From 4a1f703f1c1808d390ebf80e80659fe161f69fab Mon Sep 17 00:00:00 2001 From: Thomas Stephen Lee Date: Fri, 28 Aug 2015 16:53:23 +0530 Subject: add books --- .../chapter19_4.ipynb | 262 +++++++++++++++++++++ 1 file changed, 262 insertions(+) create mode 100755 Engineering_Mechanics_by_Tayal_A.K./chapter19_4.ipynb (limited to 'Engineering_Mechanics_by_Tayal_A.K./chapter19_4.ipynb') diff --git a/Engineering_Mechanics_by_Tayal_A.K./chapter19_4.ipynb b/Engineering_Mechanics_by_Tayal_A.K./chapter19_4.ipynb new file mode 100755 index 00000000..ca13c8e8 --- /dev/null +++ b/Engineering_Mechanics_by_Tayal_A.K./chapter19_4.ipynb @@ -0,0 +1,262 @@ +{ + "metadata": { + "name": "chapter19.ipynb" + }, + "nbformat": 3, + "nbformat_minor": 0, + "worksheets": [ + { + "cells": [ + { + "cell_type": "heading", + "level": 1, + "metadata": {}, + "source": [ + "Chapter 19: Relative Motion" + ] + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 19.19-1,Page no:503" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "import math\n", + "\n", + "# Initilization of variables\n", + "\n", + "v_t=10 # m/s # velocity of the train\n", + "v_s=5 # m/s # velocity of the stone\n", + "\n", + "# Calculations\n", + "\n", + "# Let v_r be the relative velocity, which is given as, (from triangle law)\n", + "v_r=(v_t**2+v_s**2)**0.5 # m/s\n", + "# The direction ofthe stone is,\n", + "theta=arctan(v_s*v_t**-1)*(180/pi) # degree\n", + "\n", + "# Results\n", + "\n", + "print\"The velocity at which the stone appears to hit the person travelling in the train is \",round(v_r,1),\"m\"\n", + "print\"The direction of the stone is \",round(theta,2),\"degree\"\n" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "The velocity at which the stone appears to hit the person travelling in the train is 11.2 m\n", + "The direction of the stone is 26.57 degree\n" + ] + } + ], + "prompt_number": 6 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 19.19-2,Page No:504" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "import math\n", + "\n", + "# Initilization of variables\n", + "\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", + "\n", + "# Calculations\n", + "\n", + "# Here,\n", + "OA=v_A # m/s\n", + "OB=v_B # m/s\n", + "\n", + "# The magnitude of relative velocity is given by cosine law as,\n", + "AB=((OA**2)+(OB**2)-(2*OA*OB*cos(theta*(pi/180))))**0.5 # m/s\n", + "\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=arcsin((OB*sin(theta*(pi/180)))/(AB))*(180/pi) # degree\n", + "\n", + "# Results\n", + "\n", + "print\"The magnitude of relative velocity of ship B with respect to ship A is \",round(AB,2),\"m/s\"\n", + "print\"The direction of the relative velocity is \",round(alpha,2),\"degree\"\n" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "The magnitude of relative velocity of ship B with respect to ship A is 6.99 m/s\n", + "The direction of the relative velocity is 14.64 degree\n" + ] + } + ], + "prompt_number": 10 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 19.19-3,Page No:505" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "import math\n", + "import numpy as np\n", + "# Initilization of variables\n", + "\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", + "\n", + "# Calculations\n", + "\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=np.array([[1 ,1],[1, 0.577]])\n", + "B=np.array([20,12])\n", + "C=np.linalg.solve(A,B) # km/hr\n", + "\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", + "\n", + "# Calculations\n", + "\n", + "# Relative velocity (v_R) is given as,\n", + "v_R=((C[0])**2+(C[1])**2)**0.5 # km/hr\n", + "# And the direction of absolute velocity of rain is theta, is given as\n", + "theta=arctan(C[1]/C[0])*(180/pi) # degree\n", + "\n", + "# Results \n", + "\n", + "print\"The magnitude of absolute velocity is \",round(v_R,2),\"km/hr\"\n", + "print\"The direction of absolute velocity is \",round(theta,1),\"degree\"\n" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "The magnitude of absolute velocity is 18.94 km/hr\n", + "The direction of absolute velocity is 86.7 degree\n" + ] + } + ], + "prompt_number": 2 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 19.19-4,Page No:508" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "import math\n", + "\n", + "# Initiization of variables\n", + "\n", + "a=1 # m/s^2 # acceleration of car A\n", + "u_B=36*1000*3600**-1 # 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", + "\n", + "# Calculations\n", + "\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)+((0.5)*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", + "\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)+((0.5)*a_B*t**2) # m\n", + "x_B=s_B # m\n", + "\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=(OA**2+OB**2)**0.5 # m\n", + "theta=arctan(OA/OB)*(180/pi) # degree\n", + "\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=(oa**2+ob**2)**0.5 # m/s\n", + "phi=arctan(oa/ob)*(180/pi) # degree\n", + "\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", + "\n", + "# Results\n", + "\n", + "print\"The relative position of car A relative to car B is \",round(BA,1),\"m\"\n", + "print\"The direction of car A w.r.t car B is \",round(theta,1),\"degree\"\n", + "print\"The velocity of car A relative to car B is \",round(v_AB,1),\"m/s\"\n", + "print\"The direction of car A w.r.t (for relative velocity)is \",round(phi,1),\"degree\"\n", + "print\"The acceleration of car A relative to car B is \",round(a_AB,1),\"m/s^2\"\n" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "The relative position of car A relative to car B is 53.9 m\n", + "The direction of car A w.r.t car B is 21.8 degree\n", + "The velocity of car A relative to car B is 11.2 m/s\n", + "The direction of car A w.r.t (for relative velocity)is 26.6 degree\n", + "The acceleration of car A relative to car B is 1.0 m/s^2\n" + ] + } + ], + "prompt_number": 17 + }, + { + "cell_type": "code", + "collapsed": false, + "input": [], + "language": "python", + "metadata": {}, + "outputs": [] + } + ], + "metadata": {} + } + ] +} \ No newline at end of file -- cgit