From bbd6787f847c9312843e14fbaa3537b9235bc054 Mon Sep 17 00:00:00 2001 From: kinitrupti Date: Wed, 24 May 2017 11:38:08 +0530 Subject: updated book Engineering_Mechanics_Statics_and_Dynamics_by_Hibler_and_Gupta --- .../Chapter_10_Moments_of_Inertia.ipynb | 1141 ++++------- .../Chapter_11__Virtual_Work.ipynb | 961 ++------- .../Chapter_12_Kinematics_of_a_Particle.ipynb | 2129 +++++++++++++------- ...tics_of_a_Particle_Force_and_Acceleration.ipynb | 1251 +++++------- ...4_Kinetics_of_a_Particle_Work_and_Energy_.ipynb | 1175 ++++------- ...netics_of_a_Particle_Impulse_and_Momentum.ipynb | 1317 ++++++------ ...pter_16_Planar_Kinematics_of_a_Rigid_Body.ipynb | 1465 +++++++------- ...cs_of_a_Rigid_Body_Force_and_Acceleration.ipynb | 1491 +++++++------- ..._Kinetics_of_a_Rigid_Body_Work_and_Energy.ipynb | 1176 ++++------- ...tics_of_a_Rigid_Body_Impulse_and_Momentum.ipynb | 1096 ++++------ .../Chapter_1_General_Principles.ipynb | 864 ++------ .../Chapter_2_Force_Vectors.ipynb | 1805 ++++++++++------- .../Chapter_3_Equilibrium_of_a_Particle.ipynb | 1215 +++++------ .../Chapter_4_Force_System_Resultants.ipynb | 2010 +++++++++++------- .../Chapter_5_Equilibrium_of_a_Rigid_Body.ipynb | 1308 ++++++------ .../Chapter_6_Structural_Analysis.ipynb | 1515 +++++++------- .../Chapter_7_Internal_Forces.ipynb | 1138 ++++------- .../Chapter_8_Friction.ipynb | 1153 ++++------- .../Chapter_9_Center_of_Gravity_and_Centroid.ipynb | 1284 +++++------- 19 files changed, 11301 insertions(+), 14193 deletions(-) (limited to 'Engineering_Mechanics_Statics_and_Dynamics_by_Hibler_and_Gupta') diff --git a/Engineering_Mechanics_Statics_and_Dynamics_by_Hibler_and_Gupta/Chapter_10_Moments_of_Inertia.ipynb b/Engineering_Mechanics_Statics_and_Dynamics_by_Hibler_and_Gupta/Chapter_10_Moments_of_Inertia.ipynb index 4425b571..c3e6cf59 100644 --- a/Engineering_Mechanics_Statics_and_Dynamics_by_Hibler_and_Gupta/Chapter_10_Moments_of_Inertia.ipynb +++ b/Engineering_Mechanics_Statics_and_Dynamics_by_Hibler_and_Gupta/Chapter_10_Moments_of_Inertia.ipynb @@ -1,747 +1,394 @@ - - - - - - - - - - - - - - - - - - - - - - - Python-Textbook-Companions/Chapter_10_Moments_of_Inertia.ipynb at 1b1bb67e9ea912be5c8591523c8b328766e3680f · FOSSEE/Python-Textbook-Companions - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
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- - - - - - +{ + "cells": [ + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# Chapter 10 Moments of Inertia" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Ex 10.2 Page No 382 " + ] + }, + { + "cell_type": "code", + "execution_count": 20, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Solution 1\n", + "I_x = 106666667.0 mm**(4)\n", + "\n", + "Solution 2\n", + "I_x = 106666667.0 mm**(4)\n" + ] + } + ], + "source": [ + "# Ex 10.2\n", + "from scipy import integrate\n", + "from __future__ import division\n", + "\n", + "# Calculation Solution 1\n", + "a = lambda y: (y**2)*(100-(y**2)/400)\n", + "I_x = round(integrate.quad(a, 0, 200)[0],0) #[millimeter**(4)]\n", + "\n", + "# Result Solution 1\n", + "print\"Solution 1\"\n", + "print\"I_x = \",(I_x),\"mm**(4)\\n\"\n", + "\n", + "# Calculation Solution 2\n", + "a = lambda x: (1/3)*(400*x)**(3/2)\n", + "I_x = round(integrate.quad(a, 0, 100)[0],0) #[millimeter**(4)]\n", + "\n", + "# Result Solution 2\n", + "print\"Solution 2\"\n", + "print\"I_x = \",(I_x),\"mm**(4)\"" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Ex 10.4 Page No 384" + ] + }, + { + "cell_type": "code", + "execution_count": 12, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Solution 1\n", + "I_x = 0.0357 m**(4)\n", + "\n", + "Solution 2\n", + "I_x = 0.0357 m**(4)\n" + ] + } + ], + "source": [ + "# Ex 10.4\n", + "\n", + "from scipy import integrate\n", + "from __future__ import division\n", + "import math\n", + "\n", + "# Calculation Solution 1\n", + "a = lambda y: y**(2)*(math.sqrt(y)-y)\n", + "I_x = round(integrate.quad(a, 0, 1)[0],4) #[meter**(4)]\n", + "\n", + "# Result Solution 1\n", + "print\"Solution 1\"\n", + "print\"I_x = \",(I_x),\"m**(4)\\n\"\n", + "\n", + "# Calculation Solution 2\n", + "a = lambda x: (1/3)*(x**(3)-x**(6))\n", + "I_x = round(integrate.quad(a, 0, 1)[0],4) #[meter**(4)]\n", + "\n", + "# Result Solution 2\n", + "print\"Solution 2\"\n", + "print\"I_x = \",(I_x),\"m**(4)\"" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Ex 10.5 Page No 387" + ] + }, + { + "cell_type": "code", + "execution_count": 13, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "I_x = 101148542.17 mm**(4)\n" + ] + } + ], + "source": [ + "# Ex 10.5\n", + "import math\n", + "from __future__ import division\n", + "\n", + "# Calculation\n", + "# Using Parallel Axis Theorem\n", + "# Circle\n", + "I_xc = (1/4)*math.pi*25**(4)+math.pi*25**(2)*75**(2) #[millimeter**(4)]\n", + "# Rectangle\n", + "I_xr = (1/12)*100*150**(3)+100*150*75**(2) #[millimeter**(4)]\n", + "# Let I_x be moment of inertia for composite area\n", + "I_x = -I_xc+I_xr #[millimeter**(4)]\n", + "\n", + "# Result\n", + "print\"I_x = \",(I_x),\"mm**(4)\"" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Ex 10.6 Page No 388" + ] + }, + { + "cell_type": "code", + "execution_count": 21, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "I_x = 2900000000.0 mm**(4)\n", + "I_y = 5600000000.0 mm**(4)\n" + ] + } + ], + "source": [ + "# Ex 10.6\n", + "import math\n", + "from __future__ import division\n", + "\n", + "# Calculation\n", + "# Using Parallel axis theorem\n", + "# Rectangle A\n", + "I_xA = (1/12)*100*300**(3)+100*300*200**(2) #[millimeter**(4)]\n", + "I_yA = (1/12)*300*100**(3)+100*300*250**(2) #[millimeter**(4)]\n", + "# Rectangle B\n", + "I_xB = (1/12)*600*100**(3) #[millimeter**(4)]\n", + "I_yB = (1/12)*100*600**(3) #[millimeter**(4)]\n", + "# Rectangle D\n", + "I_xD = (1/12)*100*300**(3)+100*300*200**(2) #[millimeter**(4)]\n", + "I_yD = (1/12)*300*100**(3)+100*300*250**(2) #[millimeter**(4)]\n", + "I_x = I_xA+I_xB+I_xD #[millimeter**(4)]\n", + "I_y = I_yA+I_yB+I_yD #[millimeter**(4)]\n", + "\n", + "# Result\n", + "print\"I_x = \",(I_x),\"mm**(4)\"\n", + "print\"I_y = \",(I_y),\"mm**(4)\"" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Ex 10.8 Page No 394" + ] + }, + { + "cell_type": "code", + "execution_count": 22, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "I_xy = -3000000000 mm**(4)\n" + ] + } + ], + "source": [ + "# Ex 10.8\n", + "\n", + "# Calculation\n", + "# Rectangle A\n", + "I_xyA = 0+300*100*(-250)*(200)\n", + "# Rectangle B\n", + "I_xyB = 0+0\n", + "# Rectangle D\n", + "I_xyD = 0+300*100*(250)*(-200)\n", + "# Let I_xy be product of inertia for entire cross section\n", + "I_xy = I_xyA+I_xyB+I_xyD\n", + "\n", + "# Result\n", + "print\"I_xy = \",(I_xy),\"mm**(4)\"\n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Ex 10.10 Page No 400" + ] + }, + { + "cell_type": "code", + "execution_count": 23, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "I_y = 0.873 kg.m**(2)\n" + ] + } + ], + "source": [ + "# Ex 10.10\n", + "from scipy import integrate\n", + "from __future__ import division\n", + "import math\n", + "\n", + "# Variable Declaration\n", + "rho = 5 #[milligram per meter cube]\n", + "\n", + "# Calculation \n", + "a = lambda y: ((5*math.pi)/2)*y**(8)\n", + "I_y = round(integrate.quad(a, 0, 1)[0],3) #[kg meter square]\n", + "\n", + "# Result\n", + "print\"I_y = \",(I_y),\"kg.m**(2)\"\n", + "\n", + "\n", + "\n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Ex 10.11 Page No 403" + ] + }, + { + "cell_type": "code", + "execution_count": 25, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "IO = 1.2 kg.m**(2)\n" + ] + } + ], + "source": [ + "# Ex 10.11\n", + "import math\n", + "\n", + "# Variable Declaration\n", + "rho = 8000 #[kg meter**(2)]\n", + "t = 0.01 #[meter]\n", + "\n", + "# Calculation\n", + "# Disk\n", + "IOd = (1/2)*15.71*0.25**(2)+15.71*0.25**(2) #[kg meter**(2)]\n", + "# Hole\n", + "IOh = (1/2)*3.93*0.125**(2)+3.93*0.25**(2) #[kg meter**(2)]\n", + "IO = round(IOd-IOh,2) #[kg meter**(2)]\n", + "# Result\n", + "print\"IO = \",(IO),\"kg.m**(2)\"\n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Ex 10.12 Page No 404" + ] + }, + { + "cell_type": "code", + "execution_count": 29, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "IO = 17.0 kg.m**(2)\n", + "IG = 8.0 kg.m**(2)\n" + ] + } + ], + "source": [ + "# Ex 10.12\n", + "import math\n", + "from __future__ import division\n", + "\n", + "# Variable Declaration\n", + "W = 3 #[kilogram]\n", + "\n", + "# Calculation\n", + "# Rod OA\n", + "IOAO = (1/3)*W*(2**(2)) #[kg meter**(2)]\n", + "# Rod BC\n", + "IBCO = (1/12)*W*(2**(2))+W*(2**(2)) #[kg meter**(2)]\n", + "# Let IO be moment of inertia of pendulum about O\n", + "IO = round(IOAO+IBCO,1) #[kg meter**(2)]\n", + "ybar = ((1*W+2*W)/(3+3)) #[meter]\n", + "IG = IO-2*W*ybar #[kg meter**(2)]\n", + "\n", + "# Result\n", + "print\"IO = \",(IO),\"kg.m**(2)\"\n", + "print\"IG = \",(IG),\"kg.m**(2)\"\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 +} diff --git a/Engineering_Mechanics_Statics_and_Dynamics_by_Hibler_and_Gupta/Chapter_11__Virtual_Work.ipynb b/Engineering_Mechanics_Statics_and_Dynamics_by_Hibler_and_Gupta/Chapter_11__Virtual_Work.ipynb index 2c1b585e..3ee3ef32 100644 --- a/Engineering_Mechanics_Statics_and_Dynamics_by_Hibler_and_Gupta/Chapter_11__Virtual_Work.ipynb +++ b/Engineering_Mechanics_Statics_and_Dynamics_by_Hibler_and_Gupta/Chapter_11__Virtual_Work.ipynb @@ -1,747 +1,214 @@ - - - - - - - - - - - - - - - - - - - - - - - Python-Textbook-Companions/Chapter_11__Virtual_Work.ipynb at 1b1bb67e9ea912be5c8591523c8b328766e3680f · FOSSEE/Python-Textbook-Companions - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
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- - - - - - +{ + "cells": [ + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# Chapter 11 Virtual Work" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Ex 11.1 Page No 418" + ] + }, + { + "cell_type": "code", + "execution_count": 1, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "theta = 63.0 degrees\n" + ] + } + ], + "source": [ + "# Ex 11.1\n", + "import math\n", + "from __future__ import division\n", + "\n", + "# Calculation\n", + "theta = round(math.degrees(math.atan(98.1/50)),1) #[Degrees]\n", + "\n", + "# Result\n", + "print\"theta = \",(theta),\"degrees\"" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Ex 11.3 Page No 420" + ] + }, + { + "cell_type": "code", + "execution_count": 8, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "xc = 0.981 m\n", + "Cx = 114.0 N\n" + ] + } + ], + "source": [ + "# Ex 11.3\n", + "import math\n", + "import numpy as np\n", + "\n", + "# Variable Declaration\n", + "theta = 45 #[Degrees]\n", + "\n", + "# Calculation\n", + "coeff = [1, -1.2*math.cos(math.pi*theta/180), -0.13]\n", + "# Taking only the positive root\n", + "xc = round(np.roots(coeff)[0],3) #[meter]\n", + "Cx = round(((-120*math.cos(math.pi*theta/180))*(1.2*math.cos(math.pi*theta/180)-2*xc))/(1.2*xc*math.sin(math.pi*theta/180)),0) #[Newton]\n", + "\n", + "# Result\n", + "print\"xc = \",(xc),\"m\"\n", + "print\"Cx = \",(Cx),\"N\"" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Ex 11.5 Page No 433" + ] + }, + { + "cell_type": "code", + "execution_count": 66, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "theta = 53.8 degrees\n", + "V1 = -29.4 (unstable equilibrium at theta = 0 degrees)\n", + "V2 = 46.9 (stable equilibrium at theta = 53.8 degrees)\n" + ] + } + ], + "source": [ + "# Ex 11.5\n", + "import math\n", + "from scipy.misc import derivative\n", + "from __future__ import division\n", + "\n", + "# Variable Declaration\n", + "W = 10*9.81 #[Newton]\n", + "k = 200 #[Newton per meter]\n", + "l = 0.6 #[meter]\n", + "\n", + "# Calculation\n", + "\n", + "# Let V1 = d**(2)V/dtheta**(2) at theta = 0 \n", + "def f1(x):\n", + " return (1/2)*k*(l**(2))*((1-math.cos(x))**(2))-(W*l/2)*(2-math.cos(x))\n", + "V1 = round(derivative(f1, 0*math.pi/180,dx=1e-6, n=2),1)\n", + "\n", + "# Let V2 = d**(2)V/dtheta**(2) at theta = 53.8 \n", + "def f2(x):\n", + " return (1/2)*k*(l**(2))*((1-math.cos(x))**(2))-(W*l/2)*(2-math.cos(x))\n", + "V2 = round(derivative(f2, 53.8*math.pi/180,dx=1e-6, n=2),1)\n", + " \n", + "# Result\n", + "print\"theta = \",(theta),\"degrees\"\n", + "print\"V1 = \",(V1),\"(unstable equilibrium at theta = 0 degrees)\"\n", + "print\"V2 = \",round(V2,1),\"(stable equilibrium at theta = 53.8 degrees)\" " + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Ex 11.6 Page No 434" + ] + }, + { + "cell_type": "code", + "execution_count": 65, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "m = 6.53 kg\n", + "V = -47.6 (unstable equilibrium at theta = 20 degrees)\n" + ] + } + ], + "source": [ + "# Ex 11.6\n", + "import math\n", + "from __future__ import division\n", + "from scipy.misc import derivative\n", + "\n", + "# Calculation\n", + "# From dV/dtheta at theta = 20 degrees\n", + "m = round(69.14/10.58,2) #[kilogram]\n", + "def f(x):\n", + " return 98.1*(1.5*math.sin(x)/2)-m*9.81*(1.92-math.sqrt(3.69-3.6*math.sin(x)))\n", + "\n", + "# Let V = d**(2)V/dtheta**(2) at theta = 20 degrees\n", + "V = round(derivative(f, 20*math.pi/180,dx=1e-6, n=2),1)\n", + "# Result\n", + "print\"m = \",(m),\"kg\"\n", + "print\"V = \",(V),\" (unstable equilibrium at theta = 20 degrees)\"\n", + "\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 +} diff --git a/Engineering_Mechanics_Statics_and_Dynamics_by_Hibler_and_Gupta/Chapter_12_Kinematics_of_a_Particle.ipynb b/Engineering_Mechanics_Statics_and_Dynamics_by_Hibler_and_Gupta/Chapter_12_Kinematics_of_a_Particle.ipynb index 2c6f12c9..59332347 100644 --- a/Engineering_Mechanics_Statics_and_Dynamics_by_Hibler_and_Gupta/Chapter_12_Kinematics_of_a_Particle.ipynb +++ b/Engineering_Mechanics_Statics_and_Dynamics_by_Hibler_and_Gupta/Chapter_12_Kinematics_of_a_Particle.ipynb @@ -1,747 +1,1382 @@ - - - - - - - - - - - - - - - - - - - - - - - Python-Textbook-Companions/Chapter_12_Kinematics_of_a_Particle.ipynb at 1b1bb67e9ea912be5c8591523c8b328766e3680f · FOSSEE/Python-Textbook-Companions - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
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- - - - - - +{ + "cells": [ + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# Chapter 12 Kinematics of a Particle" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Ex 12.1 Page No 450" + ] + }, + { + "cell_type": "code", + "execution_count": 3, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "s = 36.0 m\n", + "a = 20.0 m/s**(2)\n" + ] + } + ], + "source": [ + "# Ex 12.1\n", + "from scipy import integrate\n", + "from scipy.misc import derivative\n", + "\n", + "# Calculation\n", + "# Position\n", + "t = lambda t: 3*t**2+2*t\n", + "s = round(integrate.quad(t, 0, 3)[0],1) #[meter]\n", + "# Acceleration\n", + "# a = dv/dt\n", + "def f(t):\n", + " return 3*t**2+2*t\n", + "a = round(derivative(f, 3),1) #[meter per seconds square]\n", + "\n", + "# Result\n", + "print\"s = \",(s),\"m\"\n", + "print\"a = \",(a),\"m/s**(2)\"" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Ex 12.2 Page No 451" + ] + }, + { + "cell_type": "code", + "execution_count": 5, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "v = 0.559 m/s\n", + "s = 4.43 m\n" + ] + } + ], + "source": [ + "# Ex 12.2\n", + "from scipy import integrate\n", + "from __future__ import division\n", + "\n", + "# Calculation\n", + "# At t = 4 s\n", + "v = round(((1/(60**(2))) +0.8*4)**(-0.5),3) #[meter per second]\n", + "# ds = vdt\n", + "t = lambda t: ((1/(60**(2))) +0.8*t)**(-0.5) \n", + "s = round(integrate.quad(t, 0, 4)[0],2) #[meter]\n", + "\n", + "# Result\n", + "print\"v = \",(v),\"m/s\"\n", + "print\"s = \",(s),\"m\"" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Ex 12.3 Page No 452" + ] + }, + { + "cell_type": "code", + "execution_count": 11, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "sB = 326.7 m\n", + "vC = 80.1 m\n" + ] + } + ], + "source": [ + "# Ex 12.3\n", + "from __future__ import division\n", + "import math\n", + "\n", + "# Variable Declaration\n", + "vA = 75 #[meter per second]\n", + "aC = -9.81 #[meter per second square]\n", + "sA = 40 #[meter]\n", + "\n", + "# Calculation\n", + "# Maximum height\n", + "sB = round((-75**(2)/(2*-9.81))+40,1) #[meter]\n", + "# Velocity\n", + "# Method 1\n", + "vC = round(math.sqrt(0+2*(-9.81)*(0-327)),1) #[meter per second]\n", + "# Method 2\n", + "vC = round(math.sqrt(75**(2)+2*(-9.81)*(0-40)),1) #[meter per second]\n", + "\n", + "# Result\n", + "print\"sB = \",(sB),\"m\"\n", + "print\"vC = \",(vC),\"m\"" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Ex 12.4 Page No 453" + ] + }, + { + "cell_type": "code", + "execution_count": 14, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "vB = 346.4 mm/s\n", + "t = 0.658 s\n" + ] + } + ], + "source": [ + "# Ex 12.4\n", + "from scipy import integrate\n", + "\n", + "# Calculation\n", + "vB = round(2*(0.2**(2)-0.01)**(0.5)*1000,1) #[millimeter per second]\n", + "s = lambda s: (0.5)*(1/math.sqrt(s**(2)-0.01))\n", + "t = round(integrate.quad(s, 0.1, 0.2)[0],3) #[seconds]\n", + "\n", + "# Result\n", + "print\"vB = \",(vB),\"mm/s\"\n", + "print\"t = \",(t),\"s\"" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Ex 12.5 Page No 454" + ] + }, + { + "cell_type": "code", + "execution_count": 20, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "sT = 14.1 m\n", + "v_avg = 1.75 m/s\n", + "vsp_avg = 4.03 m/s\n" + ] + } + ], + "source": [ + "# Ex 12.5\n", + "\n", + "# Calculation\n", + "# ds = vdt\n", + "# s = t**(3)-3*t**(2) m\n", + "\n", + "# Let s1 be displacement at t = 0 sec\n", + "s1 = 0**(3)-3*0**(2) #[meter] \n", + "\n", + "# Let s2 be displacement at t = 2 sec\n", + "s2 = 2**(3)-3*2**(2) #[meter] \n", + "\n", + "# Let s3 be displacement at t = 0 sec\n", + "s3 = 3.5**(3)-3*3.5**(2) #[meter] \n", + "\n", + "# Let sT be distance travelled in 3.5 sec\n", + "sT = round(abs(s2)+abs(s2)+abs(s3),1) #[meter] \n", + "\n", + "# Velocity\n", + "# Let delta_s be displacement from t = 0 to t = 3.5 s\n", + "delta_s = s3 - s1 #[meter] \n", + "\n", + "# let v_avg be average velocity\n", + "v_avg = delta_s/(3.5-0) #[meter per second] \n", + "\n", + "# Let vsp_avg be average speed defined in terms of distance travelled sT\n", + "vsp_avg = round(sT/(3.5-0),2) #[meter per second] \n", + "\n", + "# Result\n", + "print\"sT = \",(sT),\"m\"\n", + "print\"v_avg = \",(v_avg),\"m/s\"\n", + "print\"vsp_avg = \",(vsp_avg),\"m/s\"" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Ex 12.6 Page No 460" + ] + }, + { + "cell_type": "code", + "execution_count": 32, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "data": { + 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+ "text/plain": [ + "" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "# Ex 12.6\n", + "%matplotlib inline\n", + "from matplotlib.pyplot import plot,title,xlabel,ylabel,text,axis,show\n", + "\n", + "# Calculation\n", + "# v-t graph\n", + "plot(\n", + " [0,10,30],\n", + " [0,10,10],\n", + " color='b',linewidth = 2\n", + " ) \n", + "plot(\n", + " [0,10],\n", + " [10,10],\n", + " color='g',linestyle='--'\n", + " ) \n", + "plot(\n", + " [10,10],\n", + " [0,10],\n", + " color='g',linestyle='--'\n", + " ) \n", + "plot(\n", + " [30,30],\n", + " [0,10],\n", + " color='g',linestyle='--'\n", + " ) \n", + "text(2.6,5.8,'v = t',color='r')\n", + "text(15,10.2,'v = 10',color='r')\n", + "axis([0,40,0,20])\n", + "title('Plot of v-t')\n", + "xlabel('t(s)')\n", + "ylabel('v(m/s)')\n", + "show()\n", + "print\"\\n\\n\"\n", + "# a-t graph\n", + "plot(\n", + " [0,10],\n", + " [1,1],\n", + " color='b',linewidth = 2\n", + " ) \n", + "plot(\n", + " [10,30],\n", + " [0,0],\n", + " color='b',linewidth = 2\n", + " ) \n", + "plot(\n", + " [10,10],\n", + " [0,1],\n", + " color='g',linestyle='--'\n", + " )\n", + "axis([0,40,0,2])\n", + "title('Plot of a-t')\n", + "xlabel('t(s)')\n", + "ylabel('a(m/s**(2))')\n", + "show()" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "collapsed": true + }, + "source": [ + "## Ex 12.7 Page No 462" + ] + }, + { + "cell_type": "code", + "execution_count": 22, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "data": { + "image/png": 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iIvWjtsvB9yWsuvbXZAYj37VpU/jFCaEIs2fPaOPJFo0awZ13wqBBcNFFoVdk\nwwa45BJ4662wG3C7dlFHKSKSG2rbM7IA2D+ZgUjlZs+Gb2MrpZx2WnyaqiRHv36waFGYXVOusDD0\nksyZU/XrREQkeWqbjAwHbjazYWaWb2aHJT6SGWCu0xBN6rVpA888Ay++COV7Jq5cCSeeCHfcEXYE\nFhGR1KltMtIB+Hfgfwm9JIuAhQl/SpKUJyONGoUVRCV1LrgAPvggTAWGsEvyvfeG3ZFXrIg2NhGR\nbFbbZGQSIenoB3QHulX4U5Lgo4/ivwT7949/apfU6do17AA8blxIACFstHfEETBpkopbRURSobbJ\nyPeAm2OLnX3q7n9PfCQzwFw2dWr8eW2HaDq36szoAaPp3Epr0FVXw4Zwyy1hQbQePULbpk1wxRVw\n/vmwbl208YmIZJvaJiMzCTNqJIWSUS/SuXVnxpw4hs6tlYzU1JFHQnExDB8eb3vllbC/zcyZ0cUl\nIpJtapuMvAGMN7MxZnaemQ1OfCQzwFy1dWv8F17HjmF2h9S/Vq3gySdDErL33qFt1So45RS46ab4\nTCcREam92q4z8kTszzsrOeZAw1peV2Lmzg1DAwAFBdAgKbsISW2dey4cc0yYAjxjRqgdefBBmD49\nLDOv9V9ERGqvtrv2NtjNQ4lIEmhKb/rZbz94+2146KGwIzDAwoWQlwdPPJGjxa0ffAAXXhgqf1u0\ngEMOgUcf3fWcZ5+FvfZKfSxr1oQV7A4+OBT+/PSn3z3nqafCdKm99w6PQYNChXJFEyeGpXqbN4dj\nj638HBFJGn3eTlPlyYhZ+Hkp6aFBA7jhBpg/H3r1Cm2bN8OIEXD22VBaGm189a6oKIwj/uY3sHw5\n3H473HprWMK2nHvtVusbOxYuv7z652/dCvvuCz/7GRx+eOXnzJ4dkqdZs+C992D//eHUU2H16vg5\nL70Uvsljx4Zss2/f0D355Zc1vwcRqZZqJyNmNmTPZ/3r3P3N7LjahSSrVsGSJeH5UUdB+/bRxiPf\ndfjh8P77MHJkvO2NN0Jxa+IsqJR58snQVVPR2WfvWnGbapddBuPHh+2PDzgg/KK/7DL4/e/D8dmz\nQ0JRVhYyuYYNwzbJqfC974VYLr44rGRXmeefhx//OHyjDjoo9JTs3BnG3sqNHw9XXQWXXhrG3554\nIvT6TJqUmrhFpEY9IyPMrMTMbjKzXhUPmllbMzvDzCYDxcA+SYsyxyRjSq+kXosWoTf/jTegQ4fQ\ntmZN+J6CM619AAAgAElEQVSNGgVbUrlRcvkc4z//Od721VfhH8/FF1f9uj59oHXrqh/f/37dYysr\ni1f79u8PEyaE5GDt2tADceONdX+PZNm0KSyxWx7vtm2ht2fgwPg5ZqFi+d13o4lRJAdUu4DV3QfE\nZspcA4wzs03AWmALYQffTsCXwDNAH3dfm/xwc0My60U2b9vMx199TPe9utO8cfO6XUwqdeaZoXTi\nssvi37sJE8KH7cmTw+//pGvXLvzjmDwZTjoptL38csiKTjyx6tf96U+7X9++eR3/jcybB7/9bdht\nEEJxTdu24Rd6ecaWTm6+OfQwnXJK+PrLL2HHjjD0lKhjR/ir9gUVSZUa1Yy4++vuPgjoCFwK/BL4\nDTAGOAbo4u63KBGpve3bYdq08HyvvcIwTV2UfFlCn1/1oeTLkroHJ1Xq1Cn8/n30UWjaNLQtWRLW\nKnnssRQVt150UZhzXJ5cTJ4MQ/Ywmrr//tC9e9WPzrtZj+aMM+I9KIce+t3jS5fCOefAmDG79ixU\n1//7f+HabdqEP3/+c3jhhfh7tmkTdjFMlvvuC4nTa69BkybJu66I1Fhtp/beB7zg7q8lMxgJhZFf\nfx2eDxoUX5Jc0p8ZXHNN6Ki48MKQjGzdCtdeGxKV//3fkLQkzVlnhXqHP/4xZD1z5sAvfrH71/Tp\nA3/fzSLJJ5wQrleZp58O1boQn05Ubvny0Lvw4x+HAtbaOOooWLw4/vUvfgGffw4PPBDP5ir2WNTW\nQw+F686YEWYAlWvfPtS1rK3weWrt2iR/80QkUW1/1XUApphZKVAI/MbdF+/hNVINmtKb+fr0CUnl\nrbeG4RoI39fDDgs1kGeemaQ3ato0LIDywgthE6OePfe8Ol5dhmmq6jVZtiz0hFx2WeXFqU2ahKGP\nPWnaNPTOlNt7b9iwIUyxTaYHHgibD739dth0KFHjxpCfH5KUwbH1G93D19dem9w4RORfapWMuPvZ\nZrYXcD5wIXCDmX1IGLKZ7O6fJi/E3JKYjBQURBeH1E2zZmFSxmmnwQ9/GApbS0tDZ8bIkWHBtBYt\nkvBGF10Usptly+CSS/Z8/v77J+FNEyxdGraTPv10uP76eI9Cw4bxaWAHHAAbN4Ylhfv2DTde19qU\nqixeHJKHjRvDX/jixSEZKp+Hff/9MHp0GO7p2jUeb6tW0LJleP7Tn4ZvWn4+HH10+EZ+801oE5HU\ncPc6P4B/A/4bKAG2J+OaqX4AeYAXFRV5uvjiC3czd3A/7LDkXLPo8yJnDF70efrcZ6754gv3wYPD\n97X80auX+8KFSbj4zp3uXbq4N2zo/sknSbhgDY0Z496gwXcf3brtet7Ike7t24djY8dW/9qXXVaz\neMx2H8sBB1Qeb8WYJk50/9733Js1cz/2WPcFC2oWh0iWKyoqcsKK63mehN/Jda5IMLPGwJGEAtYD\nCDNspBamTYsPjWuIJnt06BBqJP/nf8KU382boaQkfOgeNy601Xq5f7OwME1URo8Ojz2ZODE8anrt\nmtq5c/fHP/mketcZOXLXRWREJKVqvQKrmZ1kZk8Sko9ngPXAmYReEqkF1YtkL7OwjlZxcbxMYdu2\nsOTGqadGm0+IiEStVsmIma0C3gLaA1cCHd39cnef4Z6TO3TU2c6d8cXOWraE47R+bVbq2TOsQn7T\nTfEV0mfMCMWtr74abWwiIlGpbc/IGKCzu//A3X/n7luTGFNOWrQIvvgiPB84MHnLHvRq34ulI5bS\nq/13Fs2ViDRpEuoop0+Pr+i+bl2YGPOjH4XaSxGRXFLbXXufdPevkx1MLkvVEE3zxs05ZN9DtPpq\nGjr55DDZ47zz4m1PPRV2AdYmsSKSS7Rrb5rQlN7ctM8+YRX3p5+OzyxdsSJs6TJuXPWW5xARyXQZ\nk4yYWRcze97MvjSzb8xssZnlVTjnLjP7PHZ8mpkdGFW8NVFWFrb0gLCRaOK6T5L9zMLGtgsXxpf/\n374dbrst9J6sXBltfCIiqZYRyYiZtQPmAluBAqAXcAPwVcI5NwNXEwpqjwY2AVPNLO03nZgxI/4J\nWLNoclePHjB3Ltx+e7y49Z13QnHrSy9FG5uISCplRDIC3AKsdPfh7l7k7n939+nunrhowHXA3e7+\nprsvJWzk1wU4J4qAa0JTeqVc48Zwzz0wa1ZYIBRCz9mQITBsGKxfH2l4IiIpkSnJyFnA+2b2WzNb\na2bFZja8/KCZdQM6ATPK29x9PfAXoF+9R1sD7vFkpGlTGDAg2ngkPZxwQihuTdyE97nnwhol774b\nXVwiIqmQKclId2AE8FfgVOBXwKNmVr4ZRyfCsrQVV39dGzuWtkpK4LPPwvMBA5K0X4lkhXbtYPJk\neP55aN06tH38MRx/fNiPbvv2aOMTEUmWTElGGgBF7v4zd1/s7k8CTwI/jjiuOkv1EM3qDasZM2sM\nqzesTv7FJeXM4OKLQy9J//6hbceOsFL6gAHVX91cRCSd1XlvmnqymrAJX6IS4NzY8zWAAR3ZtXek\nI7BwdxceNWoUbdu23aVt6NChDB06tC7xVlvKk5GNqxk7eyyDDx5M59ZVbAEvaa9bN5g9G37+89Ar\nsmNHmIHVty88/njYvLe86FVEJJkKCwspLCzcpa2srCyp72GZsHq7mf0G+Dd3H5DQNh44yt3/I/b1\n58CD7j4+9nUbQmJyqbu/XMk184CioqIi8vLyKh6uF5s2wd57w7ffhmLFTz9N/i+U4tXF5P9PPkVX\nFpHXOZr7lOR6992QfCT2igwdGpKSdu2ii0tEckdxcTH5+fkA+e5eXNfrZcowzXjgWDO71cz+3cwu\nBIYDv0w4ZwJwh5mdZWaHAs8B/wD+UP/hVs/s2SERgdArok+2Uh39+oXtA4YNi7cVFoZekjlzootL\nRKS2MiIZcff3gR8AQ4ElwO3Ade7+YsI5DwCPAb8mzKJpDpzu7t/Wf8TVoym9Ultt2sAzz8CLL0L5\nKOPKlXDiiXDHHWFHYBGRTJERyQiAu7/l7oe5ewt3P8TdJ1Vyzhh37xI7p8Dd/xZFrNVVnow0ahRW\n2hSpqQsugA8+CFOBIez+fO+9YdfnFSuijU1EpLoyJhnJNh99FP9l0b9//NOtSE117QozZ4a9bBrF\nStIXLAhrkkyaFNayERFJZ0pGIjJ1avy5hmikrho2hFtuCcWtPXqEtk2b4Ior4PzzYd26aOMTEdkd\nJSMRqa96kWaNmtG7Q2+aNWqWujeRtHHkkVBcDMOHx9teeSXsbzNzZnRxiYjsjpKRCGzdGv/F0LFj\nmAWRKr079GbZyGX07tA7dW8iaaVVK3jyyZCE7L13aFu1Ck45BW66KT6DS0QkXSgZicDcuaELHaCg\nABrouyApcO65obh14MDwtTs8+CAceyx8+GG0sYmIJNKvwQhoSq/Ul/32g7ffhoceCjsCAyxcCHl5\n8MQTKm4VkfSgZCQC5cmIGQwaFG0skv0aNIAbboD586FXr9C2eTOMGAFnnw2lpdHGJyKiZKSerVoF\nS5aE50cdBe3bRxuP5I7DD4f334eRI+Ntb7wRilsTZ3eJiNQ3JSP1TFN6JUotWsDEiSEJ6dAhtK1Z\nE/4tjhoFW7ZEG5+I5CYlI/VM9SKSDs48MxS3Jv4bnDABjj4ali6NLi4RyU1KRurR9u0wbVp4vtde\nYZhGJCqdOsFbb8Gjj0LTpqFtyZKwVsljj6m4VUTqj5KRejR/Pnz9dXg+aFB86e5UWl66nEMeP4Tl\npctT/2aScczgmmtCLcmhh4a2rVvh2mvhjDPCEI6ISKopGalHUQzRbNm+heWly9myXcUAUrU+fUKy\nfP318bYpU0Jx65tvRheXiOQGJSP1KDEZKSiILg6RyjRrBuPHh3+nnTqFttJSOOss+MlP4Jtvoo1P\nRLKXkpF6UloausIhfNrs0iXaeESqUlAQilsHD463Pf54qCVZtCi6uEQkeykZqSfTpsULAjWLRtJd\nhw7w2mthldbmzUNbSUmYbfPww7BzZ7TxiUh2UTJSTzSlVzKNGVx1VdgF+IgjQtu2bXDjjXDqqWEB\nPxGRZFAyUg927owvdtayJRx3XLTxiNREz57w3nthx1+z0DZjRhhufPXVaGMTkeygZKQeLFoEX3wR\nng8cCE2aRBuPSE01aQL33w/Tp4fN9wDWrQs7A//oR7BxY7TxiUhmUzJSD6IcouncqjOjB4ymc6vO\n9fvGkpVOPhkWL4bzzou3PfVU2AV4wYLo4hKRzKZkpB5EOaW3c+vOjDlxDJ1bKxmR5NhnH3j5ZXj6\n6TDsCLBiBfTvD+PGwY4d0cYnIplHyUiKlZXBvHnh+UEHQffu0cYjkgxmcPnlsHBhfFuD7dvhtttC\n78nKldHGJyKZRclIis2YEf+kqFk0km169IC5c+H22+PFre+8E4pbX3op2thEJHMoGUkxTemVbNe4\nMdxzD8yaBV27hrayMhgyBIYNg/XrIw1PRDKAkpEUco8nI02bwoAB0cYjkkonnBCKW4cMibc991xY\no+Tdd6OLS0TSn5KRFCopgc8+C88HDIAWLaKNRyTV2rWDyZPh+eehdevQ9vHHcPzxcNddoa5ERKQi\nJSMppCEayUVmcPHFoZekf//QtmMHjB4dkvJPPok2PhFJP0pGUigdkpHN2zaz7ItlbN62OZoAJGd1\n6wazZ8PYsdCwYWibNw/69oUXXojv1SQiomQkRTZtCj+IIRT19ewZTRwlX5bQ51d9KPmyJJoAJKc1\nagR33glz5oTkBGDDBrjkErjoIvj662jjE5H0oGQkRWbPhm+/Dc9POy0+7VEkF/XrF7ZFGDYs3lZY\nGHpJ5syJLi4RSQ8ZmYyY2S1mttPMHqnQfpeZfW5m35jZNDM7MKoY02GIRiSdtGkDzzwDL74IbduG\ntpUr4cQT4Y47wo7AIpKbMi4ZMbOjgCuBxRXabwaujh07GtgETDWzSLalK09GGjUKK1KKSHDBBfDB\nB2EqMIRdre+9N+xmvWJFtLGJSDQyKhkxs1bAC8BwoOJo83XA3e7+prsvBS4FugDn1G+U8NFH8R+q\n/fvHPwWKSNC1K8ycGfayadQotC1YENYkmTRJxa0iuSajkhFgIvCGu89MbDSzbkAnYEZ5m7uvB/4C\n9KvXCIGpU+PPNUQjUrmGDeGWW8KCaD16hLZNm+CKK+D882HdumjjE5H6kzHJiJkNAQ4Hbq3kcCfA\ngbUV2tfGjtUr1YuIVN+RR0JxMQwfHm975ZWwv83MmVW/TkSyR0YkI2b2b8AE4CJ3T+syt61b4z9A\nO3YMswVEZPdatYInnwxJyN57h7ZVq+CUU+Cmm+Iz00QkOzWKOoBqygc6AMVm/5ok2xA4wcyuBnoC\nBnRk196RjsDC3V141KhRtK1Q1DF06FCGDh1aq0Dnzg1dzQAFBdAg4nSvV/teLB2xlO57dY82EJFq\nOPdcOOaYMAV4xoxQO/LggzB9elhmPqr1ekRyWWFhIYWFhbu0lZWVJfU9zDOgUszMWgLfq9D8DFAC\n3OfuJWb2OfCgu4+PvaYNITG51N1fruSaeUBRUVEReXl5SYv1ppvCD08IPzxrmdOI5LSdO2H8eLj1\n1viU3+bN4ZFH4KqrtG6PSNSKi4vJz88HyHf34rpeLyOGadx9k7svT3wQpu7+093LlxadANxhZmeZ\n2aHAc8A/gD/UZ6zl9SJmMGhQfb6zSPZo0ABuuAHmz4devULb5s0wYgScfTaUlkYbn4gkV0YkI1XY\npUvH3R8AHgN+TZhF0xw43d3rbbR51SpYsiQ8P+ooaN++vt5ZJDsdfji8/z6MHBlve+ONUNyaOGtN\nRDJbxiYj7n6yu/+0QtsYd+/i7i3cvcDd/1afMWlKr0jytWgBEyeGJKRDh9C2Zk34PzZqFGzZEm18\nIlJ3GZuMpCNN6RVJnTPPDCu3Jv7fmjABjj4ali6NLi4RqTslI0myfTtMmxae77VXGKYRkeTq1Ane\negsefRSaNg1tS5aEtUoee0wrt4pkKiUjSTJ/fnw79EGD4ktci0hymcE114RakkMPDW1bt8K118IZ\nZ4QhHBHJLEpGkiRdh2hWb1jNmFljWL1hddShiCRVnz7hQ8D118fbpkwJxa1vvhldXCJSc0pGkiQx\nGSkoiC6OilZvXM3Y2WNZvVHJiGSfZs3CeiRTpoQhHAjTfs86C37yE/jmm2jjE5HqUTKSBKWlocsY\nwqeyLl2ijUck1xQUhOLWwYPjbY8/HmpJFi2KLi4RqR4lI0kwbVq8cC6dhmhEckmHDvDaa/DEE2G1\nVoCSkjDb5uGHw6quIpKelIwkQbrWi4jkGrOwXHxxMRxxRGjbtg1uvBFOPTUsTCgi6UfJSB3t3Blf\n7KxlSzjuuGjjEZGwod5774W9osr3sZkxIwyjvvpqtLGJyHcpGamjRYvgiy/C84EDoUmTaOMRkaBJ\nE7j//rDj7377hbZ168LOwD/6EWzcGG18IhKnZKSONEQjkt5OPhkWL4bzzou3PfUU5OXBggXRxSUi\ncUpG6ihdp/SWa9aoGb079KZZo2ZRhyISmX32gZdfhqefDsOpACtWQP/+MG4c7NgRbXwiuU7JSB2U\nlcG8eeH5QQdB9+7RxlOZ3h16s2zkMnp36B11KCKRMoPLL4eFC+PbNWzfDrfdFnpPVq6MNj6RXKZk\npA5mzIh/otIQjUhm6NED5s6F22+PF7e+804obn3ppWhjE8lVSkbqQPUiIpmpcWO45x6YNQu6dg1t\nZWUwZAgMGwbr10cankjOUTJSS+7xZKRpUxgwINp4RKTmTjghFLcOGRJve+65sEbJu+9GF5dIrlEy\nUkslJfDZZ+H5gAHQokW08YhI7bRrB5Mnw/PPQ+vWoe3jj+H44+Guu0JdiYiklpKRWtIQjUj2MIOL\nLw69JP37h7YdO2D06PBh45NPoo1PJNspGaklJSMi2adbN5g9G8aOhYYNQ9u8edC3L7zwQnwPKhFJ\nLiUjtbBpU/iBBaH4rWfPaOMRkeRp1AjuvBPmzAnJCcCGDXDJJXDRRfD119HGJ5KNlIzUwuzZ8O23\n4flpp8WnB6aj5aXLOeTxQ1heujzqUEQySr9+YbuHYcPibYWFoZdkzpzo4hLJRkpGaiGThmi2bN/C\n8tLlbNm+JepQRDJOmzbwzDPw4ovQtm1oW7kSTjwR7rgj7AgsInWnZKQWypORRo3Cyo0ikt0uuAA+\n+CBMBYawW/e994ZdulesiDY2kWygZKSGPvoo/sOnf//4pyURyW5du8LMmWEvm0aNQtuCBWFNkkmT\nVNwqUhdKRmpo6tT483QfohGR5GrYEG65JSyI1qNHaNu0Ca64As4/H9atizY+kUylZKSGMqleRERS\n48gjobgYhg+Pt73yStjfZubM6OISyVRKRmpg69b4D5qOHUNVvYjkplat4MknQxKy996hbdUqOOUU\nuOmm+Iw7EdkzJSM1MHdu6JIFKCiABvrbE8l5554bilsHDgxfu8ODD8Kxx8KHH0Ybm0im0K/TGsjE\nIZrOrTozesBoOrfqHHUoIllrv/3g7bfhoYfCjsAACxdCXh488YSKW0X2RMlIDZQnI2YwaFC0sVRX\n59adGXPiGDq3VjIikkoNGsANN8D8+dCrV2jbvBlGjICzz4bS0mjjE0lnSkaqadUqWLIkPD/qKGjf\nPtp4RCQ9HX44vP8+jBwZb3vjjVDcmjgbT0TiMiIZMbNbzWy+ma03s7Vm9qqZHVTJeXeZ2edm9o2Z\nTTOzA5MVg6b0ikh1tWgBEyeGJKRDh9C2Zk342TFqFGzRgsgiu8iIZAQ4HngMOAY4BWgMvG1mzctP\nMLObgauBK4GjgU3AVDNrkowAMrFeRESideaZobg18WfGhAlw9NGwdGl0cYmkm4xIRtz9DHd/3t1L\n3H0J8EOgK5CfcNp1wN3u/qa7LwUuBboA59T1/bdvh2nTwvO99grDNCIi1dGpE7z1Fjz6KDRtGtqW\nLAlrlTz2mIpbRSBDkpFKtAMcWAdgZt2ATsCM8hPcfT3wF6BfXd9s/vz4tuGDBsWXghYRqQ4zuOaa\nUEty6KGhbetWuPZaOOOMMIQjkssyLhkxMwMmAP/P3ZfHmjsRkpO1FU5fGztWJxqiEZFk6NMnfLi5\n/vp425Qpobj1zTeji0skapn4Gf9xoDdwXDIuNmrUKNpW2O1u6NChDB069F9fJyYjBQXJeNf6s3nb\nZj7+6mO679Wd5o2b7/kFIpJSzZrB+PHhg80Pfxh6RUpL4ayzwgycBx8MBbAi6aKwsJDCwsJd2srK\nypL6HuYZNGBpZr8EzgKOd/eVCe3dgI+Aw939g4T2WcBCdx9VybXygKKioiLy8vKqfM/S0rD0u3v4\n9LJ4cfLupz4Ury4m/3/yKbqyiLzOVd+niNS/0tKwv83rr8fbevWCyZPDFGGRdFVcXEx+fj5AvrsX\n1/V6GTNME0tEzgZOSkxEANz9E2ANMDDh/DaE2Tfz6vK+06bFC8w0RCMiydShA7z2WliltXms47Kk\nJMy2efhh2Lkz2vhE6ktGJCNm9jhwEXA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0pN6VjrG6kjbJq4MaAzsntCnTHXfcQXfNXJSI/Pe/cMoppR9I+OyzsJPWsYlI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\n9A6JvA748svSq3/GjYNWraKLR0Qanoz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+ "text/plain": [ + "" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "# Ex 12.7\n", + "%matplotlib inline\n", + "from matplotlib.pyplot import plot,title,xlabel,ylabel,text,axis,show\n", + "\n", + "# Calculation\n", + "# v-t graph\n", + "plot(\n", + " [0,10,60],\n", + " [0,100,0],\n", + " color='b',linewidth = 2\n", + " ) \n", + "plot(\n", + " [10,10],\n", + " [0,100],\n", + " color='g',linestyle='--'\n", + " ) \n", + "plot(\n", + " [0,10],\n", + " [100,100],\n", + " color='g',linestyle='--'\n", + " ) \n", + "text(0,95,'v = 10t',color='r')\n", + "text(30,66,'v = -2t + 120',color='r')\n", + "axis([0,80,0,150])\n", + "title('Plot of v-t')\n", + "xlabel('t(s)')\n", + "ylabel('v(m/s)')\n", + "show()\n", + "print\"\\n\\n\"\n", + "# s-t graph\n", + "l1 = []\n", + "l2 = []\n", + "for i in range(0,11,1):\n", + " l1.append(i)\n", + " l2.append(5*i**(2))\n", + "plot(\n", + " l1,\n", + " l2,\n", + " color='b',linewidth = 2\n", + " ) \n", + "l1 = []\n", + "l2 = []\n", + "for i in range(10,61,1):\n", + " l1.append(i)\n", + " l2.append(-(i**(2))+120*i-600)\n", + "plot(\n", + " l1,\n", + " l2,\n", + " color='b',linewidth = 2\n", + " ) \n", + "plot(\n", + " [10,10],\n", + " [0,500],\n", + " color='g',linestyle='--'\n", + " ) \n", + "plot(\n", + " [0,10],\n", + " [500,500],\n", + " color='g',linestyle='--'\n", + " )\n", + "plot(\n", + " [60,60],\n", + " [0,3000],\n", + " color='g',linestyle='--'\n", + " )\n", + "plot(\n", + " [0,60],\n", + " [3000,3000],\n", + " color='g',linestyle='--'\n", + " )\n", + "text(8,200,'s = 5t**(2)',color='r')\n", + "text(25,1500,'s = t**(2) + 120t - 600',color='r')\n", + "axis([0,80,0,3500])\n", + "title('Plot of s-t')\n", + "xlabel('t(s)')\n", + "ylabel('s(m)')\n", + "show()" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Ex 12.8 Page No 464" + ] + }, + { + "cell_type": "code", + "execution_count": 32, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "data": { + "image/png": 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+ "text/plain": [ + "" + ] + }, + "metadata": {}, + "output_type": "display_data" + }, + { + "name": "stdout", + "output_type": "stream", + "text": [ + "\n", + "\n", + "\n", + "t = 12.07 s\n" + ] + } + ], + "source": [ + "# Ex 12.8\n", + "%matplotlib inline\n", + "from matplotlib.pyplot import plot,title,xlabel,ylabel,text,axis,show\n", + "from __future__ import division\n", + "\n", + "# Calculation\n", + "# a-s graph\n", + "l1 = []\n", + "l2 = []\n", + "for i in range(0,51,1):\n", + " l1.append(i)\n", + " l2.append(0.16*i+2)\n", + "plot(\n", + " l1,\n", + " l2,\n", + " color='b',linewidth = 2\n", + " ) \n", + "l1 = []\n", + "l2 = []\n", + "for i in range(50,101,1):\n", + " l1.append(i)\n", + " l2.append(0)\n", + "plot(\n", + " l1,\n", + " l2,\n", + " color='b',linewidth = 2\n", + " ) \n", + "plot(\n", + " [50,50],\n", + " [0,10],\n", + " color='g',linestyle='--'\n", + " ) \n", + "plot(\n", + " [0,50],\n", + " [10,10],\n", + " color='g',linestyle='--'\n", + " ) \n", + "text(4,8,'a = 0.16*s + 2',color='r')\n", + "text(52,2,'a = 0',color='r')\n", + "axis([0,120,0,15])\n", + "title('Plot of s-t')\n", + "xlabel('t(s)')\n", + "ylabel('s(m)')\n", + "show() \n", + "print\"\\n\\n\"\n", + "# Variable Declaration\n", + "s = 100 #[meter]\n", + "t = s/50 + 10.07 #[seconds]\n", + "\n", + "# Result\n", + "print\"t = \",(t),\"s\"" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Ex 12.9 Page No 473" + ] + }, + { + "cell_type": "code", + "execution_count": 35, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "r = 30.2 m\n", + "v = 26.8 m/s\n", + "theta_v = 72.6 degrees\n", + "a = 12.8 m/s**(2)\n", + "theta_a = 90 degrees\n" + ] + } + ], + "source": [ + "# Ex 12.9\n", + "import math\n", + "from __future__ import division\n", + "\n", + "# Calculation\n", + "# Position\n", + "x = 16 #[meter]\n", + "y = 16**(2)/10 #[meter]\n", + "# Let r be straight line distance from A to B\n", + "r = round(math.sqrt(x**(2)+y**(2)),1) #[meter]\n", + "\n", + "# Velocity\n", + "vx = 8 #[meter per second]\n", + "vy = (2*16*8)/10 #[meter per second]\n", + "# Let v be magnitude of velocity at t = 2 s\n", + "v = round(math.sqrt(vx**(2)+vy**(2)),1) #[meter per second]\n", + "theta_v = round(math.degrees(math.atan(vy/vx)),1) #[Degrees]\n", + "\n", + "# Accceleration\n", + "ax = 0 #[meter per second square]\n", + "ay = 2*8**(2)/10+2*16*0/10 #[meter per second square]\n", + "a = round(math.sqrt(ax**(2)+ay**(2)),1) #[meter per second square]\n", + "theta_a = 90 #[Degrees]\n", + "\n", + "# Result\n", + "print\"r = \",(r),\"m\"\n", + "print\"v = \",(v),\"m/s\"\n", + "print\"theta_v = \",(theta_v),\"degrees\"\n", + "print\"a = \",(a),\"m/s**(2)\"\n", + "print\"theta_a = \",(theta_a),\"degrees\"" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Ex 12.10 Page No 474" + ] + }, + { + "cell_type": "code", + "execution_count": 44, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "r_x = 0.499 m\n", + "r_y = 0.0354 m\n", + "r_z = -0.15 m\n", + "r = 0.522 m\n", + "alpha = 17.1 degrees\n", + "beta = 86.1 degrees\n", + "gamma = 106.7 degrees\n", + "v = 1.02 m/s\n", + "a = 2.0 m/s**(2)\n" + ] + } + ], + "source": [ + "# Ex 12.10\n", + "import math\n", + "\n", + "# Calculation\n", + "# Position\n", + "r_x = round(0.5*math.sin(1.5),3) #[meter]\n", + "r_y = round(0.5*math.cos(1.5),4) #[meter]\n", + "r_z = round(-0.2*(0.75),4) #[meter]\n", + "r = round(math.sqrt(r_x**(2)+r_y**(2)+r_z**(2)),3) #[meter]\n", + "alpha = round(math.degrees(math.acos(r_x/r)),1) #[Degrees]\n", + "beta = round(math.degrees(math.acos(r_y/r)),1) #[Degrees]\n", + "gamma = round(math.degrees(math.acos(r_z/r)),1) #[Degrees]\n", + "\n", + "# Velocity\n", + "v = round(math.sqrt((1*math.cos(1.5))**(2)+(-1*math.sin(1.5))**(2)+(-0.2)**(2)),3) #[meter per second]\n", + "\n", + "# Accelaration\n", + "a = math.sqrt((-2*math.sin(1.5))**(2)+(-2*math.cos(1.5))**(2)) #[meter per second square]\n", + "\n", + "# Result\n", + "print\"r_x = \",(r_x),\"m\"\n", + "print\"r_y = \",(r_y),\"m\"\n", + "print\"r_z = \",(r_z),\"m\"\n", + "print\"r = \",(r),\"m\"\n", + "print\"alpha = \",(alpha),\"degrees\"\n", + "print\"beta = \",(beta),\"degrees\"\n", + "print\"gamma = \",(gamma),\"degrees\"\n", + "print\"v = \",(v),\"m/s\"\n", + "print\"a = \",(a),\"m/s**(2)\"" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "collapsed": true + }, + "source": [ + "## Ex 12.11 Page No 477" + ] + }, + { + "cell_type": "code", + "execution_count": 1, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "tAB = 1.11 s\n", + "R = 13.32 m\n" + ] + } + ], + "source": [ + "# Ex 12.11\n", + "from __future__ import division\n", + "import math\n", + "\n", + "# Variable Declaration\n", + "v = 12 #[meters]\n", + "# Calculation\n", + "# Vertical motion\n", + "tAB = round(math.sqrt(-6/((1/2)*(-9.81))),2) #[seconds]\n", + "\n", + "# Horizontal motion\n", + "R = 0+v*1.11 #[meter]\n", + "\n", + "# Result\n", + "print\"tAB = \",(tAB),\"s\"\n", + "print\"R = \",(R),\"m\"" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Ex 12.12 Page No 478" + ] + }, + { + "cell_type": "code", + "execution_count": 8, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "h = 1.433 m\n" + ] + } + ], + "source": [ + "# Ex 12.12\n", + "import math\n", + "from __future__ import division\n", + "\n", + "# Variable Declaration\n", + "v0 = 10 #[meter per second]\n", + "theta = 30 #[degrees]\n", + "\n", + "# Calculation\n", + "vo_x = round(v0*math.cos(math.pi*30/180),2) #[meter per second]\n", + "vo_y = round(v0*math.sin(math.pi*30/180),2) #[meter per second]\n", + "\n", + "# Horizontal Motion\n", + "tOA = round((8-0)/vo_x,4) #[seconds]\n", + "\n", + "# Vertical Motion\n", + "h = round(0+5*tOA+(1/2)*(-9.81)*tOA**(2)+1,3) #[meter]\n", + "\n", + "# Result\n", + "print\"h = \",(h),\"m\"" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Ex 12.13 Page No 479" + ] + }, + { + "cell_type": "code", + "execution_count": 13, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "vA = 13.38 m/s\n", + "R = 17.4 m\n", + "h = 3.28 m\n" + ] + } + ], + "source": [ + "# Ex 12.13\n", + "from __future__ import division\n", + "import math\n", + "\n", + "# Calculation\n", + "# Vertical Motion\n", + "vA = round((-1-(1/2)*-9.81*1.5**(2))/(math.sin(math.pi*30/180)*1.5),2) #[meter per second]\n", + "\n", + "# Horizontal Motion\n", + "R = round(0+vA*math.cos(math.pi*30/180)*1.5,1) #[meter]\n", + "h = round(((0**(2)-(vA*math.sin(math.pi*30/180))**(2))/(2*(-9.81)))+1,2) #[meter]\n", + "\n", + "# Result\n", + "print\"vA = \",(vA),\"m/s\"\n", + "print\"R = \",(R),\"m\"\n", + "print\"h = \",(h),\"m\"" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Ex 12.14 Page No 487" + ] + }, + { + "cell_type": "code", + "execution_count": 16, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "vA = 6 m/s\n", + "a = 2.37 m/s**(2)\n" + ] + } + ], + "source": [ + "# Ex 12.14\n", + "\n", + "# Calculation\n", + "# Velocity\n", + "# Velocity is always directed tangent to the path\n", + "vA = 6 #[meter per second]\n", + "\n", + "# Acceleration\n", + "rho = round(((1+((1/10)*10)**(2))**(3/2))/(1/10),2) #[meter]\n", + "at = 2 #[meter per second**(2)]\n", + "an = round((6**(2))/rho,3) #[meter per second**(2)]\n", + "a = round(math.sqrt(at**(2)+an**(2)),2) #[meter per second**(2)]\n", + "phi = round(math.degrees(math.atan(at/an)),1) #[Degrees]\n", + "\n", + "# Result\n", + "print\"vA = \",(vA),\"m/s\"\n", + "print\"a = \",(a),\"m/s**(2)\"" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Ex 12.15 Page No 488" + ] + }, + { + "cell_type": "code", + "execution_count": 17, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "t = 7.48 s\n", + "v = 22.44 m/s\n" + ] + } + ], + "source": [ + "# Ex 12.15\n", + "\n", + "# Calculation\n", + "# Let t be time needed for acceleration to reach 3 m/s**(2)\n", + "t = round(math.sqrt((math.sqrt(3**(2)-2**(2)))/0.04),2) #[seconds]\n", + "\n", + "# Velocity\n", + "# Let v be speed at time t = 7.48 s\n", + "v = 3*t #[meter per second]\n", + "\n", + "# Result\n", + "print\"t = \",(t),\"s\"\n", + "print\"v = \",(v),\"m/s\"" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Ex 12.16 Page No 489" + ] + }, + { + "cell_type": "code", + "execution_count": 22, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "aB = 5.37 m/s**(2)\n" + ] + } + ], + "source": [ + "# Ex 12.16\n", + "import math\n", + "from __future__ import division\n", + "\n", + "# Calculation\n", + "tB = round((6.142/0.0333)**(1/3),3) #[seconds]\n", + "aBt = 0.2*5.690 #[meter per second square]\n", + "vB = 0.1*(tB**(2)) #[meter per second]\n", + "aBn = (vB**(2))/2 #[meter per second square]\n", + "aB = round(math.sqrt(aBt**(2)+aBn**(2)),2) #[meter per second square]\n", + "\n", + "# Result\n", + "print\"aB = \",(aB),\"m/s**(2)\"\n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Ex 12.18 Page No 498" + ] + }, + { + "cell_type": "code", + "execution_count": 25, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "v = 360.6 mm/s\n", + "delta = 56.3 degrees\n", + "a = 1931.3 mm/s**(2)\n", + "phi = -68.7 degrees\n" + ] + } + ], + "source": [ + "# Ex 12.18\n", + "import math\n", + "\n", + "# Calculation\n", + "vr = 200*1 #[millimeter per second]\n", + "vtheta = 100*(1)**(2)*3**(1) #[millimeter per second]\n", + "v = round(math.sqrt(vr**(2)+vtheta**(2)),1)\n", + "delta = round(math.degrees(math.atan(vtheta/vr)),1) #[Degrees]\n", + "ar = 200-100*(3**(2)) #[millimeter per second square]\n", + "atheta = 100*6+2*200*3 #[millimeter per second square]\n", + "a = round(math.sqrt(ar**(2)+atheta**(2)),1) #[millimeter per second square]\n", + "phi = round(math.degrees(math.atan(atheta/ar)),1) #[Degrees]\n", + "\n", + "# Result\n", + "print\"v = \",(v),\"mm/s\"\n", + "print\"delta = \",(delta),\"degrees\"\n", + "print\"a = \",(a),\"mm/s**(2)\"\n", + "print\"phi = \",(phi),\"degrees\"\n" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "collapsed": true + }, + "source": [ + "## Ex 12.19 Page No 499" + ] + }, + { + "cell_type": "code", + "execution_count": 4, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "v = 800.0 m/s\n", + "a = 6400.0 m/s**(2)\n" + ] + } + ], + "source": [ + "# Ex 12.19\n", + "import math\n", + "from __future__ import division\n", + "\n", + "# Calculation\n", + "vr = round(400*(1/math.cos(math.pi*45/180))*math.tan(math.pi*45/180),1) #[meter per second]\n", + "vtheta = round(100*(1/math.cos(math.pi*45/180))*4,1) #[meter per second]\n", + "v = round(math.sqrt(vr**(2)+vtheta**(2)),1) #[meter per second]\n", + "ar = round((1600*((1/math.cos(math.pi*45/180))*(math.tan(math.pi*45/180)**(2))+(1/math.cos(math.pi*45/180)**(3)))) - 100*(1/math.cos(math.pi*45/180))*4**(2),1) #[meter per second square]\n", + "atheta = round(100*(1/math.cos(math.pi*45/180))*0+2*400*(1/math.cos(math.pi*45/180))*math.tan(math.pi*45/180)*4,1) #[meter per second square]\n", + "a = round(math.sqrt(ar**(2)+atheta**(2)),1) #[meter per second square]\n", + "\n", + "# Result\n", + "print\"v = \",(v),\"m/s\"\n", + "print\"a = \",(a),\"m/s**(2)\"\n", + " " + ] + }, + { + "cell_type": "markdown", + "metadata": { + "collapsed": true + }, + "source": [ + "## Ex 12.20 Page No 500" + ] + }, + { + "cell_type": "code", + "execution_count": 10, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "theta_dot = 1.0 rad/s\n", + "theta_doubledot = 9.89 rad/s**(2)\n" + ] + } + ], + "source": [ + "# Ex 12.20\n", + "import math\n", + "\n", + "# Variable Declaration\n", + "a = 10 #[meter per second square]\n", + "v = 1 #[meter per second]\n", + "\n", + "# Calculation\n", + "theta_dot = math.sqrt((v**(2))-(0**(2))) #[radian per second]\n", + "theta_doubledot = round(math.sqrt((10**(2))-((-1.5)**(2))),2) #[radian per second square]\n", + "\n", + "# Result\n", + "print\"theta_dot = \",(theta_dot),\"rad/s\"\n", + "print\"theta_doubledot = \",(theta_doubledot),\"rad/s**(2)\" # Correction in the answer" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Ex 12.21 Page No 506" + ] + }, + { + "cell_type": "code", + "execution_count": 11, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "vA = 6 m/s\n" + ] + } + ], + "source": [ + "# Ex 12.21\n", + "\n", + "# Calculation\n", + "vA = -3*-2 #[meter per second]\n", + "\n", + "# Result\n", + "print\"vA = \",(vA),\"m/s\"" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Ex 12.22 Page No 507" + ] + }, + { + "cell_type": "code", + "execution_count": 12, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "vA = 8 m/s\n" + ] + } + ], + "source": [ + "# Ex 12.22\n", + "\n", + "# Calculation\n", + "vA = -4*-2 #[meter per second]\n", + "\n", + "# Result\n", + "print\"vA = \",(vA),\"m/s\"" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Ex 12.23 Page No 508" + ] + }, + { + "cell_type": "code", + "execution_count": 13, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "vB = -0.5 m/s\n" + ] + } + ], + "source": [ + "# Ex 12.23\n", + "\n", + "# Calculation\n", + "vB = -2/4\n", + "\n", + "# Result\n", + "print\"vB = \",(vB),\"m/s\"" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Ex 12.24 Page No 509" + ] + }, + { + "cell_type": "code", + "execution_count": 2, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "vS = 400.0 mm/s\n", + "aS = 3.6 mm/s**(2)\n" + ] + } + ], + "source": [ + "# Ex 12.24\n", + "from __future__ import division\n", + "\n", + "# Variable Declaration\n", + "vA = 0.5 #[meter per second]\n", + "\n", + "# Calculation\n", + "vS = round((20*vA)/math.sqrt(225+20**(2)),1) #[meter per second]\n", + "aS = (225*vA**(2))/((225+20**(2))**(3/2)) #[meter per second square]\n", + "\n", + "# Result\n", + "print\"vS = \",(vS*1000),\"mm/s\"\n", + "print\"aS = \",(aS*1000),\"mm/s**(2)\"" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Ex 12.25 Page No 512" + ] + }, + { + "cell_type": "code", + "execution_count": 19, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Solution 1\n", + "vTA_x = 28.2 km/hr\n", + "vTA_y = -31.8 km/hr\n", + "vTA = 42.5 km/hr\n", + "theta = 48.4 degrees\n", + "Solution 2\n", + "vTA_x = 28.2 km/hr\n", + "vTA_y = -31.8 km/hr\n" + ] + } + ], + "source": [ + "# Ex 12.25\n", + "import math\n", + "\n", + "# Calculation Solution 1 Vector Analysis\n", + "vTA_x = round(60-45*math.cos(math.pi*45/180),1) #[kilometer per hr]\n", + "vTA_y = round(-45*math.sin(math.pi*45/180),1) #[kilometer per hr]\n", + "vTA = round(math.sqrt(vTA_x**(2)+vTA_y**(2)),1) #[kilometer per hr]\n", + "theta = round(math.degrees(math.atan(abs(vTA_y)/vTA_x)),1) #[Degrees]\n", + "\n", + "# Result Solution 1\n", + "print\"Solution 1\"\n", + "print\"vTA_x = \",(vTA_x),\"km/hr\"\n", + "print\"vTA_y = \",(vTA_y),\"km/hr\"\n", + "print\"vTA = \",(vTA),\"km/hr\"\n", + "print\"theta = \",(theta),\"degrees\"\n", + "\n", + "# Calculation Solution 2 Scalar Analysis\n", + "# vT = vA + vT/A\n", + "vTA_x = round(60-45*math.cos(math.pi*45/180),1) #[kilometer per hr]\n", + "vTA_y = round(-45*math.sin(math.pi*45/180),1) #[kilometer per hr]\n", + "\n", + "# Result Solution 2\n", + "print\"Solution 2\"\n", + "print\"vTA_x = \",(vTA_x),\"km/hr\"\n", + "print\"vTA_y = \",(vTA_y),\"km/hr\"" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Ex 12.26 Page No 513" + ] + }, + { + "cell_type": "code", + "execution_count": 21, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "aBA = 912.4 km/hr**(2)\n", + "theta = 9.5 degrees\n" + ] + } + ], + "source": [ + "# Ex 12.26\n", + "import math\n", + "\n", + "# Variable Declaration\n", + "rho = 400 #[kilometers]\n", + "\n", + "# Calculation\n", + "# Velocity\n", + "vBA = 600-700 #[kilometers per hr]\n", + "# Acceleration\n", + "aBn = 600**(2)/rho #[kilometers per hr square]\n", + "aBA_x = 900 #[kilometers per hr square]\n", + "aBA_y = -100-50 #[kilometers per hr square]\n", + "aBA = round(math.sqrt(aBA_x**(2)+aBA_y**(2)),1) #[kilometers per hr square]\n", + "theta = round(math.degrees(math.atan(abs(aBA_y)/aBA_x)),1) #[Degrees]\n", + "\n", + "# Result\n", + "print\"aBA = \",(aBA),\"km/hr**(2)\"\n", + "print\"theta = \",(theta),\"degrees\"\n", + "\n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Ex 12.27 Page No 514" + ] + }, + { + "cell_type": "code", + "execution_count": 27, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "vBA = 9.69 m/s\n", + "theta = 21.7 degrees\n", + "aBA = 5.32 m/s**(2)\n", + "phi = 62.7 degrees\n" + ] + } + ], + "source": [ + "# Ex 12.27\n", + "import math\n", + "\n", + "# Variable Declaration\n", + "vA = 18 #[meter per second]\n", + "vB = 12 #[meter per second]\n", + "\n", + "# Calculation\n", + "# Velocity\n", + "vBA_x = 18*math.cos(math.pi*60/180) #[meter per second]\n", + "vBA_y = 18*math.sin(math.pi*60/180)-12 #[meter per second]\n", + "vBA = round(math.sqrt(vBA_x**(2)+vBA_y**(2)),2) #[meter per second]\n", + "theta = round(math.degrees(math.atan(vBA_y/vBA_x)),1) #[Degrees]\n", + "\n", + "# Acceleration\n", + "aBn = vB**(2)/100 #[meter per second square]\n", + "aBA_x = round(-1.440-2*math.cos(math.pi*60/180),3) #[meter per second square]\n", + "aBA_y = round(-3-2*math.sin(math.pi*60/180),3) #[meter per second square]\n", + "aBA = round(math.sqrt(aBA_x**(2)+aBA_y**(2)),2) #[meter per second square]\n", + "phi = round(math.degrees(math.atan(aBA_y/aBA_x)),1) #[Degrees]\n", + " \n", + "# Result\n", + "print\"vBA = \",(vBA),\"m/s\"\n", + "print\"theta = \",(theta),\"degrees\"\n", + "print\"aBA = \",(aBA),\"m/s**(2)\"\n", + "print\"phi = \",(phi),\"degrees\"" + ] + }, + { + "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 +} diff --git a/Engineering_Mechanics_Statics_and_Dynamics_by_Hibler_and_Gupta/Chapter_13_Kinetics_of_a_Particle_Force_and_Acceleration.ipynb b/Engineering_Mechanics_Statics_and_Dynamics_by_Hibler_and_Gupta/Chapter_13_Kinetics_of_a_Particle_Force_and_Acceleration.ipynb index 117cd26e..ada4b114 100644 --- a/Engineering_Mechanics_Statics_and_Dynamics_by_Hibler_and_Gupta/Chapter_13_Kinetics_of_a_Particle_Force_and_Acceleration.ipynb +++ b/Engineering_Mechanics_Statics_and_Dynamics_by_Hibler_and_Gupta/Chapter_13_Kinetics_of_a_Particle_Force_and_Acceleration.ipynb @@ -1,747 +1,504 @@ - - - - - - - - - - - - - - - - - - - - - - - Python-Textbook-Companions/Chapter_13_Kinetics_of_a_Particle_Force_and_Acceleration.ipynb at 1b1bb67e9ea912be5c8591523c8b328766e3680f · FOSSEE/Python-Textbook-Companions - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
