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diff --git a/Engineering_Mechanics_Statics_and_Dynamics_by_Hibbeler_and_Gupta/Chapter_8.ipynb b/Engineering_Mechanics_Statics_and_Dynamics_by_Hibbeler_and_Gupta/Chapter_8.ipynb new file mode 100644 index 00000000..f2059979 --- /dev/null +++ b/Engineering_Mechanics_Statics_and_Dynamics_by_Hibbeler_and_Gupta/Chapter_8.ipynb @@ -0,0 +1,406 @@ +{ + "cells": [ + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# Chapter 8 Friction" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Ex 8.1 Page No 305" + ] + }, + { + "cell_type": "code", + "execution_count": 4, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "F = 69.3 N\n", + "NC = 236.2 N\n", + "x = -9.08 mm\n" + ] + } + ], + "source": [ + "# Example 8.1\n", + "import math\n", + "\n", + "# Variable Declaration\n", + "P = 80 #[Newton]\n", + "\n", + "# Calculation\n", + "# Using +ΣF_x(right) = 0+ΣMO(counterclockwise) = 0\n", + "F = round(80*math.cos(math.pi*30/180),1) #[Newton]\n", + "\n", + "# Using +ΣF_y(upward) = 0\n", + "NC = round(80*math.sin(math.pi*30/180)+196.2,1) #[Newton]\n", + "\n", + "# Using +ΣMO(counterclockwise) = 0\n", + "x = (80*math.cos(math.pi*30/180)*0.2-80*math.sin(math.pi*30/180)*0.4)/NC #[meter]\n", + "\n", + "# Result\n", + "print\"F = \",(F),\"N\"\n", + "print\"NC = \",(NC),\"N\"\n", + "print\"x = \",(round(x*1000,2)),\"mm\"\n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Ex 8.2 Page No 306" + ] + }, + { + "cell_type": "code", + "execution_count": 6, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "us = 0.466\n" + ] + } + ], + "source": [ + "# Ex 8.2\n", + "import math\n", + "\n", + "# Calculation\n", + "# W*sin25 = us(W*cos25)\n", + "us = round(math.tan(math.pi*25/180),3)\n", + "\n", + "# Result\n", + "print\"us = \",(us)\n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Ex 8.3 Page No 307" + ] + }, + { + "cell_type": "code", + "execution_count": 10, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "us = 0.228\n" + ] + } + ], + "source": [ + "# Ex 8.3\n", + "import numpy as np\n", + "\n", + "# Calculation\n", + "coeff = [1, -4.619, 1]\n", + "us = np.roots(coeff)\n", + "\n", + "# Result\n", + "# Finding the smallest root\n", + "print\"us = \",(round(min(us),3))" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Ex 8.4 Page No 308" + ] + }, + { + "cell_type": "code", + "execution_count": 14, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "us_min = 0.268\n", + "ug_min = 0.0893\n" + ] + } + ], + "source": [ + "# Ex 8.4\n", + "import math\n", + "\n", + "# Calculation\n", + "# Using +ΣF_x(right) = 0,FA = F and NA = N for bottom pipe\n", + "# us_min = F/N\n", + "us_min = round(math.sin(math.pi*30/180)/(1+math.cos(math.pi*30/180)),3)\n", + "# Let smallest required coefficient of static friction be ug_min\n", + "# ug_min = F/NC\n", + "ug_min = round(0.2679*0.5/1.5,4)\n", + "\n", + "# Result\n", + "print\"us_min = \",(us_min)\n", + "print\"ug_min = \",(ug_min)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Ex 8.5 Page No 309" + ] + }, + { + "cell_type": "code", + "execution_count": 1, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "P = 266.7 N\n", + "NC = 400 N\n", + "FC = 200.0 N\n", + "FB = 66.7 N\n" + ] + } + ], + "source": [ + "# Ex 8.5\n", + "import numpy as np\n", + "\n", + "# Variable Declaration\n", + "uB = 0.2\n", + "uC = 0.5\n", + "\n", + "# Calculation\n", + "# Post slips only at B\n", + "# FB = uB*NB\n", + "FB = uB*400 #[Newton]\n", + "# Using +ΣMC(counterclockwise) = 0\n", + "P = FB/0.25 #[Newton]\n", + "# Using +ΣF_y(upward) = 0\n", + "NC = 400 #[Newton]\n", + "# Using +ΣF_x(right) = 0\n", + "FC = P-FB #[Newton]\n", + "\n", + "# Post slips