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| author | Thomas Stephen Lee | 2015-08-28 16:53:23 +0530 |
|---|---|---|
| committer | Thomas Stephen Lee | 2015-08-28 16:53:23 +0530 |
| commit | 4a1f703f1c1808d390ebf80e80659fe161f69fab (patch) | |
| tree | 31b43ae8895599f2d13cf19395d84164463615d9 /Engineering_Mechanics_by_Tayal_A.K./chapter22_2.ipynb | |
| parent | 9d260e6fae7328d816a514130b691fbd0e9ef81d (diff) | |
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diff --git a/Engineering_Mechanics_by_Tayal_A.K./chapter22_2.ipynb b/Engineering_Mechanics_by_Tayal_A.K./chapter22_2.ipynb new file mode 100755 index 00000000..c5908132 --- /dev/null +++ b/Engineering_Mechanics_by_Tayal_A.K./chapter22_2.ipynb @@ -0,0 +1,282 @@ +{
+ "metadata": {
+ "name": "chapter22.ipynb"
+ },
+ "nbformat": 3,
+ "nbformat_minor": 0,
+ "worksheets": [
+ {
+ "cells": [
+ {
+ "cell_type": "heading",
+ "level": 1,
+ "metadata": {},
+ "source": [
+ "Chapter 22: Kinetics Of Rigid Body:Force And Acceleration"
+ ]
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 22.22-1,Page No:562"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "\n",
+ "# Initilization of variables\n",
+ "\n",
+ "N=1500 # r.p.m\n",
+ "r=0.5 # m # radius of the disc\n",
+ "m=300 # N # weight of the disc\n",
+ "t=120 # seconds # time in which the disc comes to rest\n",
+ "omega=0 \n",
+ "pi=3.14 \n",
+ "g=9.81 # m/s^2\n",
+ "\n",
+ "# Calculations\n",
+ "\n",
+ "omega_0=(2*pi*N)*0.01666 # rad/s #1/60=0.01666\n",
+ "\n",
+ "# angular deceleration is given as,\n",
+ "alpha=-(omega_0/t) # radian/second^2\n",
+ "theta=(omega_0**2)/(2*(-alpha)) # radian\n",
+ "\n",
+ "# Let n be the no of revolutions taken by the disc before it comes to rest, then\n",
+ "n=theta/(2*pi)\n",
+ "\n",
+ "# Now,\n",
+ "I_G=((0.5)*m*r**2)/g\n",
+ "\n",
+ "# The frictional torque is given as,\n",
+ "M=I_G*alpha # N-m\n",
+ "\n",
+ "# Results\n",
+ "\n",
+ "print\"(a) The no of revolutions executed by the disc before coming to rest is \",round(n,2)\n",
+ "print\"(b) The frictional torque is \",round(M),\"N-m\"\n"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "(a) The no of revolutions executed by the disc before coming to rest is 1499.4\n",
+ "(b) The frictional torque is -5.0 N-m\n"
+ ]
+ }
+ ],
+ "prompt_number": 9
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 22.22-2,Page No:563"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "\n",
+ "# Initilization of variables\n",
+ "\n",
+ "s=1 # m\n",
+ "mu=0.192 # coefficient of static friction\n",
+ "g=9.81 # m/s^2\n",
+ "\n",
+ "# Calculations\n",
+ "\n",
+ "# The maximum angle of the inclined plane is given as,\n",
+ "theta=arctan(3*mu)*(180/pi) # degree\n",
+ "a=(2/3)*g*sin(theta*(pi/180)) # m/s^2 # by solving eq'n 4\n",
+ "v=(2*a*s)**0.5 # m/s\n",
+ "\n",
+ "# Let the acceleration at the centre be A which is given as,\n",
+ "A=g*sin(theta*(pi/180)) # m/s^2 # from eq'n 1\n",
+ "\n",
+ "# Results\n",
+ "\n",
+ "print\"(a) The acceleration at the centre is \",round(A,3),\"m/s^2\"\n",