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- - - - - - +{ + "cells": [ + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# Chapter 13 Kinetics of a Particle Force and Acceleration" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Ex 13.1 Page No 535" + ] + }, + { + "cell_type": "code", + "execution_count": 1, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "v = 15.6 m/s\n" + ] + } + ], + "source": [ + "# Ex 13.1\n", + "import numpy as np\n", + "import math\n", + "\n", + "# Variable Declaration\n", + "uk = 0.3\n", + "F = 400 #[Newton]\n", + "\n", + "# Calculation\n", + "# Using ΣF_x(right) = m*a_x and ΣF_y(upward) = m*a_y\n", + "a = np.array([[uk,50],[1,0] ])\n", + "b = np.array([F*math.cos(math.pi*30/180),490.5-F*math.sin(math.pi*30/180)])\n", + "x = np.linalg.solve(a, b)\n", + "NC = round(x[0],1) #[Newton]\n", + "a = round(x[1],1) #[meters per second square]\n", + "v = 0+a*3 #[meter per second]\n", + "\n", + "# Result\n", + "print\"v = \",(v),\"m/s\"\n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Ex 13.2 Page No 536" + ] + }, + { + "cell_type": "code", + "execution_count": 7, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Part(a)\n", + "h = 127.4 m\n", + "\n", + "Part(b)\n", + "h = 113.5 m\n" + ] + } + ], + "source": [ + "# Ex 13.2\n", + "from __future__ import division\n", + "from scipy import integrate\n", + "\n", + "# Calculation Part(a)\n", + "h = round(-(50**(2))/(2*-9.81),1) #[meters]\n", + "\n", + "# Result Part(a)\n", + "print\"Part(a)\"\n", + "print\"h = \",(h),\"m\\n\"\n", + "\n", + "# Calculation Part(b)\n", + "v = lambda v: -v/(0.001*v**(2)+9.81) \n", + "h = round(integrate.quad(v, 50, 0)[0],1) #[meters]\n", + "\n", + "# Result Part(b)\n", + "print\"Part(b)\"\n", + "print\"h = \",(h),\"m\"\n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Ex 13.3 Page No 537" + ] + }, + { + "cell_type": "code", + "execution_count": 10, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "v = 0.44 m/s\n", + "T = 39.4 N\n" + ] + } + ], + "source": [ + "# Ex 13.3\n", + "from scipy import integrate\n", + "from __future__ import division\n", + "\n", + "# Calculation\n", + "V = lambda t: 0.221*t\n", + "v = round(integrate.quad(V, 0, 2)[0],2) #[meters per second]\n", + "# Using ΣF_x(left) = m*a_x\n", + "T = round(40*2-(900/9.81)*0.221*2,1) #[Newton]\n", + "\n", + "# Result\n", + "print\"v = \",(v),\"m/s\"\n", + "print\"T = \",(T),\"N\"" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Ex 13.4 Page No 538" + ] + }, + { + "cell_type": "code", + "execution_count": 12, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "NC = 0.901 N\n", + "a = 9.21 m/s**(2)\n" + ] + } + ], + "source": [ + "# Ex 13.4\n", + "import numpy as np\n", + "import math\n", + "\n", + "# Variable Declaration\n", + "k = 3 #[Newtons per meter]\n", + "ul = 0.75 #[meter] (ul is the unstretched length)\n", + "y = 1 #[meter]\n", + "\n", + "# Calculation\n", + "Fs = round(k*(math.sqrt(y**(2)+0.75**(2))-ul),2) #[Newton]\n", + "theta = round(math.degrees(math.atan(y/0.75)),1) #[Degrees]\n", + "# Using ΣF_x(right) = m*a_x and ΣF_y(downward) = m*a_y\n", + "a = np.array([[1,0],[0,2] ])\n", + "b = np.array([Fs*math.cos(math.pi*theta/180),19.62-Fs*math.sin(math.pi*theta/180)])\n", + "x = np.linalg.solve(a, b)\n", + "NC = round(x[0],3) #[Newton]\n", + "a = round(x[1],2) #[meters per second square]\n", + "\n", + "# Result\n", + "print\"NC = \",(NC),\"N\"\n", + "print\"a = \",(a),\"m/s**(2)\"" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Ex 13.5 Page No 539" + ] + }, + { + "cell_type": "code", + "execution_count": 14, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "v = -13.1 m/s\n" + ] + } + ], + "source": [ + "# Ex 13.5\n", + "import numpy as np\n", + "\n", + "# Calculation\n", + "# Using ΣF_y(downward) = m*a_y (Block A), ΣF_y(downward) = m*a_y (Block B) and 2*aA = -aB\n", + "a = np.array([[2,100],[1,20*-2] ])\n", + "b = np.array([981,196.2])\n", + "x = np.linalg.solve(a, b)\n", + "T = round(x[0],1) #[Newton]\n", + "aA = round(x[1],2) #[meters per second square]\n", + "aB = -2*aA #[meters per second square]\n", + "v = round(0+aB*2,1) #[meters per second]\n", + "\n", + "# Result\n", + "print\"v = \",(v),\"m/s\"\n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Ex 13.7 Page No 548" + ] + }, + { + "cell_type": "code", + "execution_count": 18, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "t = 5.88 s\n" + ] + } + ], + "source": [ + "# Ex 13.7\n", + "from __future__ import division\n", + "\n", + "# Variable Declaration\n", + "uk = 0.1\n", + "\n", + "# Calculation\n", + "# Using ΣFb = 0\n", + "ND = 29.43 #[Newton]\n", + "# Using ΣFt = m*at\n", + "at = (0.1*ND)/3 #[meters per second square]\n", + "# Using ΣFn = m*an\n", + "vcr = round(math.sqrt(100/3),2) #[meters per second]\n", + "t = round((vcr-0)/at,2) #[seconds]\n", + "\n", + "# Result\n", + "print\"t = \",(t),\"s\"" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Ex 13.8 Page No 549" + ] + }, + { + "cell_type": "code", + "execution_count": 22, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "NA = 1651.4 N\n", + "aA = 13.33 m/s**(2)\n" + ] + } + ], + "source": [ + "# Ex 13.8\n", + "from __future__ import division\n", + "\n", + "# Variable Declaration\n", + "v = 20 #[meters per second]\n", + "\n", + "# Calculation\n", + "rho = ((1+0**(2))**(3/2))/(1/30) #[meters]\n", + "# Using ΣFn = m*an\n", + "NA = round(700+(700/9.81)*(20**(2)/rho),1) #[Newtons]\n", + "an = v**(2)/rho #[meters per second square]\n", + "aA = round(an,2) #[meters per second square]\n", + "\n", + "# Result\n", + "print\"NA = \",(NA),\"N\"\n", + "print\"aA = \",(aA),\"m/s**(2)\"" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Ex 13.9 Page No 550" + ] + }, + { + "cell_type": "code", + "execution_count": 23, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "thetamax = 42.1 degrees\n" + ] + } + ], + "source": [ + "# Ex 13.9\n", + "\n", + "# Calculation\n", + "thetamax = round(math.degrees((9.81+1)/((19.62*0.5/2)+9.81)),1) #[Degrees]\n", + "\n", + "# Result\n", + "print\"thetamax = \",(thetamax),\"degrees\"" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "collapsed": true + }, + "source": [ + "## Ex 13.10 Page No 556" + ] + }, + { + "cell_type": "code", + "execution_count": 4, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "F = 0.41 N\n", + "N = 0.28 N\n" + ] + } + ], + "source": [ + "# Ex 13.10\n", + "import numpy as np\n", + "import math\n", + "from __future__ import division\n", + "\n", + "# Calculation\n", + "a = np.array([[math.cos(math.pi*14.04/180),-math.sin(math.pi*14.04/180)],[math.sin(math.pi*14.04/180),math.cos(math.pi*14.04/180)] ])\n", + "b = np.array([(2/32.2)*(6-3*0.5**(2)),(2/32.2)*(3*0+2*6*0.5)])\n", + "x = np.linalg.solve(a, b)\n", + "F = round(x[0],2) #[Newton]\n", + "N = round(x[1],2) #[Newton]\n", + "\n", + "# Result\n", + "print\"F = \",(F),\"N\" #[Correction in the answer]\n", + "print\"N = \",(N),\"N\" #[Correction in the answer]" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Ex 13.11 Page No 557" + ] + }, + { + "cell_type": "code", + "execution_count": 10, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "FP = -0.354 N\n", + "NC = 19.4 N\n" + ] + } + ], + "source": [ + "# Ex 13.11\n", + "import numpy as np\n", + "import math\n", + "\n", + "\n", + "# Variable Declaration\n", + "theta = 60 #[Degrees]\n", + "\n", + "# Calculation\n", + "a = np.array([[0,-math.sin(math.pi*theta/180)],[1,-math.cos(math.pi*theta/180)] ])\n", + "b = np.array([2*(0.192-0.462*(0.5**(2)))-19.62*math.sin(math.pi*theta/180),2*(0+2*-0.133*0.5)-19.62*math.cos(math.pi*theta/180)])\n", + "x = np.linalg.solve(a, b)\n", + "FP = round(x[0],3) #[Newton]\n", + "NC = round(x[1],1) #[Newton]\n", + "\n", + "# Result\n", + "print\"FP = \",(FP),\"N\" \n", + "print\"NC = \",(NC),\"N\" " + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Ex 13.12 Page No 558" + ] + }, + { + "cell_type": "code", + "execution_count": 17, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "FC = 0.8 N\n", + "NC = -2.64 N\n" + ] + } + ], + "source": [ + "# Ex 13.12\n", + "import numpy as np\n", + "import math\n", + "from __future__ import division\n", + "\n", + "# Calculation\n", + "a = np.array([[0,math.cos(math.pi*17.7/180)],[1,-math.sin(math.pi*17.7/180)] ])\n", + "b = np.array([0.5*(0-0.1*math.pi*4**(2)),0.5*(0+2*0.4*4)])\n", + "x = np.linalg.solve(a, b)\n", + "FC = round(x[0],1) #[Newton]\n", + "NC = round(x[1],2) #[Newton]\n", + "\n", + "# Result\n", + "print\"FC = \",(FC),\"N\" \n", + "print\"NC = \",(NC),\"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 +} diff --git a/Engineering_Mechanics_Statics_and_Dynamics_by_Hibler_and_Gupta/Chapter_14_Kinetics_of_a_Particle_Work_and_Energy_.ipynb b/Engineering_Mechanics_Statics_and_Dynamics_by_Hibler_and_Gupta/Chapter_14_Kinetics_of_a_Particle_Work_and_Energy_.ipynb index 998e6185..2fcc32fb 100644 --- a/Engineering_Mechanics_Statics_and_Dynamics_by_Hibler_and_Gupta/Chapter_14_Kinetics_of_a_Particle_Work_and_Energy_.ipynb +++ b/Engineering_Mechanics_Statics_and_Dynamics_by_Hibler_and_Gupta/Chapter_14_Kinetics_of_a_Particle_Work_and_Energy_.ipynb @@ -1,747 +1,428 @@ - - - - - - - - - - - - - - - - - - - - - - - Python-Textbook-Companions/Chapter_14_Kinetics_of_a_Particle_Work_and_Energy_.ipynb at 1b1bb67e9ea912be5c8591523c8b328766e3680f · FOSSEE/Python-Textbook-Companions - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 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- - - - - - +{ + "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 +} diff --git a/Engineering_Mechanics_Statics_and_Dynamics_by_Hibler_and_Gupta/Chapter_15_Kinetics_of_a_Particle_Impulse_and_Momentum.ipynb b/Engineering_Mechanics_Statics_and_Dynamics_by_Hibler_and_Gupta/Chapter_15_Kinetics_of_a_Particle_Impulse_and_Momentum.ipynb index 335ebca8..1157bdc9 100644 --- a/Engineering_Mechanics_Statics_and_Dynamics_by_Hibler_and_Gupta/Chapter_15_Kinetics_of_a_Particle_Impulse_and_Momentum.ipynb +++ b/Engineering_Mechanics_Statics_and_Dynamics_by_Hibler_and_Gupta/Chapter_15_Kinetics_of_a_Particle_Impulse_and_Momentum.ipynb @@ -1,747 +1,570 @@ - - - - - - - - - - - - - - - - - - - - - - - Python-Textbook-Companions/Chapter_15_Kinetics_of_a_Particle_Impulse_and_Momentum.ipynb at 1b1bb67e9ea912be5c8591523c8b328766e3680f · FOSSEE/Python-Textbook-Companions - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 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- - - - - - +{ + "cells": [ + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# Chapter 15 Kinetics of a Particle : Impulse and Momentum" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Ex 15.1 Page No 607" + ] + }, + { + "cell_type": "code", + "execution_count": 1, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "v2 = 14.1 m/s\n", + "NC = 839.6 N\n" + ] + } + ], + "source": [ + "# Ex 15.1\n", + "import math\n", + "\n", + "# Variable Declaration\n", + "ws = 100 #[kilogram]\n", + "F = 200 #[Newton]\n", + "theta = 45 #[degrees]\n", + "\n", + "# Calculation\n", + "v2 = round(F*10*math.cos(math.pi*theta/180)/100,1) #[meters per second]\n", + "NC = round((9.81*ws*10-F*10*math.sin(math.pi*theta/180))/10,1) #[Newtons]\n", + "\n", + "# Result\n", + "print\"v2 = \",(v2),\"m/s\"\n", + "print\"NC = \",(NC),\"N\"" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Ex 15.2 Page No 608" + ] + }, + { + "cell_type": "code", + "execution_count": 3, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "v2 = 7.67 m/s\n", + "NC = 433.0 N\n" + ] + } + ], + "source": [ + "# Ex 15.2\n", + "import math\n", + "\n", + "# Calculation\n", + "# Using +ΣFy = 0\n", + "NC = round(500*math.cos(math.pi*30/180),1) #[Newtons]\n", + "v2 = round((50.97+100-0.6*NC+500)/50.97,2) #[meters per second]\n", + "\n", + "# Result\n", + "print\"v2 = \",(v2),\"m/s\"\n", + "print\"NC = \",(NC),\"N\"" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Ex 15.3 Page No 609" + ] + }, + { + "cell_type": "code", + "execution_count": 12, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "vB2 = 35.8 m/s\n", + "TB = 19.2 N\n" + ] + } + ], + "source": [ + "# Ex 15.3\n", + "import numpy as np\n", + "from __future__ import division\n", + "\n", + "# Calculation\n", + "a = np.array([[-(1/2)*3,2*6], [5,6]])\n", + "b = np.array([3*9.81*6,5*9.81*6])\n", + "x = np.linalg.solve(a, b)\n", + "vB2 = round(x[0],1) #[meters per second]\n", + "TB = round(x[1],1) #[Newtons]\n", + "\n", + "# Result\n", + "print\"vB2 = \",(vB2),\"m/s\"\n", + "print\"TB = \",(TB),\"N\"" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Ex 15.4 Page No 616" + ] + }, + { + "cell_type": "code", + "execution_count": 14, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "v2 = 0.5 m/s\n", + "Favg = 18.75 kN\n" + ] + } + ], + "source": [ + "# Ex 15.4\n", + "\n", + "# Calculation\n", + "# Part(a)\n", + "v2 = (15000*1.5-12000*0.75)/27000 #[meters per second]\n", + "# Part(b)\n", + "Favg = (15000*1.5-15000*0.5)/0.8 #[Newtons]\n", + "\n", + "# Result\n", + "print\"v2 = \",(v2),\"m/s\"\n", + "print\"Favg = \",(Favg/1000),\"kN\"" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Ex 15.5 Page No 617" + ] + }, + { + "cell_type": "code", + "execution_count": 17, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "vC2 = 4.0 m/s\n", + "Favg = 66.67 kN\n" + ] + } + ], + "source": [ + "# Ex 15.5\n", + "\n", + "# Calculation\n", + "# Part(a)\n", + "vC2 = 4*500/500 #[meters per second]\n", + "# Part(b)\n", + "Favg = 4*500/0.03 #[Newtons]\n", + "\n", + "# Result\n", + "print\"vC2 = \",(vC2),\"m/s\"\n", + "print\"Favg = \",round((Favg/1000),2),\"kN\"" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Ex 15.6 Page No 618" + ] + }, + { + "cell_type": "code", + "execution_count": 20, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "vT2 = 2.63 m/s\n" + ] + } + ], + "source": [ + "# Ex 15.6\n", + "\n", + "# Calculation\n", + "vT2 = round((350*10**(3)*3)/(350*10**(3)+50*10**(3)),2) #[meters per second]\n", + "\n", + "# Result\n", + "print\"vT2 = \",(vT2),\"m/s\"" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Ex 15.7 Page No 619" + ] + }, + { + "cell_type": "code", + "execution_count": 5, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Impulse = 682.9 N.s\n" + ] + } + ], + "source": [ + "# Ex 15.7\n", + "import math\n", + "from __future__ import division\n", + "\n", + "# Variable Declaration\n", + "mH = 300 #[kilogram]\n", + "mP = 800 #[kilogram]\n", + "\n", + "# Calculation\n", + "# Using conservation of energy\n", + "vH1 = round(math.sqrt((mH*9.81*0.5)/((1/2)*mH)),2) #[meters per second]\n", + "# Using conservation of momentum\n", + "v2 = (mH*3.13)/(mH+mP) #[meters per second]\n", + "# Using Principle of Impulse and Momentum\n", + "Impulse = round(300*vH1-300*v2,1) #[Newtons second]\n", + "\n", + "# Result\n", + "print\"Impulse = \",(Impulse),\"N.s\"\n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Ex 15.9 Page No 627" + ] + }, + { + "cell_type": "code", + "execution_count": 24, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Energy_loss = -33.15 J\n" + ] + } + ], + "source": [ + "# Ex 15.9\n", + "import numpy as np\n", + "from __future__ import division\n", + "\n", + "# Calculation\n", + "# Using conservation of energy\n", + "vA1 = round(math.sqrt((6*9.81*1)/((1/2)*6)),2)\n", + "# Using Conservation of Momentum and formula for coefficient of restitution\n", + "a = np.array([[1,3], [1,-1]])\n", + "b = np.array([4.43,-2.215])\n", + "x = np.linalg.solve(a, b)\n", + "vA2 = round(x[0],3) #[meters per second]\n", + "vB2 = round(x[1],2) #[meters per second]\n", + "Energy_loss = round((1/2)*18*vB2**(2)+(1/2)*6*vA2**(2)-(1/2)*6*vA1**(2),2) #[Joules]\n", + "\n", + "# Result\n", + "print\"Energy_loss = \",(Energy_loss),\"J\"" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Ex 15.10 Page No 628" + ] + }, + { + "cell_type": "code", + "execution_count": 6, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "s3 = 237.0 mm\n" + ] + } + ], + "source": [ + "# Ex 15.10\n", + "from __future__ import division\n", + "import numpy as np\n", + "import math\n", + "\n", + "# Variable Declaration\n", + "wB = 1.5 #[kilogram]\n", + "k = 800 #[Newton meter]\n", + "\n", + "# Calculation\n", + "# Using Principle of conservation of energy\n", + "vB1 = round(math.sqrt((-wB*9.81*1.25+(1/2)*k*0.25**(2))/((1/2)*1.5)),2) #[meters per second]\n", + "# Using Principle of coefficient of restitution\n", + "vB2 = 0.8*(0-2.97)+0 #[meters per second]\n", + "# Using Principle of conservation of energy\n", + "coeff = [400,-14.72,-18.94]\n", + "# Taking positive root\n", + "s3 = round(np.roots(coeff)[0],3) #[meters]\n", + "\n", + "# Result\n", + "print\"s3 = \",(s3*1000),\"mm\"" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Ex 15.11 Page No 629" + ] + }, + { + "cell_type": "code", + "execution_count": 32, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "vAx2 = -1.26 m/s\n", + "vBx2 = 1.22 m/s\n", + "vAy2 = 1.5 m/s\n", + "vBy2 = -0.71 m/s\n" + ] + } + ], + "source": [ + "# Ex 15.11\n", + "import numpy as np\n", + "import math\n", + "\n", + "# Calculation\n", + "vAx1 = round(3*math.cos(math.pi*30/180),2)\n", + "vAy1 = round(3*math.sin(math.pi*30/180),2)\n", + "vBx1 = round(-1*math.cos(math.pi*45/180),2)\n", + "vBy1 = round(-1*math.sin(math.pi*45/180),2)\n", + "# Using Conservation of \"x\" Momentum and Coefficient of restitution\n", + "a = np.array([[1,2], [-1,1]])\n", + "b = np.array([1.18,2.48])\n", + "x = np.linalg.solve(a, b)\n", + "vAx2 = round(x[0],3) #[meters per second]\n", + "vBx2 = round(x[1],2) #[meters per second]\n", + "# Using Conservation of \"x\" Momentum\n", + "vAy2 = vAy1\n", + "vBy2 = vBy1\n", + "\n", + "# Result\n", + "print\"vAx2 = \",(vAx2),\"m/s\"\n", + "print\"vBx2 = \",(vBx2),\"m/s\"\n", + "print\"vAy2 = \",(vAy2),\"m/s\"\n", + "print\"vBy2 = \",(vBy2),\"m/s\"" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Ex 15.13 Page No 640" + ] + }, + { + "cell_type": "code", + "execution_count": 7, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "vA2 = 20.0 m/s\n" + ] + } + ], + "source": [ + "# Ex 15.13\n", + "from __future__ import division\n", + "\n", + "# Variable Declaration\n", + "P = 10 #[Newton]\n", + "wB = 5 #[kilogram]\n", + "\n", + "# Calculation\n", + "vA2 = ((3/2)*(4**(2)-0**(2))+0.4*P*4)/(wB*0.4) #[meters per second]\n", + "\n", + "# Result\n", + "print\"vA2 = \",(vA2),\"m/s\"" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Ex 15.14 Page No 641" + ] + }, + { + "cell_type": "code", + "execution_count": 35, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "UF = 2.31 J\n" + ] + } + ], + "source": [ + "# Ex 15.14\n", + "\n", + "# Variable Declaration\n", + "v1 = 1 #[meters per second]\n", + "r1 = 0.5 #[meters]\n", + "r2 = 0.2 #[meters]\n", + "vC = 2 #[meters per second]\n", + "\n", + "# Calculation\n", + "# Part(a)\n", + "# Using principle of Conservation of Angular Momentum\n", + "v2dash = (r1*0.5*v1)/(r2*0.5) #[meters per second]\n", + "v2 = round(math.sqrt(2.5**(2)+2**(2)),2) #[meters per second]\n", + "# Part(b)\n", + "UF = (1/2)*0.5*v2**(2)-(1/2)*0.5*v1**(2) #[Joules]\n", + "\n", + "# Result\n", + "print\"UF = \",(UF),\"J\"" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Ex 15.15 Page No 642" + ] + }, + { + "cell_type": "code", + "execution_count": 38, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "vD2doubledash = 0.838 m/s\n" + ] + } + ], + "source": [ + "# Ex 15.15\n", + "import math\n", + "from __future__ import division\n", + "\n", + "# Variable Declaration\n", + "vD1 = 1.5 #[meters per second]\n", + "kc = 20 #[Newtons per meter]\n", + "\n", + "# Calculation\n", + "# Using principle of Conservation of Angular Momentum\n", + "vD2dash = (0.5*2*1.5)/(0.7*2) #[meters per second]\n", + "# Using Conservation of Energy\n", + "vD2 = round(math.sqrt(((1/2)*2*vD1**(2)-(1/2)*kc*0.2**(2))/((1/2)*2)),2) #[meters per second]\n", + "vD2doubledash = round(math.sqrt(vD2**(2)-vD2dash**(2)),3) #[meters per second]\n", + "\n", + "# Result\n", + "print\"vD2doubledash = \",(vD2doubledash),\"m/s\"" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], + "source": [] + } + ], + "metadata": { + "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 +} diff --git a/Engineering_Mechanics_Statics_and_Dynamics_by_Hibler_and_Gupta/Chapter_16_Planar_Kinematics_of_a_Rigid_Body.ipynb b/Engineering_Mechanics_Statics_and_Dynamics_by_Hibler_and_Gupta/Chapter_16_Planar_Kinematics_of_a_Rigid_Body.ipynb index c49859ea..677b13e4 100644 --- a/Engineering_Mechanics_Statics_and_Dynamics_by_Hibler_and_Gupta/Chapter_16_Planar_Kinematics_of_a_Rigid_Body.ipynb +++ b/Engineering_Mechanics_Statics_and_Dynamics_by_Hibler_and_Gupta/Chapter_16_Planar_Kinematics_of_a_Rigid_Body.ipynb @@ -1,747 +1,718 @@ - - - - - - - - - - - - - - - - - - - - - - - Python-Textbook-Companions/Chapter_16_Planar_Kinematics_of_a_Rigid_Body.ipynb at 1b1bb67e9ea912be5c8591523c8b328766e3680f · FOSSEE/Python-Textbook-Companions - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
