From 6279fa19ac6e2a4087df2e6fe985430ecc2c2d5d Mon Sep 17 00:00:00 2001 From: kinitrupti Date: Fri, 12 May 2017 18:53:46 +0530 Subject: Removed duplicates --- .../chapter21.ipynb | 658 --------------------- 1 file changed, 658 deletions(-) delete mode 100755 backup/Engineering_Mechanics_by_Tayal_A.K._version_backup/chapter21.ipynb (limited to 'backup/Engineering_Mechanics_by_Tayal_A.K._version_backup/chapter21.ipynb') diff --git a/backup/Engineering_Mechanics_by_Tayal_A.K._version_backup/chapter21.ipynb b/backup/Engineering_Mechanics_by_Tayal_A.K._version_backup/chapter21.ipynb deleted file mode 100755 index c58e0b47..00000000 --- a/backup/Engineering_Mechanics_by_Tayal_A.K._version_backup/chapter21.ipynb +++ /dev/null @@ -1,658 +0,0 @@ -{ - "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