{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "# Chapter 14 Kinetics of a Particle : Work and Energy" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Ex 14.1 Page No 569" ] }, { "cell_type": "code", "execution_count": 5, "metadata": { "collapsed": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "UT = 504.7 J\n" ] } ], "source": [ "# Ex 14.1\n", "import math\n", "from __future__ import division\n", "\n", "# Variable Declaration\n", "P = 400 #[Newtons]\n", "s = 2 #[meters]\n", "\n", "# Calculation\n", "# Horizontal Force P\n", "UP = round(P*s*math.cos(math.pi*30/180),1) #[Joules]\n", "# Spring force Fs\n", "Us = round(-((1/2)*30*2.5**(2)-(1/2)*30*0.5**(2)),1) #[Joules]\n", "# Weight W\n", "UW = round(-98.1*(2*math.sin(math.pi*30/180)),1) #[Joules]\n", "# Total Work\n", "UT = UP+Us+UW #[Joules]\n", "\n", "# Result\n", "print\"UT = \",(UT),\"J\"" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Ex 14.2 Page No 574" ] }, { "cell_type": "code", "execution_count": 1, "metadata": { "collapsed": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "s = 4.0 m\n" ] } ], "source": [ "# Ex 14.2\n", "from __future__ import division\n", "import math\n", "\n", "# Variable Declaration\n", "uk = 0.5\n", "m = 20 #[kilo Newton]\n", "\n", "# Calculation\n", "# Using +ΣFn = 0\n", "NA = round(m*math.cos(math.pi*10/180),2) #[kilo Newtons]\n", "FA = uk*NA #[kilo Newtons]\n", "# Principle of Work and Energys\n", "s = round((-(1/2)*(m/9.81)*(5**(2)))/(m*math.sin(math.pi*10/180)-9.85),1) #[meters]\n", " \n", "# Result\n", "print\"s = \",(s),\"m\"" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Ex 14.3 Page No 575" ] }, { "cell_type": "code", "execution_count": 17, "metadata": { "collapsed": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "v = 5.47 m/s\n", "t = 1.79 s\n" ] } ], "source": [ "# Ex 14.3\n", "from __future__ import division\n", "from scipy import integrate\n", "\n", "# Calculation\n", "v = round((2.78*3+0.8*3**(3))**(1/2),2) #[meters per second]\n", "x = lambda s : 1/((2.78*s+0.8*s**(3))**(1/2))\n", "t = round(integrate.quad(x,0,3)[0],2) #[seconds]\n", " \n", "# Result\n", "print\"v = \",(v),\"m/s\"\n", "print\"t = \",(t),\"s\"" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Ex 14.4 Page No 576" ] }, { "cell_type": "code", "execution_count": 21, "metadata": { "collapsed": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "h = 0.963 m\n" ] } ], "source": [ "# Ex 14.4\n", "from __future__ import division\n", "\n", "# Calculation\n", "# Using Principle of Work and Energy\n", "h = round(((-(1/2)*200*(0.6**(2))+(1/2)*200*(0.7**(2)))/(19.62))+0.3,3) #[meters]\n", "\n", "# Result\n", "print\"h = \",(h),\"m\"" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Ex 14.5 Page No 577" ] }, { "cell_type": "code", "execution_count": 24, "metadata": { "collapsed": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "thetamax = 42.7 degrees\n" ] } ], "source": [ "# Ex 14.5\n", "import math\n", "\n", "# Calculation\n", "thetamax = round(math.degrees(math.acos((9.81+1)/(4.905+9.81))),1) #[Degrees]\n", "\n", "# Result\n", "print\"thetamax = \",(thetamax),\"degrees\"" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Ex 14.6 Page No 578" ] }, { "cell_type": "code", "execution_count": 29, "metadata": { "collapsed": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "delta_sB = 0.883 m\n" ] } ], "source": [ "# EX 14.6\n", "from __future__ import division\n", "\n", "# Calculation\n", "vA = -4*2 #[meters per second]\n", "# Substituting delta_sA = -4*delta_sB\n", "delta_sB = round(((1/2)*10*(vA**(2))+(1/2)*100*(2**(2)))/(-4*98.1+981),3) #[meters]\n", "\n", "# Result\n", "print\"delta_sB = \",(delta_sB),\"m\"" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Ex 14.8 Page No 586" ] }, { "cell_type": "code", "execution_count": 39, "metadata": { "collapsed": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "P = 162.0 kW\n" ] } ], "source": [ "# Ex 14.8\n", "import math\n", "from __future__ import division\n", "\n", "# Variable Declaration\n", "uk = 0.35\n", "\n", "# Calculation\n", "# Using +ΣFy(upward) = 0\n", "NC = 19.62 #[kilo Newtons]\n", "FC = uk*NC #[kilo Newtons]\n", "v = round(math.sqrt(((1/2)*2000*(25**(2))-6.867*(10**(3))*10)/((1/2)*2000)),2) #[meters per second]\n", "P = round(FC*v,1) #[kilo Watts]\n", "\n", "# Result\n", "print\"P = \",(P),\"kW\" # Correction in the answer" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Ex 14.9 Page No 595" ] }, { "cell_type": "code", "execution_count": 44, "metadata": { "collapsed": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "T = 148.7 kN\n" ] } ], "source": [ "# Ex 14.9\n", "import math\n", "\n", "# Calculation\n", "# Using Principle of Conservation of Energy\n", "vB = round(math.sqrt((8000*9.81*20*math.cos(math.pi*15/180)-8000*9.81*20*math.cos(math.pi*60/180))/((1/2)*8000)),1) #[meters per second]\n", "# Using ΣFn = m*an\n", "T = 8000*9.81*math.cos(math.pi*15/180)+8000*(13.5**(2))/20 #[Newtons]\n", "\n", "# Result\n", "print\"T = \",round((T/1000),1),\"kN\"" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Ex 14.10 Page No 596" ] }, { "cell_type": "code", "execution_count": 47, "metadata": { "collapsed": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "sA = 0.331 m\n" ] } ], "source": [ "# Ex 14.10\n", "import numpy as np\n", "\n", "# Calculation\n", "coeff = [13500, -2481, -660.75]\n", "# Taking positive root\n", "sA = round(np.roots(coeff)[0],3) #[meters]\n", "\n", "# Result\n", "print\"sA = \",(sA),\"m\"" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Ex 14.11 Page No 597" ] }, { "cell_type": "code", "execution_count": 51, "metadata": { "collapsed": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Part(a)\n", "vC = 4.39 m/s\n", "\n", "Part(b)\n", "vC = 4.82 m/s\n" ] } ], "source": [ "# Ex 14.11\n", "import math\n", "from __future__ import division\n", "\n", "# Calculation\n", "# Part(a) Potential Energy\n", "vC = round(math.sqrt((-(1/2)*3*(0.5**(2))+2*9.81*1)/((1/2)*2)),2) #[meters per second]\n", "\n", "# Result Part(a)\n", "print\"Part(a)\"\n", "print\"vC = \",(vC),\"m/s\\n\"\n", "\n", "# Part(b) Conservation of Energy\n", "vC = round(math.sqrt(((1/2)*2*(2**(2))-(1/2)*3*(0.5**(2))+2*9.81*1)/((1/2)*2)),2) #[meters per second]\n", "\n", "# Result Part(b)\n", "print\"Part(b)\"\n", "print\"vC = \",(vC),\"m/s\"\n" ] }, { "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 }