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- - - - - - +{ + "cells": [ + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# Chapter 16 Planar Kinematics of a Rigid Body" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Ex 16.2 Page No 659" + ] + }, + { + "cell_type": "code", + "execution_count": 5, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "vP = 1.23 m/s\n", + "alphaP = 3.78 m/s**(2)\n" + ] + } + ], + "source": [ + "# Ex 16.2\n", + "import math\n", + "\n", + "# Variable Declaration\n", + "alphaA = 2 #[radians per second square]\n", + "\n", + "# Calculation\n", + "thetaB = round(1*(2*math.pi)/1,3) #[radians]\n", + "thetaA = round(thetaB*0.4/0.15,2) #[radians]\n", + "wA = round(math.sqrt(0+2*2*(thetaA-0)),3) #[radians per second]\n", + "wB = wA*0.15/0.4 #[radians per second]\n", + "alphaB = alphaA*0.15/0.4 #[radians per second square]\n", + "vP = round(wB*0.4,2) #[meters per second]\n", + "alphaPt = alphaB*0.4 #[radians per second square]\n", + "alphaPn = wB**(2)*0.4 #[radians per second square]\n", + "alphaP = round(math.sqrt(alphaPt**(2)+alphaPn**(2)),2) #[radians per second square]\n", + "\n", + "# Result\n", + "print\"vP = \",(vP),\"m/s\"\n", + "print\"alphaP = \",(alphaP),\"m/s**(2)\"" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "collapsed": true + }, + "source": [ + "## Ex 16.5 Page No 666" + ] + }, + { + "cell_type": "code", + "execution_count": 1, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "w = 0.62 rad/s\n", + "alpha = -0.416 rad/s**(2)\n" + ] + } + ], + "source": [ + "# Ex 16.5\n", + "import math\n", + "from __future__ import division\n", + "\n", + "# Variable Declaration\n", + "theta = 30 #[degrees]\n", + "vC = 0.5 #[meter per second]\n", + "\n", + "# Calculation\n", + "s = round(math.sqrt(5-4*math.cos(math.pi*theta/180)),3) #[meters]\n", + "w = round((s*0.5)/(2*math.sin(math.pi*theta/180)),3) #[radians per second]\n", + "alpha = round((0.5**(2)-2*math.cos(math.pi*theta/180)*w**(2))/(2*math.sin(math.pi*theta/180)),3) #[Degrees]\n", + "\n", + "# Result\n", + "print\"w = \",(w),\"rad/s\"\n", + "print\"alpha = \",(alpha),\"rad/s**(2)\"" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Ex 16.6 Page No 673" + ] + }, + { + "cell_type": "code", + "execution_count": 17, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "w = 14.1 rad/s\n", + "vB = 2.0 m/s\n" + ] + } + ], + "source": [ + "# Ex 16.6\n", + "import math\n", + "\n", + "# Variable Declaration\n", + "vA = 2 #[meters per second]\n", + "theta = 45 #[Degrees]\n", + "\n", + "# Calculation\n", + "# Equating j component\n", + "w = round(vA/(0.2*math.sin(math.pi*theta/180)),1) #[radians per second]\n", + "# Equating i component\n", + "vB = round(0.2*w*math.sin(math.pi*theta/180),1) #[meters per second]\n", + "\n", + "# Result\n", + "print\"w = \",(w),\"rad/s\"\n", + "print\"vB = \",(vB),\"m/s\"" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Ex 16.7 Page No 674" + ] + }, + { + "cell_type": "code", + "execution_count": 11, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Solution 1 Vector Analysis\n", + "vA = 5.0 m/s\n", + "theta = 36.9 degrees\n", + "\n", + "Solution 2 Scalar Analysis\n", + "vA = 5.0 m/s\n", + "theta = 36.9 degrees\n" + ] + } + ], + "source": [ + "# Ex 16.7\n", + "import math\n", + "\n", + "# Calculation\n", + "# Solution 1 Vector Analysis\n", + "vA_x = 1+3.0 #[meters per second]\n", + "vA_y = 3 #[meters per second]\n", + "vA = round(math.sqrt(vA_x**(2)+vA_y**(2)),1) #[meters per second]\n", + "theta = round(math.degrees(math.atan(vA_y/vA_x)),1) #[Degrees]\n", + "\n", + "# Result 1 Vector Analysis\n", + "print\"Solution 1 Vector Analysis\"\n", + "print\"vA = \",(vA),\"m/s\"\n", + "print\"theta = \",(theta),\"degrees\\n\"\n", + "\n", + "# Solution 2 Scalar Analysis\n", + "vA_x = 1+4.24*math.cos(math.pi*45/180) #[meters per second]\n", + "vA_y = 0+4.24*math.sin(math.pi*45/180) #[meters per second]\n", + "vA = round(math.sqrt(vA_x**(2)+vA_y**(2)),1) #[meters per second]\n", + "theta = round(math.degrees(math.atan(vA_y/vA_x)),1) #[Degrees]\n", + "\n", + "# Result 2 Scalar Analysis\n", + "print\"Solution 2 Scalar Analysis\"\n", + "print\"vA = \",(vA),\"m/s\"\n", + "print\"theta = \",(theta),\"degrees\"" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Ex 16.8 Page No 675" + ] + }, + { + "cell_type": "code", + "execution_count": 14, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "vB = 2.0 m/s\n", + "wAB = 10.0 rad/s\n" + ] + } + ], + "source": [ + "# Ex 16.8\n", + "\n", + "# Calculation\n", + "# Link CB\n", + "wCB = 2/0.2 #[radians per second]\n", + "vB = 0.2*wCB #[meters per second]\n", + "# Link AB\n", + "wAB = 2/0.2 #[radians per second]\n", + "\n", + "# Result\n", + "print\"vB = \",(vB),\"m/s\"\n", + "print\"wAB = \",(wAB),\"rad/s\"" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Ex 16.9 Page No 676" + ] + }, + { + "cell_type": "code", + "execution_count": 25, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "wBC = 15.0 rad/s\n", + "wD = 52.0 rad/s\n" + ] + } + ], + "source": [ + "# Ex 16.9\n", + "\n", + "# Calculation\n", + "# Link BC\n", + "vC = 5.20 #[meters per second]\n", + "wBC = 3.0/0.2 #[radians per second]\n", + "# Wheel\n", + "wD = 5.20/0.1 #[radians per second]\n", + "\n", + "# Result\n", + "print\"wBC = \",(wBC),\"rad/s\"\n", + "print\"wD = \",(wD),\"rad/s\"" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Ex 16.11 Page No 684" + ] + }, + { + "cell_type": "code", + "execution_count": 22, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "wBD = 5.3 rad/s\n", + "wAB = 5.3 rad/s\n" + ] + } + ], + "source": [ + "# Ex 16.10\n", + "import math\n", + "\n", + "# Variable Declaration\n", + "vD = 3 #[meters per second]\n", + "\n", + "# Calculation\n", + "rBIC = round(0.4*math.tan(math.pi*45/180),1) #[meters]\n", + "rDIC = round(0.4/math.cos(math.pi*45/180),3) #[meters]\n", + "wBD = round(vD/rDIC,2) #[radians per second]\n", + "vB = wBD*rBIC #[meters per second]\n", + "wAB = vB/0.4 #[radians per second]\n", + "\n", + "# Result\n", + "print\"wBD = \",(wBD),\"rad/s\"\n", + "print\"wAB = \",(wAB),\"rad/s\"\n", + "\n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Ex 16.12 Page No 685" + ] + }, + { + "cell_type": "code", + "execution_count": 24, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "w = 2.6 rad/s\n", + "vC = 0.075 m/s\n" + ] + } + ], + "source": [ + "# Ex 16.12\n", + "\n", + "# Calculation\n", + "x = 0.1/0.65 #[meters]\n", + "w = 0.4/x #[radians per second]\n", + "vC = w*(x-0.125) #[meters per second]\n", + "\n", + "# Result\n", + "print\"w = \",(w),\"rad/s\"\n", + "print\"vC = \",(vC),\"m/s\"" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Ex 16.13 Page No 691" + ] + }, + { + "cell_type": "code", + "execution_count": 28, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "alpha = 0.344 rad/s**(2)\n" + ] + } + ], + "source": [ + "# Ex 16.13\n", + "import numpy as np\n", + "import math\n", + "\n", + "# Calculation\n", + "a = np.array([[math.cos(math.pi*45/180),0],[math.sin(math.pi*45/180),-10]])\n", + "b = np.array([3*math.cos(math.pi*45/180)-0.283**(2)*10,-3*math.sin(math.pi*45/180)])\n", + "x = np.linalg.solve(a, b)\n", + "aB = x[0] #[meters per second square]\n", + "alpha = round(x[1],3) #[radians per second square]\n", + " \n", + "# Result\n", + "print\"alpha = \",(alpha),\"rad/s**(2)\" " + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Ex 16.15 Page No 693" + ] + }, + { + "cell_type": "code", + "execution_count": 29, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "aB_x = -20.0 m/s**(2)\n", + "aB_y = 2.0 m/s**(2)\n", + "aA_x = -4.0 m/s**(2)\n", + "aA_y = -18.0 m/s**(2)\n" + ] + } + ], + "source": [ + "# Ex 16.15\n", + "\n", + "# Calculation\n", + "# For point B\n", + "aB_x = -2-6**(2)*0.5 #[meters per second square]\n", + "aB_y = 4*0.5 #[meters per second square]\n", + "# For point A\n", + "aA_x = -2-4*0.5 #[meters per second square]\n", + "aA_y = -6**(2)*0.5 #[meters per second square]\n", + "\n", + "# Result\n", + "print\"aB_x = \",(aB_x),\"m/s**(2)\"\n", + "print\"aB_y = \",(aB_y),\"m/s**(2)\"\n", + "print\"aA_x = \",(aA_x),\"m/s**(2)\"\n", + "print\"aA_y = \",(aA_y),\"m/s**(2)\"" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Ex 16.16 Page No 694" + ] + }, + { + "cell_type": "code", + "execution_count": 2, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "aB = 9.25 m/s**(2)\n", + "theta = 71.1 degrees\n" + ] + } + ], + "source": [ + "# Ex 16.16\n", + "import math\n", + "\n", + "# Variable Declaration\n", + "w = 3 #[radians per second]\n", + "alpha = 4 #[radians per second square]\n", + "\n", + "# Calculation\n", + "aB_x = alpha*0.75 #[meters per second square]\n", + "aB_y = -2-w**(2)*0.75 #[meters per second square]\n", + "aB = round(math.sqrt(aB_x**(2)+aB_y**(2)),2) #[meters per second square]\n", + "theta = round(math.degrees(math.atan(-aB_y/aB_x)),1) #[Degrees]\n", + "\n", + "# Result\n", + "print\"aB = \",(aB),\"m/s**(2)\"\n", + "print\"theta = \",(theta),\"degrees\"" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Ex 16.17 Page No 695" + ] + }, + { + "cell_type": "code", + "execution_count": 34, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "alphaCB = 5.0 rad/s**(2)\n", + "alphaAB = -95.0 rad/s**(2)\n" + ] + } + ], + "source": [ + "# Ex 16.17\n", + "import numpy as np\n", + "\n", + "# Calculation\n", + "a = np.array([[0.2,-0.2],[0,0.2]])\n", + "b = np.array([-20,1])\n", + "x = np.linalg.solve(a, b)\n", + "alphaAB = round(x[0],1) #[meters per second square]\n", + "alphaCB = round(x[1],1) #[radians per second square]\n", + " \n", + "# Result\n", + "print\"alphaCB = \",(alphaCB),\"rad/s**(2)\" \n", + "print\"alphaAB = \",(alphaAB),\"rad/s**(2)\" " + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Ex 16.18 Page No 696" + ] + }, + { + "cell_type": "code", + "execution_count": 40, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "alphaBC = 27.7 rad/s**(2)\n", + "aC = -13.6 m/s**(2)\n" + ] + } + ], + "source": [ + "# Ex 16.18\n", + "import numpy as np\n", + "import math\n", + "\n", + "# Calculation\n", + "rB_x = -0.25*math.sin(math.pi*45/180) #[meters]\n", + "rB_y = 0.25*math.cos(math.pi*45/180) #[meters]\n", + "rCB_x = 0.75*math.sin(math.pi*13.6/180) #[meters]\n", + "rCB_y = 0.75*math.cos(math.pi*13.6/180) #[meters]\n", + "aB_x = np.cross([0,0,-20],[-0.177,0.177,0])[0]-10**(2)*-0.177 #[meters per second square]\n", + "aB_y = np.cross([0,0,-20],[-0.177,0.177,0])[1]-10**(2)*0.177 #[meters per second square]\n", + "alphaBC = round(20.17/0.729,1) #[radians per second square]\n", + "aC = round(0.176*alphaBC-18.45,1) #[meters per second square]\n", + "\n", + "# Result\n", + "print\"alphaBC = \",(alphaBC),\"rad/s**(2)\"\n", + "print\"aC = \",(aC),\"m/s**(2)\"" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Ex 16.19 Page No 705" + ] + }, + { + "cell_type": "code", + "execution_count": 43, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "aCor_x = 0 m/s**(2)\n", + "aCor_y = -12 m/s**(2)\n", + "vC_x = 2 m/s\n", + "vC_y = -0.6 m/s\n", + "aC_x = 1.2 m/s\n", + "aC_y = -12.4 m/s\n" + ] + } + ], + "source": [ + "# Ex 16.19\n", + "import numpy as np\n", + "\n", + "# Calculation\n", + "aCor_x = np.cross([0,0,2*-3],[2,0,0])[0] #[meters per second square]\n", + "aCor_y = np.cross([0,0,2*-3],[2,0,0])[1] #[meters per second square]\n", + "vC_x = 2 #[meters per second]\n", + "vC_y = -0.6 #[meters per second]\n", + "aC_x = 3-1.80 #[meters per second square]\n", + "aC_y = -0.4-12 #[meters per second square]\n", + "\n", + "# Result\n", + "print\"aCor_x = \",(aCor_x),\"m/s**(2)\"\n", + "print\"aCor_y = \",(aCor_y),\"m/s**(2)\"\n", + "print\"vC_x = \",(vC_x),\"m/s\"\n", + "print\"vC_y = \",(vC_y),\"m/s\"\n", + "print\"aC_x = \",(aC_x),\"m/s\"\n", + "print\"aC_y = \",(aC_y),\"m/s\"" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Ex 16.20 Page No 706" + ] + }, + { + "cell_type": "code", + "execution_count": 45, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "wDE = 3 rad/s\n", + "alphaDE = -5.0 rad/s**(2)\n" + ] + } + ], + "source": [ + "# Ex 16.20\n", + "\n", + "# Calculation\n", + "vCDxyz = 1.2 #[meters per second]\n", + "wDE = 3 #[radians per second]\n", + "aCDxyz = 3.6-2 #[meters per second square]\n", + "alphaDE = (7.2-5.2)/-0.4 #[radians per second square]\n", + "\n", + "# Result\n", + "print\"wDE = \",(wDE),\"rad/s\"\n", + "print\"alphaDE = \",(alphaDE),\"rad/s**(2)\"" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "collapsed": true + }, + "source": [ + "## Ex 16.21 Page No 707" + ] + }, + { + "cell_type": "code", + "execution_count": 6, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "vABxyz_x = 0 km/h\n", + "vABxyz_y = 94.0 km/h\n", + "aABxyz_x = -609 km/h**(2)\n", + "aABxyz_y = 152 km/h**(2)\n" + ] + } + ], + "source": [ + "# Ex 16.21\n", + "\n", + "# Calculation\n", + "vABxyz_x = 0 #[kilometer per hour]\n", + "vABxyz_y = 700-600-(-1.5*-4) #[kilometer per hour]\n", + "aABxyz_x = -900+9+282 #[kilometer per hour square]\n", + "aABxyz_y = 50+100+2 #[kilometer per hour square]\n", + "\n", + "# Result\n", + "print\"vABxyz_x = \",(vABxyz_x),\"km/h\"\n", + "print\"vABxyz_y = \",(vABxyz_y),\"km/h\"\n", + "print\"aABxyz_x = \",(aABxyz_x),\"km/h**(2)\"\n", + "print\"aABxyz_y = \",(aABxyz_y),\"km/h**(2)\"" + ] + }, + { + "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 +} diff --git a/Engineering_Mechanics_Statics_and_Dynamics_by_Hibler_and_Gupta/Chapter_17_Planar_Kinetics_of_a_Rigid_Body_Force_and_Acceleration.ipynb b/Engineering_Mechanics_Statics_and_Dynamics_by_Hibler_and_Gupta/Chapter_17_Planar_Kinetics_of_a_Rigid_Body_Force_and_Acceleration.ipynb index c845f04a..ea63db73 100644 --- a/Engineering_Mechanics_Statics_and_Dynamics_by_Hibler_and_Gupta/Chapter_17_Planar_Kinetics_of_a_Rigid_Body_Force_and_Acceleration.ipynb +++ b/Engineering_Mechanics_Statics_and_Dynamics_by_Hibler_and_Gupta/Chapter_17_Planar_Kinetics_of_a_Rigid_Body_Force_and_Acceleration.ipynb @@ -1,747 +1,744 @@ - - - - - - - - - - - - - - - - - - - - - - - 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- - - - - - +{ + "cells": [ + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# Chapter 17 Planar Kinetics of a Rigid Body Force and Acceleration" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Ex 17.2 Page No 719" + ] + }, + { + "cell_type": "code", + "execution_count": 2, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Iy = 0.349 Mg.m**(2)\n" + ] + } + ], + "source": [ + "# Ex 17.2\n", + "from scipy import integrate\n", + "import math\n", + "\n", + "# Calculation\n", + "y = lambda y: ((math.pi*2)/2)*y**(8)\n", + "Iy = round(integrate.quad(y, 0, 1)[0],3) #[milligram meter square]\n", + "\n", + "# Result\n", + "print\"Iy = \",(Iy),\"Mg.m**(2)\"" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Ex 17.3 Page No 722" + ] + }, + { + "cell_type": "code", + "execution_count": 2, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "IO = 1.2 kg m**(2)\n" + ] + } + ], + "source": [ + "# Ex 17.3\n", + "from __future__ import division\n", + "import math\n", + "\n", + "# Variable Declaration\n", + "d = 8000 #[kilogram per meter cube]\n", + "t = 0.01 #[meter]\n", + "\n", + "# Calculation\n", + "md = round(d*math.pi*0.25**(2)*t,2)\n", + "# Disk\n", + "IdO = (1/2)*md*0.25**(2)+md*0.25**(2) #[kilogram meter square]\n", + "\n", + "# Hole\n", + "IhO = (1/2)*3.93*0.125**(2)+3.93*0.25**(2) #[kilogram meter square]\n", + "\n", + "# Let IO be moment of inertia about point O\n", + "IO = round(IdO-IhO,2) #[kilogram meter square]\n", + "\n", + "# Result\n", + "print\"IO = \",(IO),\"kg m**(2)\"" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Ex 17.4 Page No 723" + ] + }, + { + "cell_type": "code", + "execution_count": 7, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "IO = 14.167 kg.m**(2)\n", + "IG = 2.917 kg.m**(2)\n" + ] + } + ], + "source": [ + "# Ex 17.4\n", + "from __future__ import division\n", + "\n", + "# Variable Declaration\n", + "m = 10 #[kilogram]\n", + "\n", + "# Calculation\n", + "# Part(a)\n", + "IOAO = (1/3)*m*1**(2) #[kilogram meter square]\n", + "IBCO = (1/12)*m*1**(2)+m*1**(2) #[kilogram meter square]\n", + "# Let IO be moment of inertia about O\n", + "IO = round(IOAO+IBCO,3) #[kilogram meter square]\n", + "\n", + "# Part(b)\n", + "ybar = (0.5*10+1*10)/(10+10) #[meter]\n", + "IG = round(IO-2*m*ybar**(2),3) #[kilogram meter square]\n", + "\n", + "# Result\n", + "print\"IO = \",(IO),\"kg.m**(2)\"\n", + "print\"IG = \",(IG),\"kg.m**(2)\"" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Ex 17.5 Page No 733" + ] + }, + { + "cell_type": "code", + "execution_count": 8, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "NA = 6.88 kN\n", + "NB = 12.74 kN\n", + "aG = 1.59 m/s**(2)\n" + ] + } + ], + "source": [ + "# Ex 17.5\n", + "import numpy as np\n", + "\n", + "# Calculation\n", + "# Using +ΣF_x = m(aG)_x, +ΣF_y = m(aG)_y and +ΣMG(counter clockwise)=0 \n", + "a = np.array([[0,-0.25,2000],[1,1,0],[-1.25,-0.25*0.3+0.75,0]])\n", + "b = np.array([0,2000*9.81,0])\n", + "x = np.linalg.solve(a, b)\n", + "NA = round(x[0]/1000,2) #[kilo Newton]\n", + "NB = round(x[1]/1000,2) #[kilo Newton]\n", + "aG = round(x[2],2) #[meters per second square]\n", + "\n", + "# Result\n", + "print\"NA = \",(NA),\"kN\"\n", + "print\"NB = \",(NB),\"kN\"\n", + "print\"aG = \",(aG),\"m/s**(2)\"" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Ex 17.6 Page No 734" + ] + }, + { + "cell_type": "code", + "execution_count": 13, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "usmin = 0.912\n" + ] + } + ], + "source": [ + "# Ex 17.6\n", + "import numpy as np\n", + "\n", + "# Variable Declaration\n", + "mm = 125 #[kilogram]\n", + "mr = 75 #[kilogram]\n", + "\n", + "# Calculation\n", + "# Using +ΣF_x = m(aG)_x, +ΣF_y = m(aG)_y and +ΣMG(counter clockwise)=0 \n", + "a = np.array([[1,0,-(mm+mr)],[0,1,0],[0,0,mr*0.9+mm*0.6]])\n", + "b = np.array([0,735.75+1226.25,-735.75*0.4-1226.25*0.8])\n", + "x = np.linalg.solve(a, b)\n", + "FB = round(x[0],1) #[kilo Newton]\n", + "NB = round(x[1],1) #[kilo Newton]\n", + "aG = round(x[2],2) #[meters per second square]\n", + "# Let usmin be minimum coefficient of static friction\n", + "usmin = round(-FB/NB,3)\n", + "\n", + "# Result\n", + "print\"usmin = \",(usmin)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Ex 17.7 Page No 736" + ] + }, + { + "cell_type": "code", + "execution_count": 14, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "NC = 490.5 N\n", + "x = 0.467 m\n", + "aG = 10.0 m/s**(2)\n" + ] + } + ], + "source": [ + "# Ex 17.7\n", + "\n", + "# Variable Declaration\n", + "P = 600 #[Newton]\n", + "uk = 0.2\n", + "\n", + "# Calculation\n", + "# Using +ΣF_y = m(aG)_y\n", + "NC = 490.5 #[Newton]\n", + "\n", + "# Using +ΣF_x = m(aG)_x\n", + "aG = round((600-uk*NC)/50,1) #[meters per second square]\n", + "\n", + "# Using +ΣMG(counter clockwise)=0 \n", + "x = round((uk*NC*0.5+600*0.3)/NC,3) #[meter]\n", + "\n", + "# Result\n", + "print\"NC = \",(NC),\"N\"\n", + "print\"x = \",(x),\"m\"\n", + "print\"aG = \",(aG),\"m/s**(2)\"" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "collapsed": true + }, + "source": [ + "## Ex 17.8 Page No 736" + ] + }, + { + "cell_type": "code", + "execution_count": 3, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "TB = 1.32 kN\n", + "TD = 1.32 kN\n", + "aG = 4.9 m/s**(2)\n" + ] + } + ], + "source": [ + "# Ex 17.8\n", + "import numpy as np\n", + "import math\n", + "\n", + "# Variable Declaration\n", + "theta = 30 #[Degrees]\n", + "\n", + "# Calculation\n", + "# Using +ΣFn = 0, +ΣFt = 0 and +ΣMG(counterclockwise) = 0\n", + "a = np.array([[1,1,0],[0,0,100],[-math.cos(math.pi*theta/180)*0.4,0.4*math.cos(math.pi*theta/180),0]])\n", + "b = np.array([981*math.cos(math.pi*theta/180)+100*18,981*math.sin(math.pi*theta/180),0])\n", + "x = np.linalg.solve(a, b)\n", + "TB = round(x[0]/1000,2) #[kilo Newton]\n", + "TD = round(x[1]/1000,2) #[kilo Newton]\n", + "aG = round(x[2],2) #[meters per second square]\n", + "\n", + "# Result\n", + "print\"TB = \",(TB),\"kN\"\n", + "print\"TD = \",(TD),\"kN\"\n", + "print\"aG = \",(aG),\"m/s**(2)\"" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Ex 17.9 Page No 742" + ] + }, + { + "cell_type": "code", + "execution_count": 5, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Ox = 0 N\n", + "Oy = 304.3 N\n", + "theta = 2.72 rev\n" + ] + } + ], + "source": [ + "# Ex 17.9\n", + "\n", + "# Calculation\n", + "# Using +ΣFx(right) = m(aG)x\n", + "Ox = 0 #[Newton]\n", + "\n", + "# Using +ΣFy(upward) = m(aG)y\n", + "Oy = 294.3+10 #[Newton]\n", + "\n", + "# Using +ΣMO(counterclockwise) = IO*alpha\n", + "alpha = (-10*0.2-5)/-0.6\n", + "theta = (-20**(2))/(2*-11.7)\n", + "theta = round(theta*(1/(2*math.pi)),2)\n", + "\n", + "# Result\n", + "print\"Ox = \",(Ox),\"N\"\n", + "print\"Oy = \",(Oy),\"N\"\n", + "print\"theta = \",(theta),\"rev\" " + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Ex 17.10 Page No 743" + ] + }, + { + "cell_type": "code", + "execution_count": 10, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Solution 1\n", + "On = 750.0 N\n", + "Ot = 19.05 N\n", + "alpha = 5.91 rad/s**(2)\n", + "\n", + "Solution 2\n", + "alpha = 5.91 rad/s**(2)\n", + "\n", + "Solution 3\n", + "alpha = 5.91 rad/s**(2)\n", + "\n" + ] + } + ], + "source": [ + "# Ex 17.10\n", + "import numpy as np\n", + "from __future__ import division\n", + "\n", + "# Calculation Solution 1\n", + "# Using +ΣFn(left) = mw**(2)rG, +ΣFt(downwards) = malpharG and +ΣMG(clockwise) = IGalpha\n", + "a = np.array([[1,0,0],[0,1,20*1.5],[0,1.5,-(1/12)*20*3**(2)]])\n", + "b = np.array([20*5**(2)*1.5,20*9.81,-60])\n", + "x = np.linalg.solve(a, b)\n", + "On = round(x[0],2) #[Newton]\n", + "Ot = round(x[1],2) #[Newton]\n", + "alpha = round(x[2],2) #[radians per second square]\n", + "\n", + "\n", + "# Result Solution 1\n", + "print\"Solution 1\"\n", + "print\"On = \",(On),\"N\"\n", + "print\"Ot = \",(Ot),\"N\"\n", + "print\"alpha = \",(alpha),\"rad/s**(2)\\n\"\n", + "\n", + "# Calculation Solution 2\n", + "# Using +ΣMO(clockwise) = Σ(Mk)O\n", + "alpha = round((60+20*9.81*1.5)/((1/12)*20*3**(2)+20*1.5*1.5),2) #[radians per second square]\n", + "\n", + "# Result Solution 2\n", + "print\"Solution 2\"\n", + "print\"alpha = \",(alpha),\"rad/s**(2)\\n\"\n", + "\n", + "# Calculation Solution 3\n", + "# Using +ΣMO(clockwise) = IOalpha\n", + "alpha = round((60+20*9.81*1.5)/((1/3)*20*3**(2)),2) #[radians per second square]\n", + "\n", + "# Result Solution 3\n", + "print\"Solution 3\"\n", + "print\"alpha = \",(alpha),\"rad/s**(2)\\n\"\n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Ex 17.11 Page No 744" + ] + }, + { + "cell_type": "code", + "execution_count": 3, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Solution 1\n", + "alpha = 11.3 rad/s**(2)\n", + "\n", + "Solution 2\n", + "alpha = 11.3 rad/s**(2)\n" + ] + } + ], + "source": [ + "# Ex 17.11\n", + "import numpy as np\n", + "\n", + "# Variable Declaration\n", + "m = 60 #[kilogram]\n", + "k = 0.25 #[meters]\n", + "\n", + "# Calculation Solution 1\n", + "IO = m*k**(2)\n", + "# Using +ΣMO(counterclockwise) = IOalpha, +ΣFy(upward) = m(aG)y and +a(counterclockwise) = alpha*r\n", + "a = np.array([[0.4,0,-IO],[1,20,0],[0,1,-0.4]])\n", + "b = np.array([0,20*9.81,0])\n", + "x = np.linalg.solve(a, b)\n", + "T = round(x[0],2) #[Newton]\n", + "a = round(x[1],2) #[meters per second square]\n", + "alpha = round(x[2],1) #[radians per second square]\n", + "\n", + "# Result Solution 1\n", + "print\"Solution 1\"\n", + "print\"alpha = \",(alpha),\"rad/s**(2)\\n\"\n", + "\n", + "# Calculation Solution 2\n", + "# Using +ΣMO(clockwise) = Σ(Mk)O\n", + "alpha = round((20*9.81*0.4)/(3.75+20*0.4*0.4),1) #[radians per second square]\n", + "\n", + "\n", + "# Result Solution 2\n", + "print\"Solution 2\"\n", + "print\"alpha = \",(alpha),\"rad/s**(2)\"\n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Ex 17.12 Page No 745" + ] + }, + { + "cell_type": "code", + "execution_count": 15, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "On = 1600.0 N\n", + "Ot = 223.9 N\n", + "alpha = 10.66 rad/s**(2)\n" + ] + } + ], + "source": [ + "# Ex 17.12\n", + "import numpy as np\n", + "\n", + "# Calculation\n", + "# Using +ΣFn(left) = mw**(2)rG, +ΣFt(upward) = m*alpha*rG and +ΣMG(clockwise) = IG*alpha\n", + "a = np.array([[1,0,0],[0,1,50*0.5],[0,0.5,-18]])\n", + "b = np.array([50*8**(2)*0.5,50*9.81,-80])\n", + "x = np.linalg.solve(a, b)\n", + "On = round(x[0],2) #[Newton]\n", + "Ot = round(x[1],2) #[Newton]\n", + "alpha = round(x[2],2) #[radians per second square]\n", + "\n", + "\n", + "# Result\n", + "print\"On = \",(On),\"N\"\n", + "print\"Ot = \",(Ot),\"N\" # Correction in the textbook\n", + "print\"alpha = \",(alpha),\"rad/s**(2)\"" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Ex 17.14 Page No 754" + ] + }, + { + "cell_type": "code", + "execution_count": 5, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Solution 1\n", + "alpha = 10.3 rad/s**(2)\n", + "\n", + "Solution 2\n", + "alpha = 10.3 rad/s**(2)\n" + ] + } + ], + "source": [ + "# Ex 17.14\n", + "import numpy as np\n", + "\n", + "# Calculation Solution 1\n", + "IG = 8*0.35**(2) #[kilogram meter square]\n", + "# Using +ΣFy(upward) = m(aG)y, +ΣMG(clockwise) = IG*alpha