+ "print\"(b) The maximum angle of the inclined plane is \",round(theta),\"degree\"\n"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "(a) The acceleration at the centre is 4.896 m/s^2\n",
+ "(b) The maximum angle of the inclined plane is 30.0 degree\n"
+ ]
+ }
+ ],
+ "prompt_number": 11
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 22.22-5,Page No:568"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "\n",
+ "# Initilization of variables\n",
+ "\n",
+ "W_a=25 # N \n",
+ "W_b=25 # N \n",
+ "W=200 # N # weight of the pulley\n",
+ "i_g=0.2 # m # radius of gyration\n",
+ "g=9.81 # m/s^2\n",
+ "\n",
+ "# Calculations\n",
+ "\n",
+ "# Solving eqn's 1 & 2 for acceleration of weight A (assume a)\n",
+ "a=(0.15*W_a*g)/(((W*i_g**2)/(0.45))+(0.45*W_a)+((0.6*W_b)/(3))) # m/s^2\n",
+ "\n",
+ "# Results\n",
+ "\n",
+ "print\"The acceleration of weight A is \",round(a,2),\"m/s^2\"\n"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "The acceleration of weight A is 1.08 m/s^2\n"
+ ]
+ }
+ ],
+ "prompt_number": 13
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 22.22-8,Page No:571"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "\n",
+ "# Initilization of variables\n",
+ "\n",
+ "r_1=0.075 # m\n",
+ "r_2=0.15 # m\n",
+ "P=50 # N\n",
+ "W=100 # N\n",
+ "i_g=0.05 # m\n",
+ "theta=30 # degree\n",
+ "g=9.81 # m/s^2\n",
+ "\n",
+ "# Calculations\n",
+ "\n",
+ "# The eq'n for acceleration of the pool is given by solving eqn's 1,2 &3 as,\n",
+ "a=(50*g*(r_2*cos(theta*(pi/180))-r_1))/(100*((i_g**2/r_2)+r_2)) # m/s^2\n",
+ "\n",
+ "# Results\n",
+ "\n",
+ "print\"The acceleration of the pool is \",round(a,2),\"m/s^2\"\n"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "The acceleration of the pool is 1.62 m/s^2\n"
+ ]
+ }
+ ],
+ "prompt_number": 15
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 22.22-10,Page No:574"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "\n",
+ "# Initilization of variables\n",
+ "\n",
+ "L=1 # m # length of rod AB\n",
+ "m=10 # kg # mass of the rod\n",
+ "g=9.81 \n",
+ "theta=30 # degree\n",
+ "\n",
+ "# Calculations\n",
+ "\n",
+ "# solving eq'n 4 for omega we get,\n",
+ "omega=(2*16.82*sin(theta*(pi/180)))**0.5 # rad/s\n",
+ "\n",
+ "# Now solving eq'ns 1 &3 for alpha we get,\n",
+ "alpha=(1.714)*g*cos(theta*(pi/180)) # rad/s\n",
+ "\n",
+ "# Components of reaction are given as,\n",
+ "R_t=((m*g*cos(theta*(pi/180)))-((m*alpha*L)/4)) # N\n",
+ "R_n=((m*omega**2*L)/4)+(m*g*sin(theta*(pi/180))) # N\n",
+ "R=(R_t**2+R_n**2)**0.5 # N \n",
+ "\n",
+ "# Results\n",
+ "\n",
+ "print\"(a) The angular velocity of the rod is \",round(omega,2),\"rad/sec\"\n",
+ "print\"(b) The reaction at the hinge is \",round(R,1),\"N\"\n"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "(a) The angular velocity of the rod is 4.1 rad/sec\n",
+ "(b) The reaction at the hinge is 103.2 N\n"
+ ]
+ }
+ ],
+ "prompt_number": 31
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [],
+ "language": "python",
+ "metadata": {},
+ "outputs": []
+ }
+ ],
+ "metadata": {}
+ }
+ ]
+}
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