From d36fc3b8f88cc3108ffff6151e376b619b9abb01 Mon Sep 17 00:00:00 2001 From: kinitrupti Date: Fri, 12 May 2017 18:40:35 +0530 Subject: Revised list of TBCs --- .../chapter19_5.ipynb | 262 --------------------- 1 file changed, 262 deletions(-) delete mode 100755 Engineering_Mechanics_by_Tayal_A.K./chapter19_5.ipynb (limited to 'Engineering_Mechanics_by_Tayal_A.K./chapter19_5.ipynb') diff --git a/Engineering_Mechanics_by_Tayal_A.K./chapter19_5.ipynb b/Engineering_Mechanics_by_Tayal_A.K./chapter19_5.ipynb deleted file mode 100755 index ca13c8e8..00000000 --- a/Engineering_Mechanics_by_Tayal_A.K./chapter19_5.ipynb +++ /dev/null @@ -1,262 +0,0 @@ -{ - "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