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diff --git a/Engineering_Mechanics_by_A_K_Tayal/19-Relative_Motion.ipynb b/Engineering_Mechanics_by_A_K_Tayal/19-Relative_Motion.ipynb new file mode 100644 index 0000000..650d4cb --- /dev/null +++ b/Engineering_Mechanics_by_A_K_Tayal/19-Relative_Motion.ipynb @@ -0,0 +1,191 @@ +{ +"cells": [ + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# Chapter 19: Relative Motion" + ] + }, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 19.1: Relative_Velocity.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"// Initilization of variables\n", +"v_t=10 // m/s // velocity of the train\n", +"v_s=5 // m/s // velocity of the stone\n", +"// Calculations\n", +"// Let v_r be the relative velocity, which is given as, (from triangle law)\n", +"v_r=sqrt(v_t^2+v_s^2) // m/s\n", +"// The direction ofthe stone is,\n", +"theta=atand(v_s/v_t) // degree\n", +"// Results\n", +"clc\n", +"printf('The velocity at which the stone appears to hit the person travelling in the train is %f m/s \n',v_r)\n", +"printf('The direction of the stone is %f degree \n',theta)" + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 19.2: Relative_Velocity.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"// Initilization of variables\n", +"v_A=5 // m/s // speed of ship A\n", +"v_B=2.5 // m/s // speed of ship B\n", +"theta=135 // degree // angle between the two ships\n", +"// Calculations\n", +"// Here,\n", +"OA=v_A // m/s\n", +"OB=v_B // m/s\n", +"// The magnitude of relative velocity is given by cosine law as,\n", +"AB=sqrt((OA^2)+(OB^2)-(2*OA*OB*cosd(theta))) // m/s\n", +"// where AB gives the relative velocity of ship B with respect to ship A\n", +"// Applying sine law to find the direction, Let alpha be the direction of the reative velocity, then\n", +"alpha=asind((OB*sind(theta))/(AB)) // degree\n", +"// Results\n", +"clc\n", +"printf('The magnitude of relative velocity of ship B with respect to ship A is %f m/s \n',AB)\n", +"printf('The direction of the relative velocity is %f degree \n',alpha)" + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 19.3: Relative_Velocity.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"// Initilization of variables\n", +"v_c=20 // km/hr // speed at which the cyclist is riding to west\n", +"theta_1=45 // degree // angle made by rain with the cyclist when he rides at 20 km/hr\n", +"V_c=12 // km/hr // changed speed\n", +"theta_2=30 // degree // changed angle when the cyclist rides at 12 km/hr\n", +"// Calculations\n", +"// Solving eq'ns 1 & 2 simultaneously to get the values of components(v_R_x & v_R_y) of absolute velocity v_R. We use matrix to solve eqn's 1 & 2.\n", +"A=[1 1;1 0.577]\n", +"B=[20;12]\n", +"C=inv(A)*B // km/hr\n", +"// The X component of relative velocity (v_R_x) is C(1)\n", +"// The Y component of relative velocity (v_R_y) is C(2)\n", +"// Calculations\n", +"// Relative velocity (v_R) is given as,\n", +"v_R=sqrt((C(1))^2+(C(2))^2) // km/hr\n", +"// And the direction of absolute velocity of rain is theta, is given as\n", +"theta=atand(C(2)/C(1)) // degree\n", +"// Results \n", +"clc\n", +"printf('The magnitude of absolute velocity is %f km/hr \n',v_R)\n", +"printf('The direction of absolute velocity is %f degree \n',theta)" + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 19.4: Relative_Velocity.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"// Initiization of variables\n", +"a=1 // m/s^2 // acceleration of car A\n", +"u_B=36*(1000/3600) // m/s // velocity of car B\n", +"u=0 // m/s // initial velocity of car A\n", +"d=32.5 // m // position of car A from north of crossing\n", +"t=5 // seconds\n", +"// Calculations\n", +"// CAR A: Absolute motion using eq'n v=u+at we have,\n", +"v=u+(a*t) // m/s\n", +"// Now distance travelled by car A after 5 seconds is given by, s_A=u*t+(1/2)*a*t^2\n", +"s_A=(u*t)+((1/2)*a*t^2)\n", +"// Now, let the position of car A after 5 seconds be y_A\n", +"y_A=d-s_A // m // \n", +"// CAR B:\n", +"// let a_B be the acceleration of car B\n", +"a_B=0 // m/s\n", +"// Now position of car B is s_B\n", +"s_B=(u_B*t)+((1/2)*a_B*t^2) // m\n", +"x_B=s_B // m\n", +"// Let the Relative position of car A with respect to car B be BA & its direction be theta, then from fig. 19.9(b)\n", +"OA=y_A\n", +"OB=x_B\n", +"BA=sqrt(OA^2+OB^2) // m\n", +"theta=atand(OA/OB) // degree\n", +"// Let the relative velocity of car A w.r.t. the car B be v_AB & the angle be phi. Then from fig 19.9(c). Consider small alphabets\n", +"oa=v\n", +"ob=u_B\n", +"v_AB=sqrt(oa^2+ob^2) // m/s\n", +"phi=atand(oa/ob) // degree\n", +"// Let the relative acceleration of car A w.r.t. car B be a_A/B.Then,\n", +"a_AB=a-a_B // m/s^2\n", +"// Results\n", +"clc\n", +"printf('The relative position of car A relative to car B is %f m \n',BA)\n", +"printf('The direction of car A w.r.t car B is %f degree \n',theta)\n", +"printf('The velocity of car A relative to car B is %f m/s \n',v_AB)\n", +"printf('The direction of car A w.r.t (for relative velocity)is %f degree \n',phi)\n", +"printf('The acceleration of car A relative to car B is %f m/s^2 \n',a_AB)" + ] + } +], +"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 +} |