and +aG(clockwise) = alpha*r\n", + "a = np.array([[1,-8,0],[0.5,0,IG],[0,1,-0.5]])\n", + "b = np.array([-100+78.48,100*0.2,0])\n", + "x = np.linalg.solve(a, b)\n", + "T = round(x[0],2) #[Newton]\n", + "aG = round(x[1],2) #[meters per second square]\n", + "alpha = round(x[2],1) #[radians per second square]\n", + "\n", + "# Result Solution 1\n", + "print\"Solution 1\"\n", + "print\"alpha = \",(alpha),\"rad/s**(2)\\n\"\n", + "\n", + "# Calculation Solution 2\n", + "# Using +ΣMA(clockwise) = Σ(Mk)A and aG = 0.5*alpha\n", + "alpha = round((100*0.7-78.48*0.5)/(0.980+8*0.5*0.5),1) #[radians per second square]\n", + "\n", + "# Result Solution 2\n", + "print\"Solution 2\"\n", + "print\"alpha = \",(alpha),\"rad/s**(2)\"" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Ex 17.15 Page No 755" + ] + }, + { + "cell_type": "code", + "execution_count": 8, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "aG = 2.453 m/s**(2)\n" + ] + } + ], + "source": [ + "# Ex 17.15\n", + "import numpy as np\n", + "\n", + "# Calculation\n", + "# Slipping\n", + "# Using +ΣFx(right) = m(aG)x, +ΣFy(upward) = m(aG)y, +ΣMG(clockwise) = IG*alpha and FA = 0.25*NA\n", + "a = np.array([[1,0,-5,0],[0,1,0,0],[1.25,0,0,2.45],[1,-0.25,0,0]])\n", + "b = np.array([0,5*9.81,35,0])\n", + "x = np.linalg.solve(a, b)\n", + "FA = round(x[0],2) #[Newton]\n", + "NA = round(x[1],2) #[Newton]\n", + "aG = round(x[2],3) #[meters per second square]\n", + "alpha = round(x[3],2) #[radians per second square]\n", + "\n", + "# Result\n", + "print\"aG = \",(aG),\"m/s**(2)\"" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Ex 17.16 Page No 756" + ] + }, + { + "cell_type": "code", + "execution_count": 12, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "alpha = -0.428 rad/s**(2)\n" + ] + } + ], + "source": [ + "# Ex 17.16\n", + "import numpy as np\n", + "\n", + "# Calculation\n", + "# Slipping\n", + "# Using +ΣFx(right) = m(aG)x, +ΣFy(upward) = m(aG)y, +ΣMG(clockwise) = IG*alpha and FA = 0.25*NA\n", + "a = np.array([[1,0,100,0],[0,1,0,0],[1.5,0,0,-75],[1,-0.25,0,0]])\n", + "b = np.array([400,981,400,0])\n", + "x = np.linalg.solve(a, b)\n", + "FA = round(x[0],2) #[Newton]\n", + "NA = round(x[1],2) #[Newton]\n", + "aG = round(x[2],3) #[meters per second square]\n", + "alpha = round(x[3],3) #[radians per second square]\n", + "\n", + "# Result\n", + "print\"alpha = \",(alpha),\"rad/s**(2)\"" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Ex 17.17 Page No 757" + ] + }, + { + "cell_type": "code", + "execution_count": 14, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "alpha = 10.3 rad/s**(2)\n" + ] + } + ], + "source": [ + "# Ex 17.17\n", + "import numpy as np\n", + "\n", + "# Calculation\n", + "# Using +ΣMA(counterclockwise) = Σ(Mk)A, aGx = alpha*0.25 and aGy = alpha*0.1\n", + "a = np.array([[0.675,30*0.25,30*0.1],[0.25,-1,0],[0.1,0,-1]])\n", + "b = np.array([30*9.81*0.1,0,0])\n", + "x = np.linalg.solve(a, b)\n", + "alpha = round(x[0],1) #[radians per second square]\n", + "aGx = round(x[1],2) #[meters per second square]\n", + "aGy = round(x[2],2) #[meters per second square]\n", + "\n", + "# Result\n", + "print\"alpha = \",(alpha),\"rad/s**(2)\"" + ] + }, + { + "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 +} diff --git a/Engineering_Mechanics_Statics_and_Dynamics_by_Hibler_and_Gupta/Chapter_18_Planar_Kinetics_of_a_Rigid_Body_Work_and_Energy.ipynb b/Engineering_Mechanics_Statics_and_Dynamics_by_Hibler_and_Gupta/Chapter_18_Planar_Kinetics_of_a_Rigid_Body_Work_and_Energy.ipynb index 15925661..321b8558 100644 --- a/Engineering_Mechanics_Statics_and_Dynamics_by_Hibler_and_Gupta/Chapter_18_Planar_Kinetics_of_a_Rigid_Body_Work_and_Energy.ipynb +++ b/Engineering_Mechanics_Statics_and_Dynamics_by_Hibler_and_Gupta/Chapter_18_Planar_Kinetics_of_a_Rigid_Body_Work_and_Energy.ipynb @@ -1,747 +1,429 @@ - - - - - - - - - - - - - - - - - - - - - - - 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- - - - - - +{ + "cells": [ + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# Chapter 18 Planar Kinetics of a Rigid Body Work and Energy" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Ex 18.1 Page No 768" + ] + }, + { + "cell_type": "code", + "execution_count": 3, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "T = 4.96 J\n" + ] + } + ], + "source": [ + "# Ex 18.1\n", + "from __future__ import division\n", + "\n", + "# Variable Declaration \n", + "mB = 6 #[kilogram]\n", + "mD = 10 #[kilogram]\n", + "mC = 12 #[kilogram]\n", + "\n", + "# Calculation\n", + "# Block\n", + "TB = (1/2)*mB*0.8**(2) #[Joules]\n", + "# Disk\n", + "TD = (1/2)*(1/2)*mD*0.1**(2)*8**(2) #[Joules]\n", + "# Cylinder\n", + "TC = (1/2)*12*0.4**(2)+(1/2)*(1/2)*mC*0.1**(2)*4**(2) #[Joules]\n", + "# Let T be total kinetic energy of system\n", + "T = TB+TD+TC #[Joules]\n", + "\n", + "# Result\n", + "print\"T = \",(T),\"J\"" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Ex 18.2 Page No 772" + ] + }, + { + "cell_type": "code", + "execution_count": 5, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "U = 527.6 J\n" + ] + } + ], + "source": [ + "# Ex 18.2\n", + "import math\n", + "from __future__ import division\n", + "\n", + "# Variable Declaration\n", + "M = 50 #[Newton meter]\n", + "P = 80 #[Newton]\n", + "\n", + "# Calculation\n", + "# Weight W\n", + "UW = 98.1*1.5 #[Joules]\n", + "# Couple Moment\n", + "UM = M*math.pi/2 #[Joules]\n", + "# Spring Force Fs\n", + "Us = -((1/2)*30*2.25**(2)-(1/2)*30*0.25**(2)) #[Joules]\n", + "# Force P\n", + "UP = P*4.712 #[Joules]\n", + "# let U be total work\n", + "U = round(UW+UM+Us+UP,1) #[Joules]\n", + "\n", + "# Result\n", + "print\"U = \",(U),\"J\"" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "collapsed": true + }, + "source": [ + "## Ex 18.3 Page No 775" + ] + }, + { + "cell_type": "code", + "execution_count": 4, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "theta = 2.73 rev\n" + ] + } + ], + "source": [ + "# Ex 18.3\n", + "from __future__ import division\n", + "import math\n", + "\n", + "# Variable Declaration\n", + "F = 10 #[Newton]\n", + "w = 20 #[radians per second]\n", + "M = 5 #[Newton meter]\n", + "\n", + "# Calculation\n", + "# Kinetic Energy\n", + "T1 = 0 #[Joules]\n", + "T2 = (1/2)*(1/2)*30*(0.2**(2))*(w**(2)) #[Joules]\n", + "# Using principle of Work and Energy\n", + "theta = (T2-T1)/(M+F*0.2) #[radians]\n", + "theta = round((theta*1)/(2*math.pi),2) #[rev]\n", + "\n", + "# Result\n", + "print\"theta = \",(theta),\"rev\"" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Ex 18.4 Page No 776" + ] + }, + { + "cell_type": "code", + "execution_count": 8, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "FdashT = 0.0 kN\n", + "NdashT = 4.24 kN\n" + ] + } + ], + "source": [ + "# Ex 18.4\n", + "import math\n", + "\n", + "# Calculation\n", + "w2 = math.sqrt((700*9.81*0.05359)/63.875) #[radians per second]\n", + "# Using +ΣFn(upward) = m(aG)n\n", + "NT = 700*9.81+700*2.40**(2)*0.4 #[kilo Newton]\n", + "# Using +ΣMO = IO*alpha\n", + "alpha = 0/(700*0.15**(2)+700*0.4**(2)) #[radians per second square]\n", + "# Using +ΣFt(left) = m(aG)t and (aG)t = 0.4*alpha\n", + "FT = 700*0.4*alpha #[kilo Newton]\n", + "# there are two tines to support the load\n", + "FdashT = 0 #[Newton]\n", + "NdashT = NT/2 #[Newton]\n", + "\n", + "# Result\n", + "print\"FdashT = \",(FdashT/1000),\"kN\"\n", + "print\"NdashT = \",round((NdashT/1000),2),\"kN\"" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Ex 18.5 Page No 778" + ] + }, + { + "cell_type": "code", + "execution_count": 9, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "w2 = 1.48 rad/s\n" + ] + } + ], + "source": [ + "# Ex 18.5\n", + "import math\n", + "\n", + "# Variable Declaration\n", + "M = 75 #[Newton meter]\n", + "k = 50 #[Newton per meter]\n", + "W = 20 #[kilogram]\n", + "\n", + "# Calculation\n", + "# Using Principle of work and energy\n", + "w2 = round(math.sqrt((M*0.625-(1/2)*k*1**(2))/10),2) #[radians per second]\n", + "\n", + "# Result\n", + "print\"w2 = \",(w2),\"rad/s\"" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Ex 18.6 Page No 779" + ] + }, + { + "cell_type": "code", + "execution_count": 12, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "w2 = 6.11 rad/s\n" + ] + } + ], + "source": [ + "# Ex 18.6\n", + "import math\n", + "\n", + "# Variable Declaration\n", + "P = 50 #[Newton]\n", + "\n", + "# Calculation\n", + "# Using Principle of work and energy\n", + "w2 = round(math.sqrt((98.1*(0.4-0.4*math.cos(math.pi*45/180))+50*0.8*math.sin(math.pi*45/180))/(1.067)),2) #[radians per second]\n", + "\n", + "# Result\n", + "print\"w2 = \",(w2),\"rad/s\"" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Ex 18.7 Page No 787" + ] + }, + { + "cell_type": "code", + "execution_count": 14, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "w2 = 4.81 rad/s\n" + ] + } + ], + "source": [ + "# Ex 18.7\n", + "import math\n", + "from __future__ import division\n", + "\n", + "# Variable Declaration\n", + "m = 10 #[kilogram]\n", + "k = 800 #[Newton per meter]\n", + "\n", + "# Calculation\n", + "# Potential Energy\n", + "V1 = round(-98.1*(0.2*math.sin(math.pi*30/180))+(1/2)*k*(0.4*math.sin(math.pi*30/180))**(2),2) #[Joules]\n", + "# CG is located at datum\n", + "V2 = 0 #[Joules]\n", + "# Kinetic Energy\n", + "# Since the rod is released from rest position 1\n", + "T1 = 0 #[Joules]\n", + "# Using principle of conservation of energy\n", + "w2 = round(math.sqrt((T1+V1-V2)/0.267),2) #[radians per second]\n", + "\n", + "# Result\n", + "print\"w2 = \",(w2),\"rad/s\"" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Ex 18.8 Page No 788" + ] + }, + { + "cell_type": "code", + "execution_count": 16, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "w2 = 3.9 rad/s\n" + ] + } + ], + "source": [ + "# Ex 18.8\n", + "from __future__ import division\n", + "import math\n", + "\n", + "# Variable Declaration\n", + "k = 30 #[Newton per meter]\n", + "\n", + "# Calculation\n", + "V1 = (1/2)*k*(math.sqrt(0.9**(2)+1.2**(2))-0.3)**(2) #[Joules]\n", + "V2 = (1/2)*k*(1.2-0.3)**(2) #[Joules]\n", + "# The disk is releaseg from rest \n", + "T1 = 0 #[Joules]\n", + "# Using principle of conservation of energy\n", + "w2 = round(math.sqrt((T1+V1-V2)/0.6227),2) #[radians per second]\n", + "\n", + "# Result\n", + "print\"w2 = \",(w2),\"rad/s\"" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Ex 18.9 Page No 789" + ] + }, + { + "cell_type": "code", + "execution_count": 18, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "wR2 = 6.52 rad/s\n" + ] + } + ], + "source": [ + "# Ex 18.9\n", + "import math\n", + "\n", + "# Calculation\n", + "# Potential energy\n", + "V1 = 49.05*0.3*math.sin(math.pi*60/180) #[Joules]\n", + "# At position 2 weight of rod and disk have zero potential energy\n", + "V2 = 0 #[Joules]\n", + "# Kinetic energy\n", + "# Since the entire system is at rest\n", + "T1 = 0 #[Joules]\n", + "# Using conservation of energy\n", + "wR2 = round(math.sqrt((T1+V1-V2)/0.3),2) #[radians per second]\n", + "\n", + "# Result\n", + "print\"wR2 = \",(wR2),\"rad/s\"" + ] + }, + { + "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 +} diff --git a/Engineering_Mechanics_Statics_and_Dynamics_by_Hibler_and_Gupta/Chapter_19_Planar_Kinetics_of_a_Rigid_Body_Impulse_and_Momentum.ipynb b/Engineering_Mechanics_Statics_and_Dynamics_by_Hibler_and_Gupta/Chapter_19_Planar_Kinetics_of_a_Rigid_Body_Impulse_and_Momentum.ipynb index 1d81692d..d7c43858 100644 --- a/Engineering_Mechanics_Statics_and_Dynamics_by_Hibler_and_Gupta/Chapter_19_Planar_Kinetics_of_a_Rigid_Body_Impulse_and_Momentum.ipynb +++ b/Engineering_Mechanics_Statics_and_Dynamics_by_Hibler_and_Gupta/Chapter_19_Planar_Kinetics_of_a_Rigid_Body_Impulse_and_Momentum.ipynb @@ -1,747 +1,349 @@ - - - - - - - - - - - - - - - - - - - - - - - Python-Textbook-Companions/Chapter_19_Planar_Kinetics_of_a_Rigid_Body_Impulse_and_Momentum.ipynb at 1b1bb67e9ea912be5c8591523c8b328766e3680f · FOSSEE/Python-Textbook-Companions - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
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- - - - - - +{ + "cells": [ + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# Chapter 19 Planar Kinetics of a Rigid Body Impulse and Momentum" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Ex 19.1 Page No 802" + ] + }, + { + "cell_type": "code", + "execution_count": 3, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "HG = 2.5 m**(2)/s\n", + "HB = 7.5 m**(2)/s\n", + "HG = 3.85 m**(2)/s\n", + "HIC = 15.4 m**(2)/s\n" + ] + } + ], + "source": [ + "# Ex 19.1\n", + "from __future__ import division \n", + "\n", + "# Variable Declaration\n", + "md = 10 #[kilogram]\n", + "mb = 5 #[kilogram]\n", + "\n", + "# Calculation Disk\n", + "# Using +HG(clockwise) = IG*w\n", + "HG = (1/2)*md*0.25**(2)*8 #[meters square per second]\n", + "# Using +HB(clockwise) = IG*w +m(vG)rG\n", + "HB = HG+md*2*0.25 #[meters square per second]\n", + "\n", + "# Result Disk\n", + "print\"HG = \",(HG),\"m**(2)/s\"\n", + "print\"HB = \",(HB),\"m**(2)/s\"\n", + "\n", + "\n", + "# Calculation Bar\n", + "# Using +HG(clockwise) = IG*w\n", + "HG = round((1/12)*mb*4**(2)*0.5774,2) #[meters square per second]\n", + "HIC = round(HG+2*mb*1.155,2) #[meters square per second]\n", + "\n", + "# Result Bar\n", + "print\"HG = \",(HG),\"m**(2)/s\"\n", + "print\"HIC = \",(HIC),\"m**(2)/s\"\n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Ex 19.2 Page No 806" + ] + }, + { + "cell_type": "code", + "execution_count": 4, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Ax = 0.0 N\n", + "Ay = 140.0 N\n", + "w2 = 69.7 rad/s\n" + ] + } + ], + "source": [ + "# Ex 19.2\n", + "import numpy as np\n", + "from __future__ import division \n", + "\n", + "# Calculation\n", + "IA = round((1/2)*(100/9.81)*0.3**(2),3) #[kilogram meter square]\n", + "# Using principle of impulse and momentum\n", + "a = np.array([[2,0,0],[0,2,0],[0,0,IA]])\n", + "b = np.array([0,100*2+40*2,4*2+40*2*0.3])\n", + "x = np.linalg.solve(a, b)\n", + "Ax = round(x[0],1) #[Newton]\n", + "Ay = round(x[1],1) #[Newton]\n", + "w2 = round(x[2],1) #[radians per second]\n", + "\n", + "# Result\n", + "print\"Ax = \",(Ax),\"N\"\n", + "print\"Ay = \",(Ay),\"N\"\n", + "print\"w2 = \",(w2),\"rad/s\"" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Ex 19.3 Page No 807" + ] + }, + { + "cell_type": "code", + "execution_count": 6, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "w2 = 1.05 rad/s\n" + ] + } + ], + "source": [ + "# Ex 19.3\n", + "import numpy as np\n", + "from __future__ import division \n", + "\n", + "# Calculation\n", + "IG = round(100*0.35**(2),3) #[kilogram meter square]\n", + "# Using principle of impulse and momentum\n", + "a = np.array([[1,100*0.75],[0.75,-12.25]])\n", + "b = np.array([62.5,-25])\n", + "x = np.linalg.solve(a, b)\n", + "w2 = round(x[1],2) #[radians per second]\n", + "\n", + "# Result\n", + "\n", + "print\"w2 = \",(w2),\"rad/s\"" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Ex 19.4 Page No 808" + ] + }, + { + "cell_type": "code", + "execution_count": 13, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Solution 1\n", + "vB2 = 13.0 m/s\n", + "\n", + "Solution 2\n", + "vB2 = 26.0725 m/s\n" + ] + } + ], + "source": [ + "# Ex 19.4\n", + "import numpy as np\n", + "from __future__ import division \n", + "\n", + "# Variable Declaration\n", + "IA = 0.40 #[kilogram meter square]\n", + "\n", + "# Calculation Solution 1\n", + "# Using principle of impulse and momentum\n", + "a = np.array([[3*0.2,-IA/0.2],[3,6]])\n", + "b = np.array([-IA*10,6*2+58.86*3])\n", + "x = np.linalg.solve(a, b)\n", + "T = round(x[0],1) #[Newton]\n", + "vB2 = round(x[1],1) #[meters per second]\n", + "\n", + "# Result Solution 1\n", + "print\"Solution 1\"\n", + "print\"vB2 = \",(vB2),\"m/s\\n\"\n", + "\n", + "# Calculation Solution 2\n", + "# Using principle of angular impulse and momentum\n", + "vB2 = (6*2*0.2+0.4*10+58.86*3*0.2)/(6*0.2+0.4*5*0.2) #[meters per second]\n", + "\n", + "\n", + "# Result Solution 2\n", + "print\"Solution 2\"\n", + "print\"vB2 = \",(vB2),\"m/s\"" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Ex 19.6 Page No 816" + ] + }, + { + "cell_type": "code", + "execution_count": 18, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "vG1 = 0.73 m/s\n" + ] + } + ], + "source": [ + "# Ex 19.5\n", + "from __future__ import division\n", + "import math\n", + "\n", + "# Variable Declaration\n", + "IG = 0.156 #[kilogram meter square]\n", + "\n", + "# Calculation\n", + "# Using principle of conservation of energy\n", + "vG2 = math.sqrt((98.1*0.03)/((1/2)*10+(1/2)*IG*25)) #[meters per second]\n", + "# vG2 = 0.892*vG1\n", + "vG1 = round(vG2/0.892,3) #[meters per second]\n", + "\n", + "# Result\n", + "print\"vG1 = \",(vG1),\"m/s\"\n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Ex 19.7 Page No 817" + ] + }, + { + "cell_type": "code", + "execution_count": 21, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "w2 = 0.622 rad/s\n" + ] + } + ], + "source": [ + "# Ex 19.7\n", + "from __future__ import division\n", + "\n", + "# Calculation\n", + "# Σ(HO)1 = Σ(HO)2, vG2 = 0.5*w2 and vB2 = 0.75*w2\n", + "w2 = round((1.039)/(0.003*0.75+2.5*0.5+0.417),3) #[radians per second]\n", + "\n", + "# Result\n", + "print\"w2 = \",(w2),\"rad/s\"" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Ex 19.8 Page No 821" + ] + }, + { + "cell_type": "code", + "execution_count": 24, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "w2 = 3.65 rad/s\n" + ] + } + ], + "source": [ + "# Ex 19.8\n", + "import numpy as np\n", + "\n", + "# Calculation\n", + "# Using principle of conservation of angular momentum and coefficient of restitution\n", + "a = np.array([[1.67,0.5],[0.5,-1]])\n", + "b = np.array([5,4])\n", + "x = np.linalg.solve(a, b)\n", + "w2 = round(x[0],2) #[radians per second]\n", + "vB2 = round(x[1],2) #[meters per second]\n", + "\n", + "# Result\n", + "print\"w2 = \",(w2),\"rad/s\"" + ] + }, + { + "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 +} diff --git a/Engineering_Mechanics_Statics_and_Dynamics_by_Hibler_and_Gupta/Chapter_1_General_Principles.ipynb b/Engineering_Mechanics_Statics_and_Dynamics_by_Hibler_and_Gupta/Chapter_1_General_Principles.ipynb index bae1b047..62d27f1f 100644 --- a/Engineering_Mechanics_Statics_and_Dynamics_by_Hibler_and_Gupta/Chapter_1_General_Principles.ipynb +++ b/Engineering_Mechanics_Statics_and_Dynamics_by_Hibler_and_Gupta/Chapter_1_General_Principles.ipynb @@ -1,747 +1,117 @@ - - - - - - - - - - - - - - - - - - - - - - - Python-Textbook-Companions/Chapter_1_General_Principles.ipynb at 1b1bb67e9ea912be5c8591523c8b328766e3680f · FOSSEE/Python-Textbook-Companions - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
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- - - - - - +{ + "cells": [ + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# Chapter 1 General Principles" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Ex 1.1 Page No 10 " + ] + }, + { + "cell_type": "code", + "execution_count": 27, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Part(a)\n", + "(10 mN)(5 GN) = 50 kilo Newton square\n", + "\n", + "Part(b)\n", + "(100 mm)(0.5 MN square) = 25 Gigameter Newton square\n", + "\n", + "Part(c)\n", + "(50 MN cube)(500 Gg) = 100 Kilo Newton cube per kg\n" + ] + } + ], + "source": [ + "# Example Number 1.1\n", + "\n", + "# Part(a)\n", + "# Variable Declaration\n", + "a = 10 # [micro Newton(mN)]\n", + "b = 5 # [Giga Newton(GN)]\n", + "\n", + "# Calculation\n", + "# We have to find c = a * b\n", + "c = 10*5 # [micro Newton(mN)*Giga Newton(GN)]\n", + "c = (10*10**(-3))*(5*10**(9)) # [N**(2)]\n", + "c = (10*10**(-3))*(5*10**(9))*10**(-6) #[kN**(2)]\n", + "\n", + "#Result\n", + "print\"Part(a)\"\n", + "print \"(10 mN)(5 GN) = \",int(c),\"kilo Newton square\\n\"\n", + "\n", + "# Part(b)\n", + "# Variable Declaration\n", + "a = 100 #[millimeter(mm)]\n", + "b = 0.5**(2) #[mega Newton square(MN**(2))]\n", + "\n", + "# Calculation\n", + "# We have to find c = a * b\n", + "c = (100*10**(-3))*(0.25*10**(12)) #[m.N**(2)]\n", + "c = (100*10**(-3))*(0.25*10**(12))*10**(-9) #[Gm.N**(2)]\n", + "\n", + "#Result\n", + "print\"Part(b)\"\n", + "print \"(100 mm)(0.5 MN square) = \",int(c),\"Gigameter Newton square\\n\"\n", + "\n", + "# Part(c) (Correction in the question (50 MN cube)(500 Gg))\n", + "# Variable Declaration\n", + "a = 50 #[mega newton cube((MN)**(3))]\n", + "b = 500 #[gigagram(Gg)]\n", + "\n", + "# Calculation\n", + "# We have to find c = a / b\n", + "c = 50*(10**(6))**3 / 500*10**(6) #[N**(3)/kg]\n", + "c = (50*((10**(6))**3) / (500*10**(6)))*10**(-9) #[kN**(3)/kg]\n", + "\n", + "#Result\n", + "print\"Part(c)\"\n", + "print \"(50 MN cube)(500 Gg) = \",int(c),\"Kilo Newton cube per kg\"\n" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], + "source": [] + } + ], + "metadata": { + "kernelspec": { + "display_name": "Python 2", + "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": 2 +} diff --git a/Engineering_Mechanics_Statics_and_Dynamics_by_Hibler_and_Gupta/Chapter_2_Force_Vectors.ipynb b/Engineering_Mechanics_Statics_and_Dynamics_by_Hibler_and_Gupta/Chapter_2_Force_Vectors.ipynb index f2246eb8..8b8efd6a 100644 --- a/Engineering_Mechanics_Statics_and_Dynamics_by_Hibler_and_Gupta/Chapter_2_Force_Vectors.ipynb +++ b/Engineering_Mechanics_Statics_and_Dynamics_by_Hibler_and_Gupta/Chapter_2_Force_Vectors.ipynb @@ -1,747 +1,1058 @@ - - - - - - - - - - - - - - - - - - - - - - - Python-Textbook-Companions/Chapter_2_Force_Vectors.ipynb at 1b1bb67e9ea912be5c8591523c8b328766e3680f · FOSSEE/Python-Textbook-Companions - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
