaction is %3.3f N',r1)" + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 2.18: planet_mean_density.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"clc\n", +"clear\n", +"//input\n", +"r=5500//radius\n", +"g1=6.7*10^-11\n", +"g=7//acceleration due to gravity\n", +"//calculation of mean density\n", +"p=3*g/(4*%pi*r*10^3*g1)//mean density\n", +"//output\n", +"printf('the mean density of planet is %3.3f kgm^-3',p)" + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 2.19: orbit_radius_and_linearvelocity.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"clc\n", +"clear\n", +"//input\n", +"m=5*10^24//mass of earth\n", +"g1=6.7*10^-11\n", +"//calculation\n", +"r=((6.7*10^-11*5*10^24*(3600*24)^2)/(4*%pi^2))^(1/3)//orbit radius\n", +"v=(2*%pi*r)/(3600*24)//linear velocity\n", +"//output\n", +"printf('the orbit radius is %3.3f',r)\n", +"printf('\n the linear velocity is %3.3f ms^-1',v)" + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 2.1: acceleration_and_distance.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"clc\n", +"clear\n", +"//input from given graph\n", +"//calculation of initial accleration\n", +"ia=18/4\n", +"// calculation of final accleration\n", +"fa=-18/10\n", +"decel=-(fa)//calculation of deceleration\n", +"//calculation of total distance covered\n", +"d=0.5*(4*18)+(8*18)+0.5*(10*18)//area under velocity time graph\n", +"//output\n", +"printf('\n the initial acceleration is %3.3f m/s^2',ia)\n", +"printf('\n the final acceleration is %3.3f m/s^2',decel)\n", +"printf('\n the distance covered is is %3.3f m',d)" + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 2.20: mass_of_galaxy.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"clc\n", +"clear\n", +"//input\n", +"v=3*10^5//orbit speed\n", +"r=4.6*10^20//distance\n", +"g1=6.7*10^-11\n", +"//calculation of mass\n", +"m=v*v*r/g1 //Newtons law\n", +"//output\n", +"printf('the mass is %2.3e kg',m)" + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 2.21: total_kinetic_energy.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"clc\n", +"clear\n", +"//input\n", +"v=0.6//speed\n", +"m=0.3//mass\n", +"//calculation\n", +"e=0.75*m*v*v//total kinetic energy is kinetic energy+moment of inertia\n", +"//output\n", +"printf('the total kinetic energy is %3.3f J',e)" + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 2.22: time_taken_to_move.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"clc\n", +"clear\n", +"//input\n", +"t1=34\n", +"u=0//starts from rest\n", +"x=3//distance to move\n", +"//calculation\n", +"t=(3*3/(10*sind(t1)))^0.5//from law of conservation of energy\n", +"//output\n", +"printf('the time taken is %3.3f s',t)" + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 2.23: angular_velocity_ratio.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"clc\n", +"clear\n", +"//input\n", +"i1=53//inertia when it spins with panels carrying solar cells\n", +"i2=37//inertia about axis of rotation\n", +"//calculation\n", +"r=i1/i2//law of conservation of angular momentum\n", +"//output\n", +"printf('the ratio of angular velocities is %3.3f',r)" + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 2.25: attributes_of_shm.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"clc\n", +"clear\n", +"//input\n", +"f=9//frequency\n", +"x=0//at midpoint of stroke x=0\n", +"//calculation\n", +"t=1/f\n", +"a=-4*%pi^2*f^2*x//acceleration for shm\n", +"v=2*%pi*f*0.05//velocity for shm\n", +"a1=-4*%pi^2*9^2*0.05//acceleration at amplitude\n", +"v1=0//velocity at amplitude is 0\n", +"//output\n", +"printf('the period of oscillation is %3.3f s^-1',t)\n", +"printf('\n the velocity at midpoint of stroke is %3.3f ms^-1',v)\n", +"printf('\n the acceleration at midpoint of stroke is %3.3f ms^-2',a)\n", +"\n", +"printf('\n the velocity at amplitude is %3.3f ms^-1',v1)\n", +"printf('\n the acceleration at amplitude is %3.3f ms^-2',a1)" + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 2.26: simple_harmonic_motion.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"clc\n", +"clear\n", +"//input\n", +"g=10\n", +"t=0.3//period of shm\n", +"//calculation\n", +"x=g*t^2/(4*%pi^2)//for shm maximum amplitude\n", +"//output\n", +"printf('the maximum amplitude for bead to be in contact is %3.3f m',x)" + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 2.27: attrbutes_simple_pendulum.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"clc\n", +"clear\n", +"//input\n", +"p1=2.3//period of pendulum\n", +"p2=3.1//period when pendulum is lengthened\n", +"//calculation\n", +"g=4*%pi^2/(p2^2-p1^2)//acceleration of free fall\n", +"l=p1^2*g/(4*%pi^2)//length of pendulum\n", +"//output\n", +"printf('the acceleration of free fall is %3.3f m/s^2',g)\n", +"printf('\n the length of pendulum is %3.3f m',l)" + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 2.28: maximum_displacement_shm.