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 --- .../chapter21_14.ipynb | 658 +++++++++++++++++++++ 1 file changed, 658 insertions(+) create mode 100644 Engineering_Mechanics_by_Tayal_A.K./chapter21_14.ipynb (limited to 'Engineering_Mechanics_by_Tayal_A.K./chapter21_14.ipynb') diff --git a/Engineering_Mechanics_by_Tayal_A.K./chapter21_14.ipynb b/Engineering_Mechanics_by_Tayal_A.K./chapter21_14.ipynb new file mode 100644 index 00000000..c58e0b47 --- /dev/null +++ b/Engineering_Mechanics_by_Tayal_A.K./chapter21_14.ipynb @@ -0,0 +1,658 @@ +{ + "metadata": { + "name": "chapter21.ipynb" + }, + "nbformat": 3, + "nbformat_minor": 0, + "worksheets": [ + { + "cells": [ + { + "cell_type": "heading", + "level": 1, + "metadata": {}, + "source": [ + "Chapter 21: Kinematics Of Rigid Body" + ] + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 21.21-1,Page No:536" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "import math\n", + "\n", + "# Initilization of variables\n", + "\n", + "N=1800 # r.p.m # Speed of the shaft\n", + "t=5 # seconds # time taken to attain the rated speed # case (a)\n", + "T=90 # seconds # time taken by the unit to come to rest # case (b)\n", + "pi=3.14 # constant\n", + "\n", + "# Calculations\n", + "\n", + "omega=(2*pi*N)/(60)\n", + "\n", + "# (a)\n", + "# we take alpha_1,theta_1 & n_1 for case (a)\n", + "alpha_1=omega/t # rad/s^2 #\n", + "theta_1=(omega**2)/(2*alpha_1) # radian\n", + "# Let n_1 be the number of revolutions turned,\n", + "n_1=theta_1*(1/(2*pi))\n", + "\n", + "# (b)\n", + "# similarly we take alpha_1,theta_1 & n_1 for case (b)\n", + "alpha_2=(omega/T) # rad/s^2 # However here alpha_2 is -ve\n", + "theta_2=(omega**2)/(2*alpha_2) # radians\n", + "# Let n_2 be the number of revolutions turned,\n", + "n_2=theta_2*(1/(2*pi))\n", + "\n", + "# Results\n", + "\n", + "print\"(a) The no of revolutions the unit turns to attain the rated speed is \",round(n_1)\n", + "print\"(b) The no of revolutions the unit turns to come to rest is \",round(n_2)\n" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "(a) The no of revolutions the unit turns to attain the rated speed is 75.0\n", + "(b) The no of revolutions the unit turns to come to rest is 1350.0\n" + ] + } + ], + "prompt_number": 1 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 21.21-2,Page No:540" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "import math\n", + "\n", + "# Initilization of variables\n", + "\n", + "r=1 # m # radius of the cylinder\n", + "v_c=20 # m/s # velocity of the cylinder at its centre\n", + "\n", + "# Calculations\n", + "\n", + "# The velocity of point E is given by using the triangle law as,\n", + "v_e=(2)**0.5*v_c # m/s \n", + "\n", + "# Similarly the velocity at point F is given as,\n", + "v_f=2*v_c # m/s \n", + "\n", + "# Results\n", + "\n", + "print\"The velocity of point E is \",round(v_e,2),\"m/s\"\n", + "print\"The velocity of point F is \",round(v_f),\"m/s\"\n" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "The velocity of point E is 28.28 m/s\n", + "The velocity of point F is 40.0 m/s\n" + ] + } + ], + "prompt_number": 3 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 21.21-3,Page No:541" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "import math\n", + "\n", + "# Initilization of Variables\n", + "\n", + "v_1=3 # m/s # uniform speed of the belt at top\n", + "v_2=2 # m/s # uniform speed of the belt at the bottom\n", + "r=0.4 # m # radius of the roller\n", + "\n", + "# Calculations\n", + "\n", + "# equating eq'ns 2 & 4 and solving for v_c & theta' (angular velocity). We use matrix to solve the eqn's\n", + "A=[1 r;1 -r]\n", + "B=[v_1;v_2]\n", + "C=inv(A)*B\n", + "\n", + "# Results\n", + "\n", + "print\"The linear velocity (v_c) at point C is \",round(C(1)),\"m/s\"\n", + "print\"The