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- - - - - - +{ + "cells": [ + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# Chapter 2 : Force Vectors" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Ex 2.1 Page No. 20" + ] + }, + { + "cell_type": "code", + "execution_count": 8, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Resultant Force F_R = 213 N\n", + "theta = 39.8 degrees\n", + "phi = 54.8 degrees\n" + ] + } + ], + "source": [ + "#Example 2.1\n", + "import math\n", + "\n", + "# The parallelogram law of addition is shown in Fig.2-10b\n", + "\n", + "# F_R is determined using law of cosines\n", + "\n", + "#Calculation\n", + "F_R = math.sqrt((100**(2))+(150**(2))-2*100*150*math.cos(115*math.pi/180)) #[Newton]\n", + "\n", + "#Result\n", + "print\"Resultant Force F_R = \",int(round(F_R)),\"N\"\n", + "\n", + "# Angle theta is determined by law of sines\n", + "\n", + "#Calculation\n", + "theta = math.asin(150*0.9063/212.6) #[Radians]\n", + "\n", + "#Result\n", + "print \"theta = \",(round(math.degrees(theta),1)),\"degrees\"\n", + "\n", + "#The direction of phi as masured from horizontal is given by\n", + "phi = 39.8 + 15.0 #[Degrees]\n", + "print\"phi = \",phi,\"degrees\"" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Ex 2.2 Page No. 21" + ] + }, + { + "cell_type": "code", + "execution_count": 1, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "F_x = 1532 N\n", + "F_y = 1285 N\n", + "F_x_dash = 1769 N\n", + "F_y = 2170 N\n" + ] + } + ], + "source": [ + "# Example 2.2\n", + "import math\n", + "\n", + "# Variable Declaration\n", + "F = 2000 #[newton]\n", + "# In each case parallelogram law is used to resolve F into its two components\n", + "\n", + "# Part(a)\n", + "# The vector addition F = F_x + F_y is shown in fig2-11b\n", + "# Calculation\n", + "F_x = F*math.cos(40*math.pi/180) #[Newton]\n", + "F_y = F*math.sin(40*math.pi/180) #[Newton]\n", + "\n", + "# Result\n", + "print\"F_x = \",int((F_x)),\"N\"\n", + "print\"F_y = \",int((F_y)),\"N\"\n", + "\n", + "# Part(b)\n", + "# The vector addition F = F_x_dash + F_y is shown in fig2-11b\n", + "# Calculation\n", + "F_x_dash = F*math.sin(50*math.pi/180)/math.sin(60*math.pi/180) #[Newton]\n", + "F_y = F*math.sin(70*math.pi/180)/math.sin(60*math.pi/180) #[Newton]\n", + "\n", + "# Result\n", + "print\"F_x_dash = \",int((F_x_dash)),\"N\"\n", + "print\"F_y = \",int((F_y)),\"N\"" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Ex 2.3 Page No. 22" + ] + }, + { + "cell_type": "code", + "execution_count": 4, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "theta = 76.1 degrees\n" + ] + } + ], + "source": [ + "# Example 2.3\n", + "import math\n", + "from __future__ import division\n", + "\n", + "# The angle phi can be determined using law of cosines\n", + "\n", + "# Calculation\n", + "phi = math.asin((400/500)*math.sin(60*math.pi/180)) #[Radians]\n", + "phi = math.degrees(phi) #[Degrees]\n", + "theta = 180-60-phi #[Degrees]\n", + "\n", + "# Result\n", + "print\"theta = \",round(theta,1),\"degrees\"" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Ex 2.4 Page No. 23" + ] + }, + { + "cell_type": "code", + "execution_count": 95, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Part(a)\n", + "F1 = 653 N\n", + "F2 = 446 N\n", + "\n", + "Part(b)\n", + "F1 = 940 N\n", + "F2 = 342 N\n" + ] + } + ], + "source": [ + "# Example 2.4\n", + "import math\n", + "\n", + "# Part(a) Refer fig 2-13b\n", + "# Using parallelogram law\n", + "\n", + "# Calculation\n", + "F1 = 1000*math.sin(30*math.pi/180)/math.sin(130*math.pi/180) #[Newton]\n", + "F2 = 1000*math.sin(20*math.pi/180)/math.sin(130*math.pi/180) #[Newton]\n", + "\n", + "# Result\n", + "print\"Part(a)\"\n", + "print\"F1 = \",int(round(F1,0)),\"N\"\n", + "print\"F2 = \",int(round(F2,0)),\"N\\n\"\n", + "\n", + "# Part(b) Refer fig 2-13d\n", + "\n", + "# Calculation\n", + "F1 = 1000*math.sin(70*math.pi/180) #[Newton]\n", + "F2 = 1000*math.cos(70*math.pi/180) #[Newton]\n", + "\n", + "# Result\n", + "print\"Part(b)\"\n", + "print\"F1 = \",int(round(F1,0)),\"N\"\n", + "print\"F2 = \",int(round(F2,0)),\"N\"" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Ex 2.5 Page No. 31" + ] + }, + { + "cell_type": "code", + "execution_count": 98, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "F1_x = -100 N\n", + "F1_y = 173 N\n", + "F2_x = 240 N\n", + "F2_y = 100 N\n" + ] + } + ], + "source": [ + "# Example 2.5\n", + "import math\n", + "# F1_x acts in -x direction and F1_y acts in +y direction Refer fig 2-17b\n", + "\n", + "# Calculation\n", + "F1_x = -200*math.sin(30*math.pi/180) #[Newton]\n", + "F1_y = 200*math.cos(30*math.pi/180) #[Newton]\n", + "\n", + "# Result\n", + "print\"F1_x = \",int(round(F1_x,0)),\"N\"\n", + "print\"F1_y = \",int(round(F1_y,0)),\"N\"\n", + "\n", + "# F2 is resolved into its x and y components Refer fig 2-17c\n", + "\n", + "# Calculation\n", + "F2_x = 260*(12/13) #[Newton]\n", + "F2_y = 260*(5/13) #[Newton]\n", + "\n", + "# Result\n", + "print\"F2_x = \",int(round(F2_x,0)),\"N\"\n", + "print\"F2_y = \",int(round(F2_y,0)),\"N\"" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Ex 2.6 Page No. 32" + ] + }, + { + "cell_type": "code", + "execution_count": 5, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "FR_x = 236.8 N\n", + "FR_y = 582.8 N\n", + "FR = 629 N\n", + "Theta = 67.9 degrees\n" + ] + } + ], + "source": [ + "# Example 2.6\n", + "import math\n", + "\n", + "# Variable Declaration\n", + "F1 = 600 #[Newton]\n", + "F2 = 400 #[Newton]\n", + "\n", + "# We resolve each force into x and y components Refer fig 2-18b\n", + "# Let FR be resultant force\n", + "# Let FR_x be resultant force along x direction\n", + "# Let FR_y be resultant force along y direction\n", + "\n", + "# Calculation\n", + "FR_x = F1*math.cos(30*math.pi/180) - F2*math.sin(45*math.pi/180) #[Newton]\n", + "FR_y = F1*math.sin(30*math.pi/180) + F2*math.cos(45*math.pi/180) #[Newton]\n", + "FR = math.sqrt(round(FR_x,1)**(2)+round(FR_y,1)**(2)) #[Newton]\n", + "theta = math.atan(round(FR_y,1)/round(FR_x,1)) #[Radians]\n", + "theta = math.degrees(theta) #[Degrees]\n", + "\n", + "# Result\n", + "print\"FR_x = \",round(FR_x,1),\"N\"\n", + "print\"FR_y = \",round(FR_y,1),\"N\"\n", + "print\"FR = \",int(round(FR,0)),\"N\"\n", + "print\"Theta = \",round(theta,1),\"degrees\"" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "collapsed": true + }, + "source": [ + "## Ex 2.7 Page No. 33" + ] + }, + { + "cell_type": "code", + "execution_count": 6, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "F_R_x = -383.2 N\n", + "F_R_y = 296.8 N\n", + "F_R = 485 N\n", + "Theta = 37.8 degrees\n" + ] + } + ], + "source": [ + "# Example 2.7\n", + "import math\n", + "from __future__ import division\n", + "\n", + "# Variable Declaration\n", + "F1 = 400 #[Newton]\n", + "F2 = 250 #[Newton]\n", + "F3 = 200 #[Newton]\n", + "\n", + "# We resolve each force into x and y components Refer fig 2-18b\n", + "# Let F_R be resultant force\n", + "# Let F_R_x be resultant force along x direction\n", + "# Let F_R_y be resultant force along y direction\n", + "\n", + "# Calculation\n", + "F_R_x = -F1 + F2*math.sin(45*math.pi/180) - F3*(4/5) #[Newton]\n", + "F_R_y = F2*math.cos(45*math.pi/180) + F3*(3/5) #[Newton]\n", + "F_R = math.sqrt(round(F_R_x,1)**(2)+round(F_R_y,1)**(2)) #[Newton]\n", + "theta = math.atan(abs(round(F_R_y,1)/round(F_R_x,1))) #[Radians]\n", + "theta = math.degrees(theta) #[Degrees]\n", + "\n", + "# Result\n", + "print\"F_R_x = \",round(F_R_x,1),\"N\"\n", + "print\"F_R_y = \",round(F_R_y,1),\"N\"\n", + "print\"F_R = \",int(round(F_R,0)),\"N\"\n", + "print\"Theta = \",round(theta,1),\"degrees\"" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Ex 2.8 Page No. 41" + ] + }, + { + "cell_type": "code", + "execution_count": 3, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "cos_alpha = +/- 0.5\n", + "F = 100 N\n" + ] + } + ], + "source": [ + "# Example 2.8\n", + "import math\n", + "\n", + "# Variable declaration\n", + "beta = 60 #[Degrees]\n", + "gamma = 45 #[Degrees]\n", + "f = 100 #[Newton]\n", + "\n", + "# Calculation\n", + "cos_alpha = math.sqrt(1-(math.cos(beta*math.pi/180)**(2))-(math.cos(gamma*math.pi/180)**(2))) #[Radians]\n", + "alpha1 = math.degrees(math.acos(+cos_alpha)) #[Degrees]\n", + "alpha2 = math.degrees(math.acos(-cos_alpha)) #[Degrees]\n", + "Fx = f*math.cos(alpha1*math.pi/180) #[Newton]\n", + "Fy = f*math.cos(beta*math.pi/180) #[Newton]\n", + "Fz = f*math.cos(gamma*math.pi/180) #[Newton]\n", + "F = math.sqrt(round(Fx**(2),1)+round(Fy**(2),1)+round(Fz**(2),1)) #[Newton]\n", + "\n", + "# Result\n", + "print\"cos_alpha = +/-\",(cos_alpha)\n", + "print\"F = \",int(F),\"N\"" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "collapsed": true + }, + "source": [ + "## Ex 2.9 Page No. 42" + ] + }, + { + "cell_type": "code", + "execution_count": 13, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Resultant Force FR = 191.0 N\n", + "alpha = 74.8 degrees\n", + "beta = 102.1 degrees\n", + "gamma = 19.5 degrees\n" + ] + } + ], + "source": [ + "# Example 2.9\n", + "import math\n", + "from __future__ import division\n", + "\n", + "# Variable declaration\n", + "\n", + "F1_x = 0 #[Newton]\n", + "F1_y = 60 #[Newton]\n", + "F1_z = 80 #[Newton]\n", + "F2_x = 50 #[Newton]\n", + "F2_y = -100 #[Newton]\n", + "F2_z = 100 #[Newton]\n", + "\n", + "# Calculation\n", + "FR_x = F1_x + F2_x #[Newton]\n", + "FR_y = F1_y + F2_y #[Newton]\n", + "FR_z = F1_z + F2_z #[Newton]\n", + "\n", + "# Let F_R be resultant force\n", + "FR = round(math.sqrt(FR_x**(2)+FR_y**(2)+FR_z**(2)),1)\n", + "\n", + "# The coordinate direction angles alpha,beta and gamma are determined from components of unit vector along direction of F_R\n", + "cos_alpha = FR_x/FR\n", + "cos_beta = FR_y/FR\n", + "cos_gamma = FR_z/FR\n", + "alpha = round(math.degrees(math.acos(cos_alpha)),1) #[Degrees]\n", + "beta = round(math.degrees(math.acos(cos_beta)),1) #[Degrees]\n", + "gamma = round(math.degrees(math.acos(cos_gamma)),1) #[Degrees]\n", + "\n", + "# Result\n", + "print\"Resultant Force FR = \",(FR),\"N\"\n", + "print\"alpha = \",(alpha),\"degrees\"\n", + "print\"beta = \",(beta),\"degrees\"\n", + "print\"gamma = \",(gamma),\"degrees\"\n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Ex 2.10 Page No. 43" + ] + }, + { + "cell_type": "code", + "execution_count": 25, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "F1_x = 354 N\n", + "F1_y = 354 N\n", + "F1_z = 866 N\n", + "F1 = 1000 N\n", + "\n", + "F2_x = 1.06 kN\n", + "F2_y = 1.837 kN\n", + "F2_z = 2.121 kN\n", + "F2 = 3000 N\n" + ] + } + ], + "source": [ + "# Example 2.10\n", + "import math\n", + "\n", + "# For F1\n", + "\n", + "# Calculation\n", + "F1_z = int(round(1000*math.sin(60*math.pi/180),0)) #[Newton]\n", + "F1_dash = int(round(1000*math.cos(60*math.pi/180),0)) #[Newton]\n", + "F1_x = int(round(F1_dash*math.cos(45*math.pi/180),0)) #[Newton]\n", + "F1_y = int(round(F1_dash*math.sin(45*math.pi/180),0)) #[Newton]\n", + "\n", + "# F1_y has direction defined by -j\n", + "F1 = int(round(math.sqrt(F1_x**(2)+(-F1_y)**(2)+F1_z**(2)),0)) #[Newton]\n", + "\n", + "# u1 is unit vector along F1\n", + "u1_x = round(F1_x/F1,3)\n", + "u1_y = round(F1_y/F1,3)\n", + "u1_z = round(F1_z/F1,3)\n", + "alpha1 = round(math.degrees(math.acos(u1_x)),1) #[Degrees]\n", + "betaa1 = round(math.degrees(math.acos(u1_y)),1) #[Degrees]\n", + "gamma1 = round(math.degrees(math.acos(u1_z)),1) #[Degrees]\n", + "\n", + "# Result\n", + "print\"F1_x = \",F1_x,\"N\"\n", + "print\"F1_y = \",F1_y,\"N\"\n", + "print\"F1_z = \",F1_z,\"N\"\n", + "print\"F1 = \",F1,\"N\\n\"\n", + "\n", + "# For F2\n", + "\n", + "# Calculation\n", + "F2_z = int(round(3000*math.sin(45*math.pi/180),0)) #[Newton]\n", + "F2_dash = int(round(3000*math.cos(45*math.pi/180),0)) #[Newton]\n", + "F2_x = int(round(F2_dash*math.sin(30*math.pi/180),0)) #[Newton]\n", + "F2_y = int(round(F2_dash*math.cos(30*math.pi/180),0)) #[Newton]\n", + "\n", + "# F2_z has direction defined by -k\n", + "F2 = int(round(math.sqrt(F2_x**(2)+F2_y**(2)+(-F2_z)**(2)),-1)) #[Newton]\n", + "\n", + "# u1 is unit vector along F1\n", + "\n", + "u2_x = round(F2_x/F2,3)\n", + "u2_y = round(F2_y/F2,3)\n", + "u2_z = round(F2_z/F2,3)\n", + "alpha2 = round(math.degrees(math.acos(u2_x)),1) #[Degrees]\n", + "betaa2 = round(math.degrees(math.acos(u2_y)),1) #[Degrees]\n", + "gamma2 = round(math.degrees(math.acos(u2_z)),1) #[Degrees]\n", + "\n", + "# Result\n", + "print\"F2_x = \",F2_x/1000,\"kN\"\n", + "print\"F2_y = \",F2_y/1000,\"kN\"\n", + "print\"F2_z = \",F2_z/1000,\"kN\"\n", + "print\"F2 = \",F2,\"N\"" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Ex 2.11 Page No. 44" + ] + }, + { + "cell_type": "code", + "execution_count": 35, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "alpha2 = 107.6 degrees\n", + "beta2 = 21.8 degrees\n", + "gamma2 = 77.6 degrees\n" + ] + } + ], + "source": [ + "# Example 2.11\n", + "import math\n", + "\n", + "# Variable declaration\n", + "\n", + "F1 = 300 #[Newton]\n", + "F2 = 700 #[Newton]\n", + "FR = 800 #[Newton]\n", + "alpha1 = 45 #[Degrees]\n", + "beta1 = 60 #[Degrees]\n", + "gamma1 = 120 #[Degrees]\n", + "\n", + "# Calculation\n", + "F1_x = round(F1*math.cos(alpha1*math.pi/180),1) #[Newton]\n", + "F1_y = round(F1*math.cos(beta1*math.pi/180),1) #[Newton]\n", + "F1_z = round(F1*math.cos(gamma1*math.pi/180),1) #[Newton]\n", + "\n", + "# FR acts along +y axis\n", + "FR_x = 0 #[Newton]\n", + "FR_y = 800 #[Newton]\n", + "FR_z = 0 #[Newton]\n", + "\n", + "# FR = F1 + F2\n", + "# F2 = FR - F1\n", + "F2_x = FR_x - F1_x #[Newton]\n", + "F2_y = FR_y - F1_y #[Newton]\n", + "F2_z = FR_z - F1_z #[Newton]\n", + "alpha2 = round(math.degrees(math.acos(F2_x/F2)),1) #[Degrees]\n", + "beta2 = round(math.degrees(math.acos(F2_y/F2)),1) #[Degrees]\n", + "gamma2 = round(math.degrees(math.acos(F2_z/F2)),1) #[Degrees]\n", + "\n", + "# Result\n", + "print\"alpha2 = \",(alpha2),\"degrees\"\n", + "print\"beta2 = \",(beta2),\"degrees\"\n", + "print\"gamma2 = \",(gamma2),\"degrees\"" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Ex 2.12 Page No. 49" + ] + }, + { + "cell_type": "code", + "execution_count": 40, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "alpha = 115.4 degrees\n", + "beta = 73.4 degrees\n", + "gamma = 31.0 degrees\n" + ] + } + ], + "source": [ + "# Example 2.12\n", + "import math\n", + "from __future__ import division\n", + "\n", + "# Variable Declaration\n", + "A_x = 1 #[meters]\n", + "A_y = 0 #[meters]\n", + "A_z = -3 #[meters]\n", + "B_x = -2 #[meters]\n", + "B_y = 2 #[meters]\n", + "B_z = 3 #[meters]\n", + "\n", + "# Calculation\n", + "# r = B - A\n", + "r_x = B_x - A_x #[meters]\n", + "r_y = B_y - A_y #[meters]\n", + "r_z = B_z - A_z #[meters]\n", + "r = math.sqrt(r_x**(2)+r_y**(2)+r_z**(2))\n", + "\n", + "# Assume u to be a unit vector along r\n", + "u_x = r_x/r\n", + "u_y = r_y/r\n", + "u_z = r_z/r\n", + "alpha = round(math.degrees(math.acos(u_x)),1) #[Degrees]\n", + "beta = round(math.degrees(math.acos(u_y)),1) #[Degrees]\n", + "gamma = round(math.degrees(math.acos(u_z)),1) #[Degrees]\n", + "\n", + "# Result\n", + "print\"alpha = \",(alpha),\"degrees\"\n", + "print\"beta = \",(beta),\"degrees\"\n", + "print\"gamma = \",(gamma),\"degrees\"" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "collapsed": true + }, + "source": [ + "## Ex 2.13 Page No. 51" + ] + }, + { + "cell_type": "code", + "execution_count": 8, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "F_x = 30.0 N\n", + "F_y = -20.0 N\n", + "F_z = -60.0 N\n", + "alpha = 64.6 degrees\n", + "beta = 106.6 degrees\n", + "gamma = 149.0 degrees\n" + ] + } + ], + "source": [ + "# Example 2.13\n", + "import math\n", + "from __future__ import division\n", + "\n", + "# Variable Declaration\n", + "A_x = 0 #[meters]\n", + "A_y = 0 #[meters]\n", + "A_z = 8 #[meters]\n", + "B_x = 3 #[meters]\n", + "B_y = -2 #[meters]\n", + "B_z = 2 #[meters]\n", + "\n", + "# Calculation\n", + "# r = B - A\n", + "r_x = B_x - A_x #[meters]\n", + "r_y = B_y - A_y #[meters]\n", + "r_z = B_z - A_z #[meters]\n", + "r = math.sqrt(r_x**(2)+r_y**(2)+r_z**(2))\n", + "\n", + "# Assume u to be a unit vector along r\n", + "u_x = r_x/r\n", + "u_y = r_y/r\n", + "u_z = r_z/r\n", + "\n", + "# Since F = 70 N and direction is specified by u\n", + "F_x = 70 * u_x #[Newton]\n", + "F_y = 70 * u_y #[Newton]\n", + "F_z = 70 * u_z #[Newton]\n", + "alpha = round(math.degrees(math.acos(u_x)),1) #[Degrees]\n", + "beta = round(math.degrees(math.acos(u_y)),1) #[Degrees]\n", + "gamma = round(math.degrees(math.acos(u_z)),1) #[Degrees]\n", + "\n", + "# Result\n", + "print\"F_x = \",(F_x),\"N\"\n", + "print\"F_y = \",(F_y),\"N\"\n", + "print\"F_z = \",(F_z),\"N\"\n", + "print\"alpha = \",(alpha),\"degrees\"\n", + "print\"beta = \",(beta),\"degrees\"\n", + "print\"gamma = \",(gamma),\"degrees\"" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Ex 2.14 Page No. 52" + ] + }, + { + "cell_type": "code", + "execution_count": 8, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "F_x = 313.5 N\n", + "F_y = 129.8 N\n", + "F_z = -367.3 N\n", + "F = 500.0 N\n" + ] + } + ], + "source": [ + "# Example 2.14\n", + "import math\n", + "from __future__ import division\n", + "\n", + "# Variable Declaration\n", + "A_x = 0 #[meters]\n", + "A_y = 0 #[meters]\n", + "A_z = 2 #[meters]\n", + "B_x = 1.707 #[meters]\n", + "B_y = 0.707 #[meters]\n", + "B_z = 0 #[meters]\n", + "\n", + "# Calculation\n", + "# r = B - A\n", + "r_x = B_x - A_x #[meters]\n", + "r_y = B_y - A_y #[meters]\n", + "r_z = B_z - A_z #[meters]\n", + "r = math.sqrt(r_x**(2)+r_y**(2)+r_z**(2))\n", + "\n", + "# Assume u to be a unit vector along r\n", + "u_x = r_x/r\n", + "u_y = r_y/r\n", + "u_z = r_z/r\n", + "\n", + "# Since F = 500 N and direction is specified by u\n", + "F_x = round(500 * u_x,1) #[Newton]\n", + "F_y = round(500 * u_y,1) #[Newton]\n", + "F_z = round(500 * u_z,1) #[Newton]\n", + "F = round(math.sqrt(F_x**(2)+F_y**(2)+F_z**(2)),1) #[Newton]\n", + "\n", + "# Result\n", + "print\"F_x = \",(F_x),\"N\"\n", + "print\"F_y = \",(F_y),\"N\"\n", + "print\"F_z = \",(F_z),\"N\"\n", + "print\"F = \",(F),\"N\"\n" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "collapsed": true + }, + "source": [ + "## Ex 2.15 Page No. 53" + ] + }, + { + "cell_type": "code", + "execution_count": 27, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "FR = 217.0 N\n" + ] + } + ], + "source": [ + "# Example 2.15\n", + "import math\n", + "from __future__ import division\n", + "\n", + "# Variable Declaration\n", + "FAB = 100 #[Newton]\n", + "FAC = 120 #[Newton]\n", + "A_x = 0 #[meters]\n", + "A_y = 0 #[meters]\n", + "A_z = 4 #[meters]\n", + "B_x = 4 #[meters]\n", + "B_y = 0 #[meters]\n", + "B_z = 0 #[meters]\n", + "C_x = 4 #[meters]\n", + "C_y = 2 #[meters]\n", + "C_z = 0 #[meters]\n", + "\n", + "# Calculation(FAB)\n", + "rAB_x = B_x - A_x #[meters]\n", + "rAB_y = B_y - A_y #[meters]\n", + "rAB_z = B_z - A_z #[meters]\n", + "rAB = round(math.sqrt(rAB_x**(2)+rAB_y**(2)+rAB_z**(2)),2)\n", + "FAB_x = round(FAB*(rAB_x/rAB),1) #[Newton]\n", + "FAB_y = round(FAB*(rAB_y/rAB),1) #[Newton]\n", + "FAB_z = round(FAB*(rAB_z/rAB),1) #[Newton]\n", + "\n", + "# Calculation(FAC)\n", + "rAC_x = C_x - A_x #[meters]\n", + "rAC_y = C_y - A_y #[meters]\n", + "rAC_z = C_z - A_z #[meters]\n", + "rAC = round(math.sqrt(rAC_x**(2)+rAC_y**(2)+rAC_z**(2)),2)\n", + "FAC_x = round(FAC*(rAC_x/rAC),1) #[Newton]\n", + "FAC_y = round(FAC*(rAC_y/rAC),1) #[Newton]\n", + "FAC_z = round(FAC*(rAC_z/rAC),1) #[Newton]\n", + "\n", + "# FR = FAB + FAC\n", + "FR_x = FAB_x + FAC_x #[Newton]\n", + "FR_y = FAB_y + FAC_y #[Newton]\n", + "FR_z = FAB_z + FAC_z #[Newton]\n", + "FR = round(math.sqrt(FR_x**(2)+FR_y**(2)+FR_z**(2)),0)\n", + "print\"FR = \",(FR),\"N\"" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Ex 2.16 Page No. 61" + ] + }, + { + "cell_type": "code", + "execution_count": 31, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "FAB = 257.1 N\n", + "FAB_x = 73.5 N\n", + "FAB_y = 220.4 N\n", + "FAB_z = 110.2 N\n", + "Fp = 155.0 N\n" + ] + } + ], + "source": [ + "# Example 2.16\n", + "import math\n", + "\n", + "# Variable Declaration\n", + "rB_x = 2 #[meters]\n", + "rB_y = 6 #[meters]\n", + "rB_z = 3 #[meters]\n", + "F_x = 0 #[Newton]\n", + "F_y = 300 #[Newton]\n", + "F_z = 0 #[Newton]\n", + "\n", + "# Calculation\n", + "F = math.sqrt(F_x**(2)+F_y**(2)+F_z**(2)) #[Newton]\n", + "# Let uB be unit vector defining direction of AB\n", + "rB = math.sqrt(rB_x**(2)+rB_y**(2)+rB_z**(2)) #[meters]\n", + "uB_x = rB_x/rB\n", + "uB_y = rB_y/rB\n", + "uB_z = rB_z/rB\n", + "\n", + "# The magnitude of component of F along AB is equal to dot product of F and unit vector uB \n", + "FAB = round(F_x*uB_x + F_y*uB_y + F_z*uB_z,1) #[Newton]\n", + "\n", + "# Expressing FAB in Cartesian form\n", + "FAB_x = round(FAB*uB_x,1) #[Newton]\n", + "FAB_y = round(FAB*uB_y,1) #[Newton]\n", + "FAB_z = round(FAB*uB_z,1) #[Newton]\n", + "FAB = round(math.sqrt(FAB_x**(2)+FAB_y**(2)+FAB_z**(2)),1) #[Newton]\n", + "\n", + "# Let Fp be perpendicular component\n", + "Fp_x = F_x - FAB_x #[Newton]\n", + "Fp_y = F_y - FAB_y #[Newton]\n", + "Fp_z = F_z - FAB_z #[Newton]\n", + "Fp = round(math.sqrt(F**(2)-FAB**(2)),0) #[Newton]\n", + "\n", + "# Result\n", + "print\"FAB = \",(FAB),\"N\"\n", + "print\"FAB_x = \",(FAB_x),\"N\"\n", + "print\"FAB_y = \",(FAB_y),\"N\"\n", + "print\"FAB_z = \",(FAB_z),\"N\"\n", + "print\"Fp = \",(Fp),\"N\"" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Ex 2.17 Page No. 62" + ] + }, + { + "cell_type": "code", + "execution_count": 7, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "theta = 42.4 degrees\n", + "FBA = 59.1 N\n", + "Fp = 53.9 N\n" + ] + } + ], + "source": [ + "# Example 2.17\n", + "import math\n", + "from __future__ import division\n", + "\n", + "# Variable Declaration\n", + "F = 80 #[Newton]\n", + "A_x = 0\n", + "A_y = 1\n", + "A_z = 0\n", + "B_x = 2\n", + "B_y = 3\n", + "B_z = -1\n", + "C_x = 2\n", + "C_y = 0\n", + "C_z = 0\n", + "\n", + "# Calculation\n", + "rBA_x = A_x - B_x \n", + "rBA_y = A_y - B_y\n", + "rBA_z = A_z - B_z\n", + "rBC_x = C_x - B_x \n", + "rBC_y = C_y - B_y\n", + "rBC_z = C_z - B_z\n", + "rBA = round(math.sqrt(rBA_x**(2)+rBA_y**(2)+rBA_z**(2)),2)\n", + "rBC = round(math.sqrt(rBC_x**(2)+rBC_y**(2)+rBC_z**(2)),2)\n", + "theta = round(math.degrees(math.acos((rBA_x*rBC_x+rBA_y*rBC_y+rBA_z*rBC_z)/(rBA*rBC))),1)\n", + "\n", + "# let uBA be unit vector along BA\n", + "uBA_x = rBA_x/rBA\n", + "uBA_y = rBA_y/rBA\n", + "uBA_z = rBA_z/rBA\n", + "F_x = round(F*(rBC_x/rBC),2) #[Newton]\n", + "F_y = round(F*(rBC_y/rBC),2) #[Newton]\n", + "F_z = round(F*(rBC_z/rBC),2) #[Newton]\n", + "\n", + "# FBA = F.uBA\n", + "FBA = round(F_x*uBA_x + F_y*uBA_y + F_z*uBA_z,1) #[Newton]\n", + "\n", + "# Since theta was calculated FBA can be calculated by FBA = F*cos(theta)\n", + "# Let Fp be perpendicular component\n", + "Fp = round(F*math.sin(theta*math.pi/180),1) #[Newton]\n", + "\n", + "# Result\n", + "print\"theta = \",(theta),\"degrees\"\n", + "print\"FBA = \",(FBA),\"N\"\n", + "print\"Fp = \",(Fp),\"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": 2 +} diff --git a/Engineering_Mechanics_Statics_and_Dynamics_by_Hibler_and_Gupta/Chapter_3_Equilibrium_of_a_Particle.ipynb b/Engineering_Mechanics_Statics_and_Dynamics_by_Hibler_and_Gupta/Chapter_3_Equilibrium_of_a_Particle.ipynb index 4029beed..aef96ff3 100644 --- a/Engineering_Mechanics_Statics_and_Dynamics_by_Hibler_and_Gupta/Chapter_3_Equilibrium_of_a_Particle.ipynb +++ b/Engineering_Mechanics_Statics_and_Dynamics_by_Hibler_and_Gupta/Chapter_3_Equilibrium_of_a_Particle.ipynb @@ -1,747 +1,468 @@ - - - - - - - - - - - - - - - - - - - - - - - Python-Textbook-Companions/Chapter_3_Equilibrium_of_a_Particle.ipynb at 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- - - - - - +{ + "cells": [ + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# Chapter 3 : Equilibrium of a Particle" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Ex 3.2 Page No. 75" + ] + }, + { + "cell_type": "code", + "execution_count": 3, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "TB = 4.9 kN\n", + "TD = 4.25 kN\n" + ] + } + ], + "source": [ + "# Example 3.2\n", + "import math\n", + "import numpy as np\n", + "\n", + "# Variable Declaration\n", + "theta = 30 #[Degrees]\n", + "\n", + "# Calculation\n", + "# The two unknown magnitudes TB and TD can be obtained from two scalar equations of equilibrium ΣF_x = 0 and ΣF_y = 0\n", + "a = np.array([[math.cos(math.pi*theta/180),-1], [math.sin(math.pi*theta/180),0]])\n", + "b = np.array([0,2.452])\n", + "x = np.linalg.solve(a, b)\n", + "TB = round(x[0],2) #[kilo Newton]\n", + "TD = round(x[1],2) #[kilo Newton]\n", + "\n", + "# Result\n", + "print\"TB = \",(TB),\"kN\"\n", + "print\"TD = \",(TD),\"kN\"" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Ex 3.3 Page No. 76" + ] + }, + { + "cell_type": "code", + "execution_count": 9, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "TB = 54.6 N\n", + "TD = 38.6 N\n", + "TCD = 34.1 N\n", + "WB = 47.8 N\n" + ] + } + ], + "source": [ + "# Example 3.3\n", + "import math\n", + "import numpy as np\n", + "from __future__ import division\n", + "\n", + "# Variable Declaration\n", + "WA = 20 #[Newton]\n", + "\n", + "# Calculation\n", + "# The two unknown magnitudes TEG and TEC can be obtained from two scalar equations of equilibrium ΣF_x = 0 and ΣF_y = 0 at point E\n", + "a = np.array([[math.sin(math.pi*30/180),-math.cos(math.pi*45/180)], [math.cos(math.pi*30/180),-math.sin(math.pi*45/180)]])\n", + "b = np.array([0,20])\n", + "x = np.linalg.solve(a, b)\n", + "TEG = round(x[0],1) #[Newton]\n", + "TEC = round(x[1],1) #[Newton]\n", + "\n", + "# The two unknown magnitudes TCD and WB can be obtained from two scalar equations of equilibrium ΣF_x = 0 and ΣF_y = 0 at point C\n", + "a = np.array([[-(4/5),0], [3/5,-1]])\n", + "b = np.array([-38.6*math.cos(math.pi*45/180), -38.6*math.sin(math.pi*45/180)])\n", + "x = np.linalg.solve(a, b)\n", + "TCD = round(x[0],1) #[Newton]\n", + "WB = round(x[1],1) #[Newton]\n", + "\n", + "# Result\n", + "print\"TB = \",(TEG),\"N\"\n", + "print\"TD = \",(TEC),\"N\"\n", + "print\"TCD = \",(TCD),\"N\"\n", + "print\"WB = \",(WB),\"N\"" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Ex 3.4 Page No. 77" + ] + }, + { + "cell_type": "code", + "execution_count": 12, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "lAC = 1.32 m\n" + ] + } + ], + "source": [ + "# Example 3.4\n", + "import math\n", + "import numpy as np\n", + "from __future__ import division\n", + "\n", + "# Variable Declaration\n", + "lAB_dash = 0.4 #[meter]\n", + "kAB = 300 #[Newton/meter]\n", + "\n", + "# Calculation\n", + "# Let W be weight of lamp\n", + "W = 8*9.81 #[Newton]\n", + "\n", + "# The two unknown magnitudes TAB