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"clc\n", +"clear\n", +"//INPUT DATA\n", +"f=55 //frequency\n", +"a=7*10^-3 //amplitude\n", +"\n", +"\n", +"//calculation\n", +"a=(-2*%pi*f)^2*a\n", +"\n", +"//output\n", +"printf('the acceleration of the body when it is at its maximum displacement from its zero position is -%3.1f ms^-2',a)" + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 2.29: maximum_potential_energy_shm.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"clc\n", +"clear\n", +"//input\n", +"f=55//frequency\n", +"amp=7*10^-3//amplitude\n", +"m=1.2//mass\n", +"//calculation\n", +"e=0.5*m*4*%pi^2*f^2*amp^2//maximum pe occurs at zero position\n", +"//output\n", +"printf('the maximum pe is %3.3f J',e)" + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 2.2: acceleration_and_distance.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"clc\n", +"clear\n", +"//input\n", +"v=0 //car stops => final velocity=0\n", +"u=29 //initial velocity\n", +"t=11 //time \n", +"//calculation of acceleration\n", +"a=(v-u)/t//eqn of uniformly accelerated body\n", +"//calculating distance travelled during this period\n", +"d=(v+u)*t*0.5//eqn of uniformly accelerated body\n", +"//output\n", +"printf('the accleration is %3.3f ms^-2 ',a)\n", +"printf('\nthe distance travelled is %3.3f m',d)" + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 2.30: extension_of_steel_wire.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"clc\n", +"clear\n", +"//input\n", +"l=6.5//length\n", +"m=0.06//mass of wire\n", +"m1=10//mass attached\n", +"g=9.8//acceleration due to gravity\n", +"e=2.1*10^11//youngs modulus\n", +"ro=8*10^3//density of steel\n", +"//calculation\n", +"e1=m1*g*ro*l*l/(e*m)//extension caused \n", +"pe=0.5*g*m1*e1//potential energy \n", +"//output\n", +"printf('the extension caused is %3.3e m',e1)\n", +"printf('\n the potential energy is %3.3f J',pe)" + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 2.31: Youngs_modulus.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"clc\n", +"clear\n", +"//input\n", +"w=250*10^3\n", +"s=0.00003//strain\n", +"a=0.04//area\n", +"w1=320*10^3\n", +"//calculation\n", +"e=w/(a*s)//youngs module\n", +"st=w1/a//stress\n", +"//output\n", +"printf('the youngs modulus is %3.3e N/m^2',e)\n", +"printf('\n the stress is %3.0e N/m^2',st)" + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 2.32: wire_length_change.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"clc\n", +"clear\n", +"//input\n", +"m=40//mass\n", +"g=9.8//acceleration due to gravity\n", +"E=2*10^11//youngs modulus\n", +"//calculation\n", +"t1=m*g/5//principle of momentum\n", +"t2=4*m*g/5 //principle of momentum\n", +"d=4*(t2-t1)/(4*%pi*10^-6*E)//difference in length\n", +"//output\n", +"printf('the difference is %3.0e m',d)" + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 2.3: time_to_reach_aircraft.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"clc\n", +"clear\n", +"//input\n", +"v=120 //velocity\n", +"a=75 //accleration\n", +"//calculation of time\n", +"t=2*v/(a*cosd(45))//eqn of uniformly accelerated body\n", +"//output\n", +"printf('the time taken is %3.3f s',t)" + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 2.4: resultant_force.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"clc\n", +"clear\n", +"//input\n", +"f1=50\n", +"f2=50\n", +"//calculation of net force\n", +"f=f1+f2 // the two forces act in same direction\n", +"//output\n", +"printf('the resultant force is %3.3f N',f)" + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 2.5: car_and_wind.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"clc\n", +"clear\n", +"//input\n", +"vc=25 //velocity of car\n", +"va=10 //velocity of wind\n", +"va1=15 //velocity of wind westward\n", +"//calculation\n", +"v1=vc+va//resultant velocity for a tail of wind\n", +"v2=vc-va//when wind blows westward at 10 m/s^resultant velocity \n", +"v3=vc-va1//resultant velocity when wind blows westward at 15m/s^2\n", +"//output\n", +"printf('1. the resultant velocity of wind is %3.3f ms^-1 eastwards ',v1)\n", +"printf('\n2. the resultant velocity of wind is %3.3f ms^-1 westwards ',v2)\n", +"printf('\n3. the resultant velocity of wind is %3.3f ms^-1westwards ',v3)" + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 2.7: velocity_of_speedboat.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"clc \n", +"clear\n", +"//input\n", +"v=30 //velocity of speedboat\n", +"vw=40 //velocity of wind\n", +"//calculation\n", +"x=(30/40)//angle between original velocity of boat and resultant velocity\n", +"y=atand(x)//applying trigonometry\n", +"b=90+y//bearing of boat\n", +"//output\n", +"printf('the bearing of speedboat is %3.3f deg',b)" + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 2.8: tension_on_string.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"clc \n", +"clear\n", +"//input\n", +"f1=6 //tension on string AB\n", +"f2=6 //tension on string BC\n", +"//calculation of tension\n", +"t=2*f1*sind(55)// the resultant tension is the diagonal of rhombus formed\n", +"//output\n", +"printf('/n the resultant tension is %3.3f N',t)" + ] + } +], +"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 +} |