only at C\n", + "FC = uC*NC #[Newton]\n", + "# Using +ΣF_x(right) = 0 and # Using +ΣMC(counterclockwise) = 0\n", + "a = np.array([[1,-1],[-0.25,1]])\n", + "b = np.array([200,0])\n", + "x = np.linalg.solve(a, b)\n", + "P = round(x[0],1) #[Newton]\n", + "FB = round(x[1],1) #[Newton]\n", + "\n", + "# Result\n", + "print\"P = \",(P),\"N\"\n", + "print\"NC = \",(NC),\"N\"\n", + "print\"FC = \",(FC),\"N\"\n", + "print\"FB = \",(FB),\"N\"" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "collapsed": true + }, + "source": [ + "## Ex 8.6 Page No 310" + ] + }, + { + "cell_type": "code", + "execution_count": 6, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "NA = 1084.5 N\n", + "FA = 162.7 N\n", + "FB = 162.7 N\n", + "P = 498.2 N\n" + ] + } + ], + "source": [ + "# Ex 8.6\n", + "import math\n", + "import numpy as np\n", + "\n", + "# Variable Declaration\n", + "usA = 0.15\n", + "usB = 0.4\n", + "\n", + "# Calculation\n", + "\n", + "# Pipe rolls up incline\n", + "# Using +ΣF_x(right) = 0, +ΣMO(counterclockwise) = 0 and FB = 0.4*P\n", + "a = np.array([[-1,1],[-400,0.4*400]])\n", + "b = np.array([981*math.sin(math.pi*20/180),0])\n", + "x = np.linalg.solve(a, b)\n", + "FA = round(x[0],1) #[Newton]\n", + "P = round(x[1],1) #[Newton]\n", + "FB = FA #[Newton]\n", + "NA = round(FB+981*math.cos(math.pi*20/180),1) #[Newton]\n", + "P = round(981*math.sin(math.pi*20/180)+FA,1) #[Newton]\n", + "\n", + "# Pipe slides up incline\n", + "# Using +ΣMO(counterclockwise) = 0 and FA = 0.15*NA\n", + "a = np.array([[-0.15*400,400],[1,-1]])\n", + "b = np.array([0,981*math.cos(math.pi*20/180)])\n", + "x = np.linalg.solve(a, b)\n", + "NA = round(x[0],1) #[Newton]\n", + "FB = round(x[1],1) #[Newton]\n", + "FA = FB #[Newton]\n", + "P = round(FA+981*math.sin(math.pi*20/180),1) #[Newton]\n", + "\n", + "# Result\n", + "print\"NA = \",(NA),\"N\"\n", + "print\"FA = \",(FA),\"N\"\n", + "print\"FB = \",(FB),\"N\"\n", + "print\"P = \",(P),\"N\"\n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Ex 8.8 Page No 319" + ] + }, + { + "cell_type": "code", + "execution_count": 14, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "M = 6.38 N.m\n" + ] + } + ], + "source": [ + "# Ex 8.8\n", + "import math\n", + "from __future__ import division\n", + "\n", + "# Variable Declaration\n", + "us = 0.25\n", + "W = 2000 #[Newton]\n", + "r = 5 #[millimeter]\n", + "\n", + "# Calculation\n", + "phi_s = round(math.degrees(math.atan(us)),2)\n", + "theta = round(math.degrees(math.atan(2/(2*math.pi*5))),2)\n", + "M = 2*W*r*math.tan(math.pi*(phi_s+theta)/180) #[Newton millimeter]\n", + "\n", + "# Result\n", + "print\"M = \",round(M/1000,2),\"N.m\"\n" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "collapsed": true + }, + "source": [ + "## Ex 8.9 Page No 324" + ] + }, + { + "cell_type": "code", + "execution_count": 2, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "m = 15.7 kg\n" + ] + } + ], + "source": [ + "# Ex 8.9\n", + "import math\n", + "from __future__ import division\n", + "\n", + "# Variable Declaration\n", + "us = 0.25\n", + "\n", + "# Calculation\n", + "T1 = round(500/(math.exp(us*(3/4)*math.pi)),1)\n", + "W = round(T1/(math.exp(us*(3/4)*math.pi)),1)\n", + "m = round(W/9.81,1)\n", + "\n", + "# Result\n", + "print\"m = \",(m),\"kg\"" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], + "source": [] + } + ], + "metadata": { + "anaconda-cloud": {}, + "kernelspec": { + "display_name": "Python [default]", + "language": "python", + "name": "python2" + }, + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 2 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython2", + "version": "2.7.12" + } + }, + "nbformat": 4, + "nbformat_minor": 1 +} |