and TAC can be obtained from two scalar equations of equilibrium ΣF_x = 0 and ΣF_y = 0 at point A\n", + "a = np.array([[1,-math.cos(math.pi*30/180)], [0,math.sin(math.pi*30/180)]])\n", + "b = np.array([0, 78.5])\n", + "x = np.linalg.solve(a, b)\n", + "TAB = round(x[0],1) #[Newton]\n", + "TAC = round(x[1],1) #[Newton]\n", + "\n", + "# Let sAB denote the stretch of string\n", + "sAB = TAB/kAB\n", + "\n", + "# Let lAB denote the stretch of string\n", + "lAB = lAB_dash + sAB\n", + "lAC = round((2 - lAB)/math.cos(math.pi*30/180),2)\n", + "\n", + "# Result\n", + "print\"lAC = \",(lAC),\"m\"\n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Ex 3.5 Page No. 84" + ] + }, + { + "cell_type": "code", + "execution_count": 16, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "FB = 207.8 N\n", + "FC = 150.0 N\n", + "FD = 240.0 N\n", + "sAB = 41.6 mm\n" + ] + } + ], + "source": [ + "# Example 3.5\n", + "import math\n", + "import numpy as np\n", + "from __future__ import division\n", + "\n", + "# Variable Declaration\n", + "L = 90 #[Newton]\n", + "k = 5000 #[Newton/meter]\n", + "\n", + "# Calculation\n", + "# The three unknown magnitudes FB, FC and FD can be obtained from three scalar equations of equilibrium ΣF_x = 0,ΣF_y = 0 and ΣF_z = 0 at point A\n", + "a = np.array([[0,-4/5,math.sin(math.pi*30/180)], [1,0,-math.cos(math.pi*30/180)], [0,3/5,0]])\n", + "b = np.array([0, 0, 90])\n", + "x = np.linalg.solve(a, b)\n", + "FB = round(x[0],1) #[Newton]\n", + "FC = round(x[1],1) #[Newton]\n", + "FD = round(x[2],1) #[Newton]\n", + "\n", + "# Let sAB denote stretch of a string\n", + "sAB= round((FB*1000)/k,1) #[millimeter]\n", + "\n", + "# Result\n", + "print\"FB = \",(FB),\"N\"\n", + "print\"FC = \",(FC),\"N\"\n", + "print\"FD = \",(FD),\"N\"\n", + "print\"sAB = \",(sAB),\"mm\"" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Ex 3.6 Page No. 85" + ] + }, + { + "cell_type": "code", + "execution_count": 19, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "F = 300.0 N\n", + "alpha = 48.2 degrees\n", + "beta = 109.5 degrees\n", + "gamma = 48.2 degrees\n" + ] + } + ], + "source": [ + "# Example 3.6\n", + "import math\n", + "from __future__ import division\n", + "\n", + "# Variable Declaration\n", + "B_x = -2 #[meter]\n", + "B_y = -3 #[meter]\n", + "B_z = 6 #[meter]\n", + "F1_x = 0 #[Newton]\n", + "F1_y = 400 #[Newton]\n", + "F1_z = 0 #[Newton]\n", + "F2_x = 0 #[Newton]\n", + "F2_y = 0 #[Newton]\n", + "F2_z = -800 #[Newton]\n", + "F3 = 700 #[Newton]\n", + "\n", + "# Calculation\n", + "# Let rB be unit vector along OB\n", + "rB_x = -2\n", + "rB_y = -3\n", + "rB_z = 6\n", + "rB = math.sqrt(rB_x**(2)+rB_y**(2)+rB_z**(2))\n", + "F3_x = F3*(rB_x/rB) #[Newton]\n", + "F3_y = F3*(rB_y/rB) #[Newton]\n", + "F3_z = F3*(rB_z/rB) #[Newton]\n", + "\n", + "# For equilibrium ΣF = 0 and F1+F2+F3+F = 0\n", + "F_x = 0 - (F1_x +F2_x +F3_x) #[Newton]\n", + "F_y = 0 - (F1_y +F2_y +F3_y) #[Newton]\n", + "F_z = 0 - (F1_z +F2_z +F3_z) #[Newton]\n", + "F = round(math.sqrt(F_x**(2)+F_y**(2)+F_z**(2)),1) #[Newton]\n", + "alpha = round(math.degrees(math.acos(F_x/F)),1) #[Degrees]\n", + "beta = round(math.degrees(math.acos(F_y/F)),1) #[Degrees]\n", + "gamma = round(math.degrees(math.acos(F_z/F)),1) #[Degrees]\n", + "\n", + "\n", + "# Result\n", + "print\"F = \",(F),\"N\"\n", + "print\"alpha = \",(alpha),\"degrees\"\n", + "print\"beta = \",(beta),\"degrees\"\n", + "print\"gamma = \",(gamma),\"degrees\"\n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Ex 3.7 Page No. 86" + ] + }, + { + "cell_type": "code", + "execution_count": 6, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "FB = 23.6 N\n", + "FC = 23.6 N\n", + "FD = 15.0 N\n" + ] + } + ], + "source": [ + "# Example 3.7\n", + "import math\n", + "import numpy as np\n", + "from __future__ import division\n", + "\n", + "# Variable Declaration\n", + "B_x = -3 #[meter]\n", + "B_y = -4 #[meter]\n", + "B_z = 8 #[meter]\n", + "C_x = -3 #[meter]\n", + "C_y = 4 #[meter]\n", + "C_z = 8 #[meter]\n", + "\n", + "# Calculation\n", + "# let FB_x/FB = b_x, FB_y/FB = b_y, FB_z/FB = b_z \n", + "b_x = round(B_x/(math.sqrt(B_x**(2)+B_y**(2)+B_z**(2))),3) #[Newton]\n", + "b_y = round(B_y/(math.sqrt(B_x**(2)+B_y**(2)+B_z**(2))),3) #[Newton]\n", + "b_z = round(B_z/(math.sqrt(B_x**(2)+B_y**(2)+B_z**(2))),3) #[Newton]\n", + "\n", + "# let FC_x/FC = c_x, FC_y/FC = c_y, FC_z/FC = c_z \n", + "c_x = round(C_x/(math.sqrt(C_x**(2)+C_y**(2)+C_z**(2))),3) #[Newton]\n", + "c_y = round(C_y/(math.sqrt(C_x**(2)+C_y**(2)+C_z**(2))),3) #[Newton]\n", + "c_z = round(C_z/(math.sqrt(C_x**(2)+C_y**(2)+C_z**(2))),3) #[Newton]\n", + "\n", + "# let FD_x/FD = d_x, FD_y/FD = d_y, FD_z/FD = d_z \n", + "d_x = 1\n", + "d_y = 0\n", + "d_z = 0\n", + "\n", + "W_x = 0\n", + "W_y = 0\n", + "W_z = -40\n", + "\n", + "# The three unknown magnitudes FB, FC and FD can be obtained from three scalar equations of equilibrium ΣF_x = 0,ΣF_y = 0 and ΣF_z = 0 at point A\n", + "a = np.array([[b_x,c_x,d_x], [b_y,c_y,d_y], [b_z,c_z,d_z]])\n", + "b = np.array([0, 0, -W_z])\n", + "x = np.linalg.solve(a, b)\n", + "FB = round(x[0],1) #[Newton]\n", + "FC = round(x[1],1) #[Newton]\n", + "FD = round(x[2],1) #[Newton]\n", + "\n", + "# Result\n", + "print\"FB = \",(FB),\"N\"\n", + "print\"FC = \",(FC),\"N\"\n", + "print\"FD = \",(FD),\"N\"" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "collapsed": true + }, + "source": [ + "## Ex 3.8 Page No. 87" + ] + }, + { + "cell_type": "code", + "execution_count": 5, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "FB = 693.2 N\n", + "FC = 812.7 N\n", + "FD = 861.6 N\n", + "s = 0.462 m\n" + ] + } + ], + "source": [ + "# Ex 3.8\n", + "import math\n", + "import numpy as np\n", + "from __future__ import division\n", + "\n", + "# Variable Declaration\n", + "W = 981 #[Newton]\n", + "D_x = -1 #[meter]\n", + "D_y = 2 #[meter]\n", + "D_z = 2 #[meter]\n", + "k = 1500 #[Newton meter]\n", + "\n", + "# Calculation\n", + "# let FB_x/FB = b_x, FB_y/FB = b_y, FB_z/FB = b_z \n", + "b_x = 1 \n", + "b_y = 0\n", + "b_z = 0\n", + "\n", + "# let FC_x/FC = c_x, FC_y/FC = c_y, FC_z/FC = c_z \n", + "c_x = math.cos(120*math.pi/180) #[Newton]\n", + "c_y = math.cos(135*math.pi/180) #[Newton]\n", + "c_z = math.cos(60*math.pi/180) #[Newton]\n", + "\n", + "# let FD_x/FD = d_x, FD_y/FD = d_y, FD_z/FD = d_z \n", + "d_x = round(D_x/(math.sqrt(D_x**(2)+D_y**(2)+D_z**(2))),3) #[Newton]\n", + "d_y = round(D_y/(math.sqrt(D_x**(2)+D_y**(2)+D_z**(2))),3) #[Newton]\n", + "d_z = round(D_z/(math.sqrt(D_x**(2)+D_y**(2)+D_z**(2))),3) #[Newton]\n", + "\n", + "W_x = 0 #[Newton]\n", + "W_y = 0 #[Newton]\n", + "W_z = -981 #[Newton]\n", + "\n", + "# The three unknown magnitudes FB, FC and FD can be obtained from three scalar equations of equilibrium ΣF_x = 0,ΣF_y = 0 and ΣF_z = 0 at point A\n", + "a = np.array([[b_x,c_x,d_x], [b_y,c_y,d_y], [b_z,c_z,d_z]])\n", + "b = np.array([0, 0, -W_z])\n", + "x = np.linalg.solve(a, b)\n", + "FB = round(x[0],1) #[Newton]\n", + "FC = round(x[1],1) #[Newton]\n", + "FD = round(x[2],1) #[Newton]\n", + "\n", + "# Let stretch of spring be denoted by s\n", + "s = round(FB/k,3)\n", + "\n", + "# Result\n", + "print\"FB = \",(FB),\"N\"\n", + "print\"FC = \",(FC),\"N\"\n", + "print\"FD = \",(FD),\"N\"\n", + "print\"s = \",(s),\"m\"" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], + "source": [] + } + ], + "metadata": { + "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": 2 +} diff --git a/Engineering_Mechanics_Statics_and_Dynamics_by_Hibler_and_Gupta/Chapter_4_Force_System_Resultants.ipynb b/Engineering_Mechanics_Statics_and_Dynamics_by_Hibler_and_Gupta/Chapter_4_Force_System_Resultants.ipynb index 6d7d0e5d..7de45a57 100644 --- a/Engineering_Mechanics_Statics_and_Dynamics_by_Hibler_and_Gupta/Chapter_4_Force_System_Resultants.ipynb +++ b/Engineering_Mechanics_Statics_and_Dynamics_by_Hibler_and_Gupta/Chapter_4_Force_System_Resultants.ipynb @@ -1,747 +1,1263 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- - - - - - +{ + "cells": [ + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# Chapter 4 : Force System Resultants" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Ex 4.1 Page No 98" + ] + }, + { + "cell_type": "code", + "execution_count": 5, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Fig 4-4a MO = 200 N.m(clockwise)\n", + "Fig 4-4b MO = 37.5 N.m(clockwise)\n", + "Fig 4-4c MO = 229.3 N.m(clockwise)\n", + "Fig 4-4d MO = 42.4 N.m(anti clockwise)\n", + "Fig 4-4e MO = 21.0 kN.m(anti clockwise)\n" + ] + } + ], + "source": [ + "# Ex 4.1\n", + "import math\n", + "\n", + "# Calculation Fig 4-4a\n", + "MO = 100*2 #[Newton meter]\n", + "\n", + "# Result Fig 4-4a\n", + "print\"Fig 4-4a MO = \",(MO),\"N.m(clockwise)\"\n", + "\n", + "# Calculation Fig 4-4b\n", + "MO = 50*0.75 #[Newton meter]\n", + "\n", + "# Result Fig 4-4b\n", + "print\"Fig 4-4b MO = \",(MO),\"N.m(clockwise)\"\n", + "\n", + "# Calculation Fig 4-4c\n", + "MO = round(40*(4+2*math.cos(math.pi*30/180)),1) #[Newton meter]\n", + "\n", + "# Result Fig 4-4b\n", + "print\"Fig 4-4c MO = \",(MO),\"N.m(clockwise)\"\n", + "\n", + "# Calculation Fig 4-4d\n", + "MO = round(60*1*math.sin(math.pi*45/180),1) #[Newton meter]\n", + "\n", + "# Result Fig 4-4d\n", + "print\"Fig 4-4d MO = \",(MO),\"N.m(anti clockwise)\"\n", + "\n", + "# Calculation Fig 4-4e\n", + "MO = round(7*(4-1),1) #[Newton meter]\n", + "\n", + "# Result Fig 4-4e\n", + "print\"Fig 4-4e MO = \",(MO),\"kN.m(anti clockwise)\"" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Ex 4.2 Page No 99" + ] + }, + { + "cell_type": "code", + "execution_count": 1, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "MA = 2000.0 N.m(clockwise)\n", + "MB = 1200.0 N.m(clockwise)\n", + "MC = 0\n", + "MD = 400.0 N.m(anti clockwise)\n" + ] + } + ], + "source": [ + "# Example 4.2\n", + "\n", + "# Variable Declaration\n", + "F = 800 #[Newton]\n", + "\n", + "# Calculation\n", + "MA = F*2.5 #[Newton meter]\n", + "MB = F*1.5 #[Newton meter]\n", + "MC = F*0 #[Newton meter]\n", + "MD = F*0.5 #[Newton meter]\n", + "\n", + "# Result\n", + "print\"MA = \",(MA),\"N.m(clockwise)\"\n", + "print\"MB = \",(MB),\"N.m(clockwise)\"\n", + "print\"MC = \",(MC)\n", + "print\"MD = \",(MD),\"N.m(anti clockwise)\"" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Ex 4.3 Page No 99" + ] + }, + { + "cell_type": "code", + "execution_count": 11, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "MRO = -334.0 N.m = 334.0 N.m(clockwise)\n" + ] + } + ], + "source": [ + "# Ex 4.3\n", + "import math\n", + "\n", + "# Calculation\n", + "# Assuming positive moments act in +k direction i.e counterclockwise\n", + "# +MRO(counterclockwise) = ΣFd\n", + "MRO = round(-50*(2)+60*(0)+20*(3*math.sin(30*math.pi/180))-40*(4+3*math.cos(30*math.pi/180)),0) #[Newton meter]\n", + "\n", + "# Result\n", + "print\"MRO = \",(MRO),\"N.m = \",(abs(MRO)),\"N.m(clockwise)\"" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Ex 4.4 Page No 106" + ] + }, + { + "cell_type": "code", + "execution_count": 2, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "MA = 224.0 N.m\n" + ] + } + ], + "source": [ + "# Ex 4.4\n", + "import math\n", + "import numpy as np\n", + "\n", + "# Variable Declaration\n", + "F = 60 #[Newton]\n", + "B_x = 1 #[meter]\n", + "B_y = 3 #[meter]\n", + "B_z = 2 #[meter]\n", + "C_x = 3 #[meter]\n", + "C_y = 4 #[meter]\n", + "C_z = 0 #[meter]\n", + "\n", + "# Calculation\n", + "rB_x = B_x #[meter]\n", + "rB_y = B_y #[meter]\n", + "rB_z = B_z #[meter]\n", + "F_x = round(F*((C_x-B_x)/math.sqrt((C_x-B_x)**(2)+(C_y-B_y)**(2)+(C_z-B_z)**(2))),1) #[Newton]\n", + "F_y = round(F*((C_y-B_y)/math.sqrt((C_x-B_x)**(2)+(C_y-B_y)**(2)+(C_z-B_z)**(2))),1) #[Newton]\n", + "F_z = round(F*((C_z-B_z)/math.sqrt((C_x-B_x)**(2)+(C_y-B_y)**(2)+(C_z-B_z)**(2))),1) #[Newton]\n", + "\n", + "# Let a = rB X F\n", + "a = np.cross([rB_x,rB_y,rB_z],[F_x,F_y,F_z])\n", + "MA_x = a[0] #[Newton meter]\n", + "MA_y = a[1] #[Newton meter]\n", + "MA_z = a[2] #[Newton meter]\n", + "MA = round(math.sqrt(MA_x**(2)+MA_y**(2)+MA_z**(2)),0) #[Newton meter]\n", + "\n", + "# Result\n", + "print\"MA = \",(MA),\"N.m\"" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "collapsed": true + }, + "source": [ + "## Ex 4.5 Page No 107" + ] + }, + { + "cell_type": "code", + "execution_count": 4, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "MRO_x = 30 N.m\n", + "MRO_y = -40 N.m\n", + "MRO_z = 60 N.m\n", + "alpha = 67.4 degrees\n", + "beta = 120.8 degrees\n", + "gamma = 39.8 degrees\n" + ] + } + ], + "source": [ + "# Example 4.5\n", + "import math\n", + "from __future__ import division\n", + "import numpy as np\n", + "\n", + "# Variable Declaration\n", + "F1_x = -60 #[Newton]\n", + "F1_y = 40 #[Newton]\n", + "F1_z = 20 #[Newton]\n", + "F2_x = 0 #[Newton]\n", + "F2_y = 50 #[Newton]\n", + "F2_z = 0 #[Newton]\n", + "F3_x = 80 #[Newton]\n", + "F3_y = 40 #[Newton]\n", + "F3_z = -30 #[Newton]\n", + "rA_x = 0 #[meter]\n", + "rA_y = 5 #[meter]\n", + "rA_z = 0 #[meter]\n", + "rB_x = 4 #[meter]\n", + "rB_y = 5 #[meter]\n", + "rB_z = -2 #[meter]\n", + "\n", + "# Calculation\n", + "# Let MRO be resultant moment about O\n", + "# Let a = rA X F1, b = rA X F2, c = rB X F3\n", + "a = np.cross([rA_x,rA_y,rA_z],[F1_x,F1_y,F1_z])\n", + "b = np.cross([rA_x,rA_y,rA_z],[F2_x,F2_y,F2_z])\n", + "c = np.cross([rB_x,rB_y,rB_z],[F3_x,F3_y,F3_z])\n", + "MRO_x = a[0]+b[0]+c[0] #[Newton meter]\n", + "MRO_y = a[1]+b[1]+c[1] #[Newton meter]\n", + "MRO_z = a[2]+b[2]+c[2] #[Newton meter]\n", + "MRO = round(math.sqrt(MRO_x**(2)+MRO_y**(2)+MRO_z**(2)),2) #[Newton meter]\n", + "\n", + "# Let u be unit vector which defines the direction of moment axis\n", + "u_x = MRO_x/MRO\n", + "u_y = MRO_y/MRO\n", + "u_z = MRO_z/MRO\n", + "\n", + "# Let alpha,beta and gamma be coordinate direction angles of moment axis \n", + "alpha = round(math.degrees(math.acos(u_x)),1) #[degrees]\n", + "beta = round(math.degrees(math.acos(u_y)),1) #[degrees]\n", + "gamma = round(math.degrees(math.acos(u_z)),1) #[degrees]\n", + "\n", + "# Result\n", + "print\"MRO_x = \",(MRO_x),\"N.m\"\n", + "print\"MRO_y = \",(MRO_y),\"N.m\"\n", + "print\"MRO_z = \",(MRO_z),\"N.m\"\n", + "print\"alpha = \",(alpha),\"degrees\"\n", + "print\"beta = \",(beta),\"degrees\"\n", + "print\"gamma = \",(gamma),\"degrees\"" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Ex 4.6 Page No 109" + ] + }, + { + "cell_type": "code", + "execution_count": 7, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Solution 1\n", + "MA_x = 0 N.m\n", + "MA_y = 0 N.m\n", + "MA_z = 14.1 N.m\n", + "\n", + "Solution 2\n", + "MA_x = 0 N.m\n", + "MA_y = 0 N.m\n", + "MA_z = 14.1 N.m\n" + ] + } + ], + "source": [ + "# Ex 4.6\n", + "import math\n", + "from __future__ import division\n", + "\n", + "# Variable Declaration\n", + "F = 200 #[Newton]\n", + "\n", + "# Calculation Solution 1\n", + "# Moment arm d can be found by trigonometry Refer Fig 4-19b\n", + "d = (100*math.cos(math.pi*45/180))/1000 #[meter]\n", + "# MA = Fd\n", + "MA = round(F*d,1) #[Newton meter]\n", + "\n", + "# Result Solution 1\n", + "# According to right hand thumb rule MA is directed in +k direction\n", + "print\"Solution 1\"\n", + "print\"MA_x = 0 N.m\"\n", + "print\"MA_y = 0 N.m\"\n", + "print\"MA_z = \",(MA),\"N.m\\n\"\n", + "\n", + "# Calculation Solution 2\n", + "# F is resolved into x and y components Refer Fig 4-19c\n", + "# MA = ΣFd\n", + "MA = round(F*math.sin(math.pi*45/180)*(0.20)-200*math.cos(math.pi*45/180)*(0.10),1) #[Newton meter]\n", + "\n", + "# Result Solution 2\n", + "# According to right hand thumb rule MA is directed in +k direction\n", + "print\"Solution 2\"\n", + "print\"MA_x = 0 N.m\"\n", + "print\"MA_y = 0 N.m\"\n", + "print\"MA_z = \",(MA),\"N.m\"\n", + "\n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Ex 4.7 Page No 110" + ] + }, + { + "cell_type": "code", + "execution_count": 5, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Solution 1(Scalar Analysis)\n", + "MO_x = 0 N.m\n", + "MO_y = 0 N.m\n", + "MO_z = -98.6 N.m\n", + "\n", + "Solution 2(Vector Analysis)\n", + "MO_x = 0.0 N.m\n", + "MO_y = -0.0 N.m\n", + "MO_z = -98.56 N.m\n", + "\n" + ] + } + ], + "source": [ + "# Example 4.7\n", + "import math\n", + "import numpy as np \n", + "\n", + "# Variable Declaration\n", + "F = 400 #[Newton]\n", + "\n", + "# Calculation(Scalar Analysis)\n", + "# F is resolved into x and y components Refer 4-20b\n", + "# Taking +ve moments about O in +k direction\n", + "MO = round(F*math.sin(math.pi*30/180)*(0.2)-F*math.cos(math.pi*30/180)*(0.4),1) #[Newton meter]\n", + "\n", + "# Result Solution 1\n", + "print\"Solution 1(Scalar Analysis)\"\n", + "print\"MO_x = 0 N.m\"\n", + "print\"MO_y = 0 N.m\"\n", + "print\"MO_z = \",(MO),\"N.m\\n\"\n", + "\n", + "# Calculation(Vector Analysis)\n", + "# let r be positon vector and F be force vector\n", + "r_x = 0.4 #[meter]\n", + "r_y = -0.2 #[meter]\n", + "r_z = 0 #[meter]\n", + "F_x = round(F*math.sin(math.pi*30/180),1) #[Newton]\n", + "F_y = round(-F*math.cos(math.pi*30/180),1) #[Newton]\n", + "F_z = 0 #[Newton]\n", + "\n", + "# Let MO be the moment given by MO = r X F\n", + "a = np.cross([r_x,r_y,r_z],[F_x,F_y,F_z])\n", + "MO_x = a[0] #[Newton meter]\n", + "MO_y = a[1] #[Newton meter]\n", + "MO_z= a[2] #[Newton meter]\n", + "\n", + "# Result Solution 2\n", + "print\"Solution 2(Vector Analysis)\"\n", + "print\"MO_x = \",(MO_x),\"N.m\"\n", + "print\"MO_y = \",(-MO_y),\"N.m\"\n", + "print\"MO_z = \",(MO_z),\"N.m\\n\"\n", + "\n", + "\n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Ex 4.8 Page No 118" + ] + }, + { + "cell_type": "code", + "execution_count": 9, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Solution 1(Vector Analysis)\n", + "Mx = -80 N.m\n", + "Ma = -120.0 N.m\n", + "\n", + "Solution 2(Scalar Analysis)\n", + "Mx = -80 N.m\n" + ] + } + ], + "source": [ + "# Example 4.8\n", + "import math\n", + "from __future__ import division\n", + "import numpy as np\n", + "\n", + "# Variable Declaration\n", + "F_x = -40 #[Newton]\n", + "F_y = 20 #[Newton]\n", + "F_z = 10 #[Newton]\n", + "rA_x = -3 #[meter]\n", + "rA_y = 4 #[meter]\n", + "rA_z = 6 #[meter]\n", + "ua_x = -3/5\n", + "ua_y = 4/5\n", + "ua_z = 0\n", + "\n", + "# Calculation Solution 1(Vector Analysis)\n", + "# Mx = i.(rA X F)\n", + "Mx = np.dot([1,0,0],np.cross([rA_x,rA_y,rA_z],[F_x,F_y,F_z])) #[Newton meter]\n", + "# Ma = ua.(rA X F)\n", + "Ma = np.dot([ua_x,ua_y,ua_z],np.cross([rA_x,rA_y,rA_z],[F_x,F_y,F_z])) #[Newton meter]\n", + "\n", + "# Result Solution 1\n", + "print\"Solution 1(Vector Analysis)\"\n", + "print\"Mx = \",(Mx),\"N.m\"\n", + "print\"Ma = \",(Ma),\"N.m\\n\"\n", + "\n", + "# Calculation Solution 2(Scalar Analysis)\n", + "# Refer Fig 4-23c\n", + "Mx = 10*4 - 20*6 #[Newton meter]\n", + "My = 10*3 - 40*6 #[Newton meter]\n", + "Mz = 40*4 - 20*3 #[Newton meter]\n", + "\n", + "# Result Solution 2\n", + "print\"Solution 2(Scalar Analysis)\"\n", + "print\"Mx = \",(Mx),\"N.m\"\n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Ex 4.9 Page No 119" + ] + }, + { + "cell_type": "code", + "execution_count": 18, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "MAB_x = -48.0 N.m\n", + "MAB_y = -24.0 N.m\n" + ] + } + ], + "source": [ + "# Example 4.9\n", + "import math\n", + "from __future__ import division\n", + "import numpy as np\n", + "\n", + "# Variable Declaration\n", + "F_x = -600 #[Newton]\n", + "F_y = 200 #[Newton]\n", + "F_z = -300 #[Newton]\n", + "rD_x = 0 #[meter]\n", + "rD_y = 0.2 #[meter]\n", + "rD_z = 0 #[meter]\n", + "\n", + "# Calculation\n", + "# Unit vector uB defines the direction of AB axis of the rod\n", + "uB_x = 0.4/math.sqrt(0.4**(2)+0.2**(2))\n", + "uB_y = 0.2/math.sqrt(0.4**(2)+0.2**(2)) \n", + "uB_z = 0\n", + "# MAB = uB.(rD X F)\n", + "MAB = np.dot([uB_x,uB_y,uB_z],np.cross([rD_x,rD_y,rD_z],[F_x,F_y,F_z])) #[Newton meter]\n", + "MAB_x = MAB*uB_x #[Newton meter]\n", + "MAB_y = MAB*uB_y #[Newton meter]\n", + "\n", + "# Result\n", + "print\"MAB_x = \",(MAB_x),\"N.m\"\n", + "print\"MAB_y = \",(MAB_y),\"N.m\"\n", + "\n", + "\n" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "collapsed": true + }, + "source": [ + "## Ex 4.10 Page No 123" + ] + }, + { + "cell_type": "code", + "execution_count": 1, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "F = 120.0 N\n" + ] + } + ], + "source": [ + "# Example 4.10\n", + "from __future__ import division\n", + "\n", + "# Calculation\n", + "# Let the couple has magnitude of M having direction out of page\n", + "M = 40*0.6 #[Newton meter]\n", + "# To preserve counterclockwise rotation of M vertical forces acting through points A and B must be directed as shown in Fig 4-29c\n", + "F = M/0.2 #[Newton]\n", + "\n", + "# Result\n", + "print\"F = \",(F),\"N\"\n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Ex 4.11 Page No 124" + ] + }, + { + "cell_type": "code", + "execution_count": 4, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Moment calculated about D\n", + "MD = 195.0 N.m(counterclockwise)\n", + "Moment calculated about A\n", + "MA = 195.0 N.m(counterclockwise)\n" + ] + } + ], + "source": [ + "# Example 4.11\n", + "from __future__ import division\n", + "\n", + "# Variable Declaration\n", + "F = 150 #[Newton]\n", + "\n", + "# Calculation\n", + "F_x = (4/5)*F #[Newton]\n", + "F_y = (3/5)*F #[Newton]\n", + "\n", + "# Let the couple moment is calculated about D\n", + "MD = F_x*0 - F_y*1 + F_y*2.5 + F_x*0.5 #[Newton meter]\n", + "\n", + "# Let the couple moment is calculated about A\n", + "MA = F_y*1.5 + F_x*0.5 #[Newton meter]\n", + "\n", + "# Result\n", + "print\"Moment calculated about D\"\n", + "print\"MD = \",(MD),\"N.m(counterclockwise)\"\n", + "print\"Moment calculated about A\"\n", + "print\"MA = \",(MA),\"N.m(counterclockwise)\"\n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Ex 4.12 Page No 125" + ] + }, + { + "cell_type": "code", + "execution_count": 20, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Solution 1 (Vector Analysis)\n", + "MO_x = 0.0 N.m\n", + "MO_y = -13.0 N.m\n", + "MO_z = 0.0 N.m\n", + "MA_x = 0.0 N.m\n", + "MA_y = -13.0 N.m\n", + "MA_z = 0.0 N.m\n", + "\n", + "Solution 2 (Scalar Analysis)\n", + "M_x = 0 N.m\n", + "M_y = -13.0 N.m\n", + "M_z = 0 N.m\n" + ] + } + ], + "source": [ + "# Example 4.12\n", + "import math\n", + "\n", + "# Variable Declaration\n", + "rA_x = 0 #[meter]\n", + "rA_y = 0.8 #[meter]\n", + "rA_z = 0 #[meter]\n", + "rB_x = 0.6*math.cos(math.pi*30/180) #[meter]\n", + "rB_y = 0.8 #[meter]\n", + "rB_z = -0.6*math.sin(math.pi*30/180) #[meter]\n", + "rAB_x = 0.6*math.cos(math.pi*30/180) #[meter]\n", + "rAB_y = 0 #[meter]\n", + "rAB_z = -0.6*math.sin(math.pi*30/180) #[meter]\n", + "# Let force acting at B be FB\n", + "FB_x = 0 #[Newton]\n", + "FB_y = 0 #[Newton]\n", + "FB_z = -25 #[Newton]\n", + "# Let force acting at A be FA\n", + "FA_x = 0 #[Newton]\n", + "FA_y = 0 #[Newton]\n", + "FA_z = 25 #[Newton]\n", + "\n", + "# Calculation Solution 1(Vector Analysis)\n", + "# Let MO be moment about about O Refer Fig 4-31b\n", + "# Let a = rA X FB, b = rB X FA\n", + "a = np.cross([rA_x,rA_y,rA_z],[FB_x,FB_y,FB_z])\n", + "b = np.cross([rB_x,rB_y,rB_z],[FA_x,FA_y,FA_z])\n", + "MO_x = round(a[0]+b[0],1) #[Newton meter]\n", + "MO_y = round(a[1]+b[1],1) #[Newton meter]\n", + "MO_z = round(a[2]+b[2],1) #[Newton meter]\n", + "\n", + "# Let MA be moment about about A Refer Fig 4-31c\n", + "# MA = rAB X FA\n", + "a = np.cross([rAB_x,rAB_y,rAB_z],[FA_x,FA_y,FA_z])\n", + "MA_x = round(a[0],1) #[Newton meter]\n", + "MA_y = round(a[1],1) #[Newton meter]\n", + "MA_z = round(a[2],1) #[Newton meter]\n", + "\n", + "# Calculation Solution 2(Vector Analysis)\n", + "M = 25*0.52 #[Newton meter]\n", + "# M acts in -j direction\n", + "M_x = 0 #[Newton meter]\n", + "M_y = -M #[Newton meter]\n", + "M_z = 0 #[Newton meter]\n", + "\n", + "# Result \n", + "print\"Solution 1 (Vector Analysis)\"\n", + "print\"MO_x = \",(MO_x),\"N.m\"\n", + "print\"MO_y = \",(MO_y),\"N.m\"\n", + "print\"MO_z = \",(MO_z),\"N.m\"\n", + "print\"MA_x = \",(MA_x),\"N.m\"\n", + "print\"MA_y = \",(MA_y),\"N.m\"\n", + "print\"MA_z = \",(MA_z),\"N.m\\n\"\n", + "print\"Solution 2 (Scalar Analysis)\"\n", + "print\"M_x = \",(M_x),\"N.m\"\n", + "print\"M_y = \",(M_y),\"N.m\"\n", + "print\"M_z = \",(M_z),\"N.m\"" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Ex 4.13 Page No 126" + ] + }, + { + "cell_type": "code", + "execution_count": 22, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "MR_x = 60.0 N.m\n", + "MR_y = 22.5 N.m\n", + "MR_z= 30.0 N.m\n" + ] + } + ], + "source": [ + "# Example 4.13\n", + "from __future__ import division\n", + "import numpy as np\n", + "\n", + "# Variable Declaration\n", + "rDC_x = 0.3 #[meter]\n", + "rDC_y = 0 #[meter]\n", + "rDC_z = 0 #[meter]\n", + "FC_x = 0 #[Newton]\n", + "FC_y = 125*(4/5) #[Newton]\n", + "FC_z = -125*(3/5) #[Newton]\n", + "\n", + "# Calculation\n", + "M1 = 150*0.4 #[Newton meter]\n", + "\n", + "# By right hand rule M1 acts in +i direction\n", + "M1_x = M1 #[Newton meter]\n", + "M1_y = 0 #[Newton meter]\n", + "M1_z = 0 #[Newton meter]\n", + "\n", + "# M2 = rDC X FC\n", + "a = np.cross([rDC_x,rDC_y,rDC_z],[FC_x,FC_y,FC_z]) \n", + "M2_x = a[0] #[Newton meter]\n", + "M2_y = a[1] #[Newton meter]\n", + "M2_z = a[2] #[Newton meter]\n", + "\n", + "# M1 and M2 are free vectors.So they may be moved to some arbitrary point P and added vectorially.\n", + "# The resultant couple moment becomes MR = M1 + M2\n", + "MR_x = M1_x + M2_x #[Newton meter]\n", + "MR_y = M1_y + M2_y #[Newton meter]\n", + "MR_z = M1_z + M2_z #[Newton meter]\n", + "\n", + "# Result\n", + "print\"MR_x = \",(MR_x),\"N.m\"\n", + "print\"MR_y = \",(MR_y),\"N.m\"\n", + "print\"MR_z= \",(MR_z),\"N.m\"" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Ex 4.14 Page No 133" + ] + }, + { + "cell_type": "code", + "execution_count": 9, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "FR = 962.3 N\n", + "theta = 66.6 degrees\n", + "MRA = -551.1 N.m = 551.1 N.m(clockwise)\n" + ] + } + ], + "source": [ + "# Example 4.14\n", + "import math \n", + "\n", + "# Calculation\n", + "# Let resultant force be FR\n", + "FR_x = -100-400*math.cos(math.pi*45/180) #[Newton]\n", + "FR_y = -600-400*math.sin(math.pi*45/180) #[Newton]\n", + "FR = round(math.sqrt(FR_x**(2)+FR_y**(2)),1) #[Newton]\n", + "theta = round(math.degrees(math.atan(FR_y/FR_x)),1) #[degrees]\n", + "\n", + "# Let resultant couple moment be MRA which is calculated by summing moments of forces about A\n", + "MRA = round(100*0-600*0.4-400*math.sin(math.pi*45/180)*0.8-400*math.cos(math.pi*45/180)*0.3,1) #[Newton meter]\n", + "\n", + "# Result\n", + "print\"FR = \",(FR),\"N\"\n", + "print\"theta = \",(theta),\"degrees\"\n", + "print\"MRA = \",(MRA),\"N.m = \",(-MRA),\"N.m(clockwise)\"\n", + "\n", + "\n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Ex 4.15 Page No 134" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": false + }, + "outputs": [], + "source": [ + "# Example 4.15\n", + "import math\n", + "from __future__ import division\n", + "import numpy as np\n", + "\n", + "# Variable Declaration\n", + "F1_x = 0 #[Newton]\n", + "F1_y = 0 #[Newton]\n", + "F1_z = -800 #[Newton]\n", + "F2 = 300 #[Newton]\n", + "rCB_x = -0.15 #[meter]\n", + "rCB_y = 0.1 #[meter]\n", + "rCB_z = 0 #[meter]\n", + "rC_x = 0 #[meter]\n", + "rC_y = 0 #[meter]\n", + "rC_z = 1 #[meter]\n", + "rB_x = -0.15 #[meter]\n", + "rB_y = 0.1 #[meter]\n", + "rB_z = 1 #[meter]\n", + "# Calculation\n", + "# Let uCB be unit vector along rCB\n", + "uCB_x = rCB_x/math.sqrt(rCB_x**(2)+rCB_y**(2)+rCB_z**(2))\n", + "uCB_y = rCB_y/math.sqrt(rCB_x**(2)+rCB_y**(2)+rCB_z**(2))\n", + "uCB_z = rCB_z/math.sqrt(rCB_x**(2)+rCB_y**(2)+rCB_z**(2))\n", + "F2_x = round(300*uCB_x,1) #[Newton]\n", + "F2_y = round(300*uCB_y,1) #[Newton]\n", + "F2_z = round(300*uCB_z,1) #[Newton]\n", + "M_x = 0 #[Newton meter]\n", + "M_y = -500*(4/5) #[Newton meter]\n", + "M_z = 500*(3/5) #[Newton meter]\n", + "# FR = F1 + F2\n", + "FR_x = F1_x + F2_x #[Newton]\n", + "FR_y = F1_y + F2_y #[Newton]\n", + "FR_z = F1_z + F2_z #[Newton]\n", + "\n", + "# MRO = M + rC X F1 + rB X F2\n", + "# Let a = rC X F1 and b = rB X F2\n", + "a = np.cross([rC_x,rC_y,rC_z], [F1_x,F1_y,F1_z])\n", + "b = np.cross([rB_x,rB_y,rB_z], [F2_x,F2_y,F2_z])\n", + "MRO_x = M_x + a[0] + b[0] #[Newton meter]\n", + "MRO_y = M_y + a[1] + b[1] #[Newton meter]\n", + "MRO_z = M_z + a[2] + b[2] #[Newton meter]\n", + "\n", + "# Result\n", + "print\"FR_x = \",(FR_x),\"N\"\n", + "print\"FR_y = \",(FR_y),\"N\"\n", + "print\"FR_z = \",(FR_z),\"N\"\n", + "print\"MRO_x = \",(MRO_x),\"N\"\n", + "print\"MRO_y = \",(MRO_y),\"N\"\n", + "print\"MRO_z = \",(MRO_z),\"N\"" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Ex 4.16 Page No 139" + ] + }, + { + "cell_type": "code", + "execution_count": 1, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "FR = 420.5 N\n", + "theta = 33.7 degrees\n", + "d = 3.57 m\n" + ] + } + ], + "source": [ + "# Example 4.16\n", + "import math\n", + "from __future__ import division\n", + "# Calculation\n", + "FR_x = 500*math.cos(math.pi*60/180)+100 #[Newton]\n", + "FR_y = -500*math.sin(math.pi*60/180)+200 #[Newton]\n", + "FR = round(math.sqrt(FR_x**(2)+FR_y**(2)),1) #[Newton]\n", + "theta = round(math.degrees(math.atan(FR_y/FR_x)),1) #[degrees]\n", + "\n", + "# +MRE(counterclockwise) = ΣME\n", + "d = round((500*math.sin(math.pi*60/180)*(4) + 500*math.cos(math.pi*60/180)*(0) - 100*0.5 - 200*2.5 - 350)/233.0,2) #[meter] \n", + "\n", + "# Result\n", + "print\"FR = \",(FR),\"N\"\n", + "print\"theta = \",(-theta),\"degrees\"\n", + "print\"d = \",(d),\"m\" # Correction in the answer" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "collapsed": true + }, + "source": [ + "## Ex 4.17 Page No 140" + ] + }, + { + "cell_type": "code", + "execution_count": 5, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "y = 1.146 m\n", + "x = 5.442 m\n" + ] + } + ], + "source": [ + "# Example 4.17\n", + "import math\n", + "from __future__ import division\n", + "\n", + "# Calculation\n", + "# Let FR be resultant force\n", + "FR_x = -250*(3/5)-175 #[Newton]\n", + "FR_y = -250*(4/5)-60 #[Newton]\n", + "FR = round(math.sqrt(FR_x**(2)+FR_y**(2)),1) #[Newton]\n", + "theta = round(math.degrees(math.atan(FR_y/FR_x)),1) #[degrees]\n", + "\n", + "# +MRA(counterclockwise) = ΣMA\n", + "y = round((175*2.5 - 60*1.5 + 250*(3/5)*5.5 - 250*(4/5)*4 - 260*(0))/325,3) #[meter]\n", + "\n", + "# By principle of transmissibility FR can be treated as intersecting BC Refer Fig 4-44b\n", + "# +MRA(counterclockwise) = ΣMA\n", + "x = round((325*5.5 - 175*2.5 + 60*1.5 - 250*(3/5)*5.5 + 250*(4/5)*4)/260,3) #[meter]\n", + "\n", + "# Result\n", + "print\"y = \",(y),\"m\"\n", + "print\"x = \",(x),\"m\"" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "collapsed": true + }, + "source": [ + "## Ex 4.18 Page No 141" + ] + }, + { + "cell_type": "code", + "execution_count": 7, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "y = 2.5 m\n", + "x = 3.0 m\n" + ] + } + ], + "source": [ + "# Example 4.18\n", + "\n", + "# Calculation\n", + "# +FR = ΣF Refer Fig 4-45a\n", + "FR = -600+100-400-500 #[Newton]\n", + "# Using right hand thumb rule where ppsitive moments act in +i direction we have MR_x = ΣM_x\n", + "y = round(-(600*(0)+100*5-400*10+500*0)/1400,2) #[meter]\n", + "# Assuming positive moments act in +j direction\n", + "# MR_y = ΣM_y\n", + "x = round((600*8-100*6+400*0+500*0)/1400,2) #[meter]\n", + "\n", + "# Result\n", + "print\"y = \",(y),\"m\"\n", + "print\"x = \",(x),\"m\"" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Ex 4.19 Page No 142" + ] + }, + { + "cell_type": "code", + "execution_count": 14, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "FR_x = 0 N\n", + "FR_y = 0 N\n", + "FR_z = -650 N\n", + "x = 0.6 m\n", + "y = -0.29 m\n" + ] + } + ], + "source": [ + "# Example 4.19\n", + "import math\n", + "import numpy as np\n", + "\n", + "# Variable Declaration\n", + "FR_x = 0 #[Newton]\n", + "FR_y = 0 #[Newton]\n", + "FR_z = -300-200-150 #[Newton]\n", + "rA_x = 2 #[meter]\n", + "rA_y = 0 #[meter]\n", + "rA_z = 0 #[meter] \n", + "rB_x = 0 #[meter]\n", + "rB_y = -2 #[meter]\n", + "rB_z = 0 #[meter]\n", + "rC_x = -2*math.sin(math.pi*45/180) #[meter] \n", + "rC_y = 2*math.cos(math.pi*45/180) #[meter]\n", + "rC_z = 0 #[meter]\n", + "\n", + "# Let a = rA X (-300k), b = rB X (-200k), c = rC X (-150k)\n", + "a = np.cross([rA_x,rA_y,rA_z], [0,0,-300])\n", + "b = np.cross([rB_x,rB_y,rB_z], [0,0,-200])\n", + "c = np.cross([rC_x,rC_y,rC_z], [0,0,-150])\n", + "x = round((a[1]+b[1]+c[1])/650,2) #[meter]\n", + "y = round(-((a[0]+b[0]+c[0]))/650,2) #[meter]\n", + "\n", + "# Result\n", + "print\"FR_x = \",(FR_x),\"N\"\n", + "print\"FR_y = \",(FR_y),\"N\"\n", + "print\"FR_z = \",(FR_z),\"N\"\n", + "print\"x = \",(x),\"m\"\n", + "print\"y = \",(y),\"m\"\n", + "\n" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "collapsed": true + }, + "source": [ + "## Ex 4.20 Page No 148" + ] + }, + { + "cell_type": "code", + "execution_count": 2, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "FR = 160.0 N\n", + "x_bar = 1.5 m\n" + ] + } + ], + "source": [ + "# Example 4.20\n", + "from scipy import integrate\n", + "import numpy as np\n", + "\n", + "# Calculation\n", + "# The coloured differential area element dA = wdx = 60x**(2)\n", + "# Summing these elements from x = 0 to x = 2m we obtain force FR\n", + "# FR = ΣF\n", + "var = lambda x: 60*x**(2)\n", + "a = integrate.quad(var, 0, 2)\n", + "FR = a[0] #[Newton]\n", + "\n", + "# Since the element of area dA is located at distance x from O, the location x_bar of FR is measured from O\n", + "var = lambda x: x*60*x**(2)\n", + "a = integrate.quad(var, 0, 2)\n", + "x_bar = a[0]/FR #[meter]\n", + "\n", + "# Result\n", + "print\"FR = \",(FR),\"N\"\n", + "print\"x_bar = \",(x_bar),\"m\"" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Ex 4.21 Page No 149" + ] + }, + { + "cell_type": "code", + "execution_count": 9, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "FR = 6.48 kN\n", + "x_bar = 6.0 m\n" + ] + } + ], + "source": [ + "# Example 4.21\n", + "from __future__ import division\n", + "\n", + "# Calculation\n", + "# The magnitude of resultant force is equal to the area under the triangle\n", + "FR = (0.5*9*1440)/1000 #[Newton]\n", + "\n", + "# The line of action of FR passes through the centroid C of the triangle\n", + "x_bar = 9-(1/3)*9 #[meter]\n", + "\n", + "# Result\n", + "print\"FR = \",(FR),\"kN\"\n", + "print\"x_bar =\",(x_bar),\"m\"\n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Ex 4.22 Page No 150" + ] + }, + { + "cell_type": "code", + "execution_count": 12, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "FR = 225.0 N\n", + "x_bar = 1.33333333333 m\n" + ] + } + ], + "source": [ + "# Example 4.22\n", + "\n", + "# Calculation\n", + "# Refer Fig 4-50b\n", + "# The magnitude of the force represented by each of these loadings is equal to its associated area\n", + "F1 = 0.5*3*50 #[Newton]\n", + "F2 = 3*50 #[Newton]\n", + "\n", + "# The lines of action of these parallel forces act through the centroid of their associated areas\n", + "x1_bar = (1/3)*3 #[meter]\n", + "x2_bar = (1/2)*3 #[meter]\n", + "\n", + "# +FR(downward) = ΣF\n", + "FR = F1 + F2 #[Newton]\n", + "\n", + "# +MRA(clockwise) = ΣMA\n", + "x_bar = (1*75+1.5*150)/225 #[meter]\n", + "\n", + "# Result\n", + "print\"FR = \",(FR),\"N\"\n", + "print\"x_bar = \",(x_bar),\"m\"" + ] + }, + { + "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": 2 +} diff --git a/Engineering_Mechanics_Statics_and_Dynamics_by_Hibler_and_Gupta/Chapter_5_Equilibrium_of_a_Rigid_Body.ipynb b/Engineering_Mechanics_Statics_and_Dynamics_by_Hibler_and_Gupta/Chapter_5_Equilibrium_of_a_Rigid_Body.ipynb index 9f7c0c55..b3b5669a 100644 --- a/Engineering_Mechanics_Statics_and_Dynamics_by_Hibler_and_Gupta/Chapter_5_Equilibrium_of_a_Rigid_Body.ipynb +++ b/Engineering_Mechanics_Statics_and_Dynamics_by_Hibler_and_Gupta/Chapter_5_Equilibrium_of_a_Rigid_Body.ipynb @@ -1,747 +1,561 @@ - - - - - - - - - - - - - - - - - - - - - - - Python-Textbook-Companions/Chapter_5_Equilibrium_of_a_Rigid_Body.ipynb at 1b1bb67e9ea912be5c8591523c8b328766e3680f · FOSSEE/Python-Textbook-Companions - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
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- - - - - - +{ + "cells": [ + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# Chapter 5 Equilibrium of a Rigid Body" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Ex 5.6 Page No 174 " + ] + }, + { + "cell_type": "code", + "execution_count": 5, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "B_x = 424.3 N\n", + "A_y = 319.5 N\n", + "B_y = 405.3 N\n" + ] + } + ], + "source": [ + "# Example 5.6\n", + "import math\n", + "\n", + "# Calculation\n", + "# Summing forces in the x direction +ΣF_x(right) = 0\n", + "B_x = round(600*math.cos(math.pi*45/180),1) #[Newton]\n", + "\n", + "# Refer Fig 5-14b we have +ΣMB(counterclockwise) = 0\n", + "A_y = round((100*2+600*math.sin(math.pi*45/180)*5-600*math.cos(math.pi*45/180)*0.2)/7,1) #[Newton]\n", + "\n", + "# Summing forces in y direction +ΣF_y(upward) = 0\n", + "B_y = round(-319+600*math.sin(math.pi*45/180)+100+200,1) #[Newton]\n", + "\n", + "# Result\n", + "print\"B_x = \",(B_x),\"N\"\n", + "print\"A_y = \",(A_y),\"N\"\n", + "print\"B_y = \",(B_y),\"N\"\n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Ex 5.7 Page No 175" + ] + }, + { + "cell_type": "code", + "execution_count": 1, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "T = 100.0 N\n", + "A_x = 50.0 N\n", + "A_y = 186.6 N\n" + ] + } + ], + "source": [ + "# Example 5.7\n", + "import math\n", + "from __future__ import division\n", + "\n", + "# Variable Declaration\n", + "F = 100 #[Newton]\n", + "\n", + "# Calculation\n", + "# Summing moments about point A to eliminate A_x and A_y Refer Fig 5-15c\n", + "# +ΣMA(counterclockwise) = 0\n", + "T = round((F*0.5)/0.5,1) #[Newton]\n", + "\n", + "# Using result of T a force summation is applied to determine the components of reaction at pin A\n", + "# +ΣF_x(right) = 0\n", + "A_x = round(F*math.sin(math.pi*30/180),1) #[Newton]\n", + "\n", + "# +ΣF_y(upward) = 0\n", + "A_y = round(F+F*math.cos(math.pi*30/180),1) #[Newton]\n", + " \n", + "# Result\n", + "print\"T = \",(T),\"N\"\n", + "print\"A_x = \",(A_x),\"N\"\n", + "print\"A_y = \",(A_y),\"N\"\n", + " " + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Ex 5.8 Page No 176" + ] + }, + { + "cell_type": "code", + "execution_count": 13, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "A_x = 100.0 N\n", + "A_y = 233.2 N\n" + ] + } + ], + "source": [ + "# Example 5.8\n", + "import math\n", + "\n", + "# Calculation\n", + "# Summing moments about A, we obtain direct solution for NB\n", + "# +ΣMA(counterclockwise) = 0\n", + "NB = (90+60)/0.75 #[Newton]\n", + "\n", + "# +ΣF_x(right) = 0\n", + "A_x = round(NB*math.sin(math.pi*30/180),1) #[Newton]\n", + "\n", + "# +ΣF_y(upward) = 0\n", + "A_y = round(NB*math.cos(math.pi*30/180)+60,1) #[Newton]\n", + "\n", + "# Result\n", + "print\"A_x = \",(A_x),\"N\"\n", + "print\"A_y = \",(A_y),\"N\"" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Ex 5.9 Page No 177" + ] + }, + { + "cell_type": "code", + "execution_count": 14, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "A_x = 5.0 N\n", + "A_y = 74.0 N\n", + "MA = 32.6 N.m\n", + "FA = 74.2 N\n" + ] + } + ], + "source": [ + "# Example 5.9\n", + "import math\n", + "from __future__ import division\n", + "\n", + "# Calculation\n", + "# +ΣF_x(right) = 0\n", + "A_x = round(52*(5/13)-30*math.cos(math.pi*60/180),1) #[Newton]\n", + "# +ΣF_y(upward) = 0\n", + "A_y = round(52*(12/13)+30*math.sin(math.pi*60/180),1) #[Newton]\n", + "# +ΣMA(counterclockwise) = 0\n", + "MA = round(52*(12/13)*0.3+30*math.sin(math.pi*60/180)*0.7,1) #[Newton meter]\n", + "FA = round(math.sqrt(A_x**(2)+A_y**(2)),1) #[Newton]\n", + "theta = math.degrees(math.atan(A_y/A_x)) #[degrees]\n", + "\n", + "# Result\n", + "print\"A_x = \",(A_x),\"N\"\n", + "print\"A_y = \",(A_y),\"N\"\n", + "print\"MA = \",(MA),\"N.m\"\n", + "print\"FA = \",(FA),\"N\"\n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Ex 5.10 Page No 178" + ] + }, + { + "cell_type": "code", + "execution_count": 1, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "C_y_dash = 1.3464 kN\n", + "B_y_dash = -1.0 kN\n", + "A_x = 173.2 Nnn\n" + ] + } + ], + "source": [ + "# Example 5.10\n", + "import math\n", + "import numpy as np\n", + "\n", + "# Calculation\n", + "# Refer Fig 5-18b\n", + "# Using +ΣF_y(upward) = 0 and +ΣMA(counterclockwise) = 0\n", + "a = np.array([[math.cos(math.pi*30/180),math.cos(math.pi*30/180)], [6,2]])\n", + "b = np.array([300,4000+300*math.cos(math.pi*30/180)*8])\n", + "x = np.linalg.solve(a, b)\n", + "C_y_dash = round(x[0],1) #[Newton]\n", + "B_y_dash = round(x[1],1) #[Newton]\n", + "\n", + "# Using +ΣF_x(right) = 0\n", + "A_x = round(C_y_dash*math.sin(math.pi*30/180)+B_y_dash*math.sin(math.pi*30/180),1) #[Newton]\n", + "\n", + "# Result\n", + "print\"C_y_dash = \",(C_y_dash/1000),\"kN\"\n", + "print\"B_y_dash = \",(B_y_dash/1000),\"kN\"\n", + "print\"A_x = \",(A_x),\"N\"" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "collapsed": true + }, + "source": [ + "## Ex 5.11 Page No 181" + ] + }, + { + "cell_type": "code", + "execution_count": 5, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "theta = 60.3 degrees\n", + "FA = 1.07 kN\n", + "F = 1.32 kN\n" + ] + } + ], + "source": [ + "# Example 5.11\n", + "import math\n", + "import numpy as np\n", + "\n", + "# Calculation\n", + "# Since ΣMO = 0 angle theta which defines the line of action of FA can be determined by trigonometry\n", + "theta = round(math.degrees(math.atan(0.7/0.4)),1) #[Degrees]\n", + "\n", + "# Using +ΣF_x(right) = 0 and +ΣF_y(upward) = 0\n", + "a = np.array([[math.cos(math.pi*theta/180),-math.cos(math.pi*45/180)], [math.sin(math.pi*theta/180),-math.sin(math.pi*45/180)]])\n", + "b = np.array([-400,0])\n", + "x = np.linalg.solve(a, b)\n", + "FA = round(x[0]/1000,2) #[Newton]\n", + "F = round(x[1]/1000,2) #[Newton]\n", + "\n", + "# Result\n", + "print\"theta = \",(theta),\"degrees\"\n", + "print\"FA = \",(FA),\"kN\"\n", + "print\"F = \",(F),\"kN\"" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Ex 5.13 Page No 197" + ] + }, + { + "cell_type": "code", + "execution_count": 10, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "B_x = 0 N\n", + "B_y = 0 N\n", + "A_z = 790.5 N\n", + "B_z = -216.7 N\n", + "TC = 707.2 N\n" + ] + } + ], + "source": [ + "# Example 5.13\n", + "\n", + "# Calculation\n", + "# Using ΣF_x = 0ΣF_z = 0\n", + "B_x = 0 #[Newton]\n", + "# Using ΣF_y= 0\n", + "B_y = 0 #[Newton]\n", + "# Using ΣF_z = 0, A_z + B_z + TC = 300 + 981(1)\n", + "# Using ΣM_x = 0, 2TC + 2B_z = 981(2)\n", + "# Using ΣM_y = 0, 3B_z + 3A_z = 300(1.5) + 981(1.5) - 200(3)\n", + "# Solving (1),(2) and (3)\n", + "a = np.array([[1,1,1], [0,2,2],[3,3,0] ])\n", + "b = np.array([300+981,981,300*1.5+981*1.5-200])\n", + "x = np.linalg.solve(a, b)\n", + "A_z = round(x[0],1) #[Newton]\n", + "B_z = round(x[1],1) #[Newton]\n", + "TC = round(x[2],1) #[Newton]\n", + "\n", + "# Result\n", + "print\"B_x = \",(B_x),\"N\"\n", + "print\"B_y = \",(B_y),\"N\"\n", + "print\"A_z = \",(A_z),\"N\"\n", + "print\"B_z = \",(B_z),\"N\"\n", + "print\"TC = \",(TC),\"N\"" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Ex 5.14 Page No 198" + ] + }, + { + "cell_type": "code", + "execution_count": 13, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "P = 377.6 N\n", + "A_z = 424.3 N\n", + "B_z = 934.3 N\n" + ] + } + ], + "source": [ + "# Example 5.14\n", + "import math \n", + "\n", + "# Calculation\n", + "# Using right hand rule and assuming positive moments act in +i direction, ΣM_x = 0\n", + "P = round((981*0.1)/(0.3*math.cos(math.pi*30/180)),1) #[Newton]\n", + "\n", + "# Using this result for P and summing moments about y and z axis, ΣM_y = 0 and ΣM_z = 0\n", + "A_z = round((981*0.5-P*0.4)/0.8,1) #[Newton]\n", + "A_y = -0/0.8 #[Newton]\n", + "\n", + "# The reactions at B are determined by using ΣF_x = 0, ΣF_y = 0 and ΣF_z = 0\n", + "A_x = 0 #[Newton]\n", + "B_y = 0 #[Newton]\n", + "B_z = round(P+981-A_z,1) #[Newton]\n", + "\n", + "# Result\n", + "print\"P = \",(P),\"N\"\n", + "print\"A_z = \",(A_z),\"N\"\n", + "print\"B_z = \",(B_z),\"N\"\n", + "\n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Ex 5.15 Page No 199" + ] + }, + { + "cell_type": "code", + "execution_count": 19, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "TC = 707.5 N\n", + "TD = 1500.0 N\n", + "A_x = -0.0 N\n", + "A_y = 0.0 N\n", + "A_z = 1500.2 N\n" + ] + } + ], + "source": [ + "# Example 5.15\n", + "import numpy as np\n", + "from __future__ import division\n", + "\n", + "# Calculation\n", + "# Summing moments about point A ΣMA = 0, rB X (F+TC+TD)\n", + "# Evaluating cross product\n", + "a = np.array([[0,-4], [4.24,-2]])\n", + "b = np.array([-6000,0])\n", + "x = np.linalg.solve(a, b)\n", + "TC = round(x[0],1) #[Newton]\n", + "TD = round(x[1],1) #[Newton]\n", + "\n", + "# Using ΣF_x = 0\n", + "A_x = round(-0.707*TC+(3/9)*TD,0) #[Newton]\n", + "\n", + "# Using ΣF_y = 0 \n", + "A_y = round(1000-(6/9)*TD,1) #[Newton]\n", + "\n", + "# Using ΣF_z= 0\n", + "A_z = round(0.707*TC+(6/9)*TD,1) #[Newton]\n", + " \n", + "# Result\n", + "print\"TC = \",(TC),\"N\" \n", + "print\"TD = \",(TD),\"N\" \n", + "print\"A_x = \",(A_x),\"N\" \n", + "print\"A_y = \",(A_y),\"N\" \n", + "print\"A_z = \",(A_z),\"N\" " + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Ex 5.16 Page No 200" + ] + }, + { + "cell_type": "code", + "execution_count": 2, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "TD = 100.0 N\n", + "TE = 100.0 N\n", + "A_x = -50.0 N\n", + "A_y = -100.0 N\n", + "A_z = 200 N\n" + ] + } + ], + "source": [ + "# Example 5.16\n", + "from __future__ import division\n", + "\n", + "# Calculation\n", + "# Summing moments about point A, ΣMA = 0 and rC X F + rB X (TE + TD) = 0\n", + "# Using ΣM_x = 0 and ΣM_y = 0\n", + "TD = 200/2 #[Newton]\n", + "TE = 100/2 #[Newton]\n", + "\n", + "# Using ΣF_x = 0, ΣF_y = 0 and ΣF_z = 0\n", + "A_x = -TE #[Newton]\n", + "A_y = -TD #[Newton]\n", + "A_z = 200 #[Newton]\n", + "\n", + "# Result\n", + "print\"TD = \",(TD),\"N\"\n", + "print\"TE = \",(TD),\"N\"\n", + "print\"A_x = \",(A_x),\"N\"\n", + "print\"A_y = \",(A_y),\"N\"\n", + "print\"A_z = \",(A_z),\"N\"" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Ex 5.17 Page No 201" + ] + }, + { + "cell_type": "code", + "execution_count": 23, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "TB = 572.3 N\n" + ] + } + ], + "source": [ + "# Example 5.17\n", + "\n", + "# Calculation\n", + "# Using u.(rB X TB + rE X W)\n", + "TB = round(490.5/0.857,1) #[Newton]\n", + "\n", + "print\"TB = \",(TB),\"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 +} diff --git a/Engineering_Mechanics_Statics_and_Dynamics_by_Hibler_and_Gupta/Chapter_6_Structural_Analysis.ipynb b/Engineering_Mechanics_Statics_and_Dynamics_by_Hibler_and_Gupta/Chapter_6_Structural_Analysis.ipynb index f1c24925..4fe7e652 100644 --- a/Engineering_Mechanics_Statics_and_Dynamics_by_Hibler_and_Gupta/Chapter_6_Structural_Analysis.ipynb +++ b/Engineering_Mechanics_Statics_and_Dynamics_by_Hibler_and_Gupta/Chapter_6_Structural_Analysis.ipynb @@ -1,747 +1,768 @@ - - - - - - - - - - - - - - - - - - - - - - - Python-Textbook-Companions/Chapter_6_Structural_Analysis.ipynb at 1b1bb67e9ea912be5c8591523c8b328766e3680f · FOSSEE/Python-Textbook-Companions - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
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- - - - - - +{ + "cells": [ + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# Chapter 6 Structural Analysis" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Ex 6.1 Page No 212" + ] + }, + { + "cell_type": "code", + "execution_count": 6, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "FBC = 707.1 N\n", + "FBA = 500.0 N\n", + "FCA = 500.0 N\n", + "C_y = 500.0 N\n", + "A_x = 500 N\n", + "A_y = 500 N\n" + ] + } + ], + "source": [ + "# Example 6.1\n", + "import math\n", + "\n", + "# Calculation\n", + "\n", + "# Joint B\n", + "# Using +ΣF_x(right) = 0\n", + "FBC = round(500/math.sin(math.pi*45/180),1) #[Newton]\n", + "\n", + "# Using +ΣF_y(upward) = 0\n", + "FBA = round(FBC*math.cos(math.pi*45/180),1) #[Newton]\n", + "\n", + "# Joint C\n", + "# Using +ΣF_x(right) = 0\n", + "FCA = round(FBC*math.cos(math.pi*45/180),1) #[Newton]\n", + "\n