angular velocity at point C is \" round(C(2)),\"radian/second\"\n", + "# NOTE: The answer of angular velocity is incorrect in the book\n" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "ename": "SyntaxError", + "evalue": "invalid syntax (, line 12)", + "output_type": "pyerr", + "traceback": [ + "\u001b[1;36m File \u001b[1;32m\"\"\u001b[1;36m, line \u001b[1;32m12\u001b[0m\n\u001b[1;33m A=[1 r;1 -r]\u001b[0m\n\u001b[1;37m ^\u001b[0m\n\u001b[1;31mSyntaxError\u001b[0m\u001b[1;31m:\u001b[0m invalid syntax\n" + ] + } + ], + "prompt_number": 4 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 21.21-4,Page No:542" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "import math\n", + "\n", + "# Initilization of Variables\n", + "\n", + "l=1 # m # length of bar AB\n", + "v_a=5 # m/s # velocity of A\n", + "theta=30 # degree # angle made by the bar with the horizontal\n", + "\n", + "# Calculations\n", + "\n", + "# From the vector diagram linear velocity of end B is given as,\n", + "v_b=v_a/tan(theta*(pi/180)) # m/s \n", + "\n", + "# Now let the relative velocity be v_ba which is given as,\n", + "v_ba=v_a/sin(theta*(pi/180)) # m/s\n", + "\n", + "# Now let the angular velocity of the bar be theta_a which is given as,\n", + "theta_a=(v_ba)/l # radian/second\n", + "\n", + "# Velocity of point A\n", + "v_a=(0.5)*theta_a # m/s\n", + "\n", + "# Magnitude of velocity at point C is,\n", + "v_c=v_a # m/s # from the vector diagram\n", + "\n", + "# Results\n", + "\n", + "print\"(a) The angular velocity of the bar is \",round(theta_a),\"radian/second\"\n", + "print\"(b) The velocity of end B is \",round(v_b,2),\"m/s\"\n", + "print\"(c) The velocity of mid point C is \",round(v_c),\"m/s\"\n" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "(a) The angular velocity of the bar is 10.0 radian/second\n", + "(b) The velocity of end B is 8.67 m/s\n", + "(c) The velocity of mid point C is 5.0 m/s\n" + ] + } + ], + "prompt_number": 7 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 21.21-5,Page No:544" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "import math\n", + "\n", + "# Initilization of Variables\n", + "\n", + "r=0.12 # m # length of the crank\n", + "l=0.6 # m # length of the connecting rod\n", + "N=300 # r.p.m # angular velocity of the crank\n", + "theta=30 # degree # angle made by the crank with the horizontal\n", + "pi=3.14\n", + "\n", + "# Calculations\n", + "\n", + "# Now let the angle between the connecting rod and the horizontal rod be phi\n", + "phi=arcsin(r*sin(theta*(pi/180))/(l))*(180/pi) # degree\n", + "\n", + "# Now let the angular velocity of crank OA be omega_oa, which is given by eq'n\n", + "omega_oa=(2*pi*N)/(60) # radian/second\n", + "\n", + "# Linear velocity at A is given as,\n", + "v_a=r*omega_oa # m/s\n", + "\n", + "# Now using the sine rule linear velocity at B can be given as,\n", + "v_b=v_a*sin(35.7*(pi/180))/sin(84.3*(pi/180)) # m/s\n", + "\n", + "# Similarly the relative velocity (assume v_ba) is given as,\n", + "v_ba=v_a*sin(60*(pi/180))/sin(84.3*(pi/180))\n", + "\n", + "# Angular velocity (omega_ab) is given as,\n", + "omega_ab=v_ba/l # radian/second\n", + "\n", + "# Results\n", + "\n", + "print\"(a) The angular velocity of the connecting rod is \",round(omega_ab,2),\"radian/second\"\n", + "print\"(b) The velocity of the piston when the crank makes an angle of 30 degree is \",round(v_b,2),\"m/s\"\n" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "(a) The angular velocity of the connecting rod is 5.46 radian/second\n", + "(b) The velocity of the piston when the crank makes an angle of 30 degree is 2.21 m/s\n" + ] + } + ], + "prompt_number": 18 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 21.21-6,Page No:548" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "import math\n", + "\n", + "# Initiization of variables\n", + "\n", + "r=1 # m # radius of the cylinder\n", + "v_c=20 # m/s # velocity at the centre\n", + "\n", + "# Calculations\n", + "\n", + "# Angular velocity is given as,\n", + "omega=v_c/r # radian/second\n", + "\n", + "# Velocity at point D is\n", + "v_d=omega*(2)**0.5*r # m/s # from eq'n 1\n", + "\n", + "# Now, the velocity at point E is,\n", + "v_e=omega*2*r # m/s \n", + "\n", + "# Results\n", + "\n", + "print\"The velocity at point D is \",round(v_d,2),\"m/s\"\n", + "print\"The velocity at point E is \",round(v_e),\"m/s\"\n" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "The velocity at point D is 28.28 m/s\n", + "The velocity at point E is 40.0 m/s\n" + ] + } + ], + "prompt_number": 20 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 21.21-7,Page No:548" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "import math\n", + "\n", + "# Initilization of Variables\n", + "\n", + "r=5 # cm # radius of the roller\n", + "AB=0.1 # m\n", + "v_a=3 # m/s # velocity at A\n", + "v_b=2 # m/s # velocity at B\n", + "\n", + "# Calculations\n", + "\n", + "# Solving eqn's 1 & 2 using matrix for IA & IB we get,\n", + "A=[-2 3;1 1]\n", + "B=[0;AB]\n", + "C=inv(A)*B\n", + "d1=C(2)*10**2 # cm # assume d1 for case 1\n", + "\n", + "# Similary solving eqn's 3 & 4 again for IA & IB we get,\n", + "P=[-v_b v_a;1 -1]\n", + "Q=[0;AB]\n", + "R=inv(P)*Q\n", + "d2=R(2)*10**2 # cm # assume d2 for case 2\n", + "\n", + "# Results\n", + "\n", + "print\"The distance d when the bars move in the opposite directions are \",round(d1),\"cm\"\n", + "print\"The distance d when the bars move in the same directions are \",round(d2),\"cm\"\n" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "ename": "SyntaxError", + "evalue": "invalid syntax (, line 13)", + "output_type": "pyerr", + "traceback": [ + "\u001b[1;36m File \u001b[1;32m\"\"\u001b[1;36m, line \u001b[1;32m13\u001b[0m\n\u001b[1;33m A=[-2 3;1 1]\u001b[0m\n\u001b[1;37m ^\u001b[0m\n\u001b[1;31mSyntaxError\u001b[0m\u001b[1;31m:\u001b[0m invalid syntax\n" + ] + } + ], + "prompt_number": 21 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 21.21-8,Page No:550" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "import math\n", + "\n", + "# Initilization of Variables\n", + "\n", + "v_c=1 # m/s # velocity t the centre\n", + "r1=0.1 # m \n", + "r2=0.20 # m\n", + "EB=0.1 # m\n", + "EA=0.3 # m\n", + "ED=(r1**2+r2**2)**0.5 # m\n", + "\n", + "# Calculations\n", + "\n", + "# angular velocity is given as,\n", + "omega=v_c/r1 # radian/seconds\n", + "\n", + "# Velocit at point B\n", + "v_b=omega*EB # m/s \n", + "\n", + "# Velocity at point A\n", + "v_a=omega*EA # m/s\n", + "\n", + "# Velocity at point D\n", + "v_d=omega*ED # m/s\n", + "\n", + "# Results\n", + "\n", + "print\"The velocity at point A is \",round(v_a),\"m/s\"\n", + "print\"The velocity at point B is \",round(v_b),\"m/s\"\n", + "print\"The velocity at point D is \",round(v_d,2),\"m/s\"\n" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "The velocity at point A is 3.0 m/s\n", + "The velocity at point B is 1.0 m/s\n", + "The velocity at point D is 2.24 m/s\n" + ] + } + ], + "prompt_number": 24 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 21.21-9,Page No:551" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "import math\n", + "\n", + "# Initilization of variables\n", + "\n", + "l=1 # m # length of bar AB\n", + "v_a=5 # m/s # velocity at A\n", + "theta=30 # degree # angle made by the bar with the horizontal\n", + "\n", + "# Calculations\n", + "\n", + "IA=l*sin(theta*(pi/180)) # m\n", + "IB=l*cos(theta*(pi/180)) # m\n", + "IC=0.5 # m # from triangle IAC\n", + "\n", + "# Angular veocity is given as,\n", + "omega=v_a/(IA) # radian/second\n", + "v_b=omega*IB # m/s\n", + "v_c=omega*IC # m/s\n", + "\n", + "# Results\n", + "\n", + "print\"The velocity at point B is \",round(v_b,2),\"m/s\"\n", + "print\"The velocity at point C is \",round(v_c),\"m/s\"\n" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "The velocity at point B is 8.67 m/s\n", + "The velocity at point C is 5.0 m/s\n" + ] + } + ], + "prompt_number": 26 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 21.21-11,Page No:552" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "import math\n", + "\n", + "# Initilization of variables\n", + "\n", + "v_a=2 # m/s # velocity at end A\n", + "r=0.05 # m # radius of the disc\n", + "alpha=30 # degree # angle made by the bar with the horizontal\n", + "\n", + "# Calculations \n", + "\n", + "# Soving eqn's 1 & 2 and substuting eqn 1 in it we get eq'n for omega as,\n", + "omega=(v_a*(sin(alpha*(pi/180)))**2)/(r*cos(alpha*(pi/180))) # radian/second\n", + "\n", + "# Results\n", + "\n", + "print\"The anguar veocity of the bar is \",round(omega,2),\"radian/second\"\n" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "The anguar veocity of the bar is 11.53 radian/second\n" + ] + } + ], + "prompt_number": 28 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 21.21-12,Page No:553" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "import math\n", + "\n", + "# Initilization of variables\n", + "\n", + "l=0.6 # m \n", + "r=0.12 # m \n", + "theta=30 # degree # angle made by OA with the horizontal\n", + "phi=5.7 # degree # from EX 21.5\n", + "N=300\n", + "pi=3.14\n", + "\n", + "# Calculations\n", + "\n", + "# Let the angular velocity of the connecting rod be (omega_ab) which is given from eqn's 1 & 4 as,\n", + "omega_oa=(2*pi*N)/(60) # radian/ second\n", + "\n", + "# Now,in triangle IBO.\n", + "IB=(l*cos(phi*(pi/180))*tan(theta*(pi/180)))+(r*sin(theta*(pi/180))) # m\n", + "IA=(l*cos(phi*(pi/180)))/(cos(theta*(pi/180))) # m\n", + "\n", + "# from eq'n 5\n", + "v_b=(r*omega_oa*IB)/(IA) # m/s\n", + "\n", + "# From eq'n 6\n", + "omega_ab=(r*omega_oa)/(IA) # radian/second\n", + "\n", + "# Results\n", + "\n", + "print\"The velocity at B is \",round(v_b,2),\"m/s\"\n", + "print\"The angular velocity of the connecting rod is \",round(omega_ab,2),\"radian/second\"\n" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "The velocity at B is 2.21 m/s\n", + "The angular velocity of the connecting rod is 5.47 radian/second\n" + ] + } + ], + "prompt_number": 30 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 21.21-13,Page No:555" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "import math\n", + "\n", + "# Initilization of variables\n", + "\n", + "omega_ab=5 # rad/s # angular veocity of the bar\n", + "AB=0.20 # m\n", + "BC=0.15 # m\n", + "CD=0.3 # m\n", + "theta=30 # degree # where theta= angle made by AB with the horizontal\n", + "alpha=60 # degree # where alpha=angle made by CD with the horizontal\n", + "\n", + "# Calculations\n", + "\n", + "# Consider triangle BIC\n", + "IB=sin(alpha*(pi/180))*BC*1 # m\n", + "IC=sin(theta*(pi/180))*BC*1 # m\n", + "v_b=omega_ab*AB # m/s\n", + "\n", + "# let the angular velocity of the bar BC be omega_bc\n", + "omega_bc=v_b/IB # radian/second\n", + "v_c=omega_bc*IC # m/s\n", + "\n", + "# let the angular velocity of bar DC be omega_dc\n", + "omega_dc=v_c/CD # radian/second\n", + "\n", + "# Results\n", + "\n", + "print\"The angular velocity of bar BC is \",round(omega_bc,3),\"rad/s\"\n", + "print\"The angular velocity of bar CD is \",round(omega_dc,2),\"rad/s\"\n" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "The angular velocity of bar BC is 7.7 rad/s\n", + "The angular velocity of bar CD is 1.92 rad/s\n" + ] + } + ], + "prompt_number": 34 + } + ], + "metadata": {} + } + ] +} \ No newline at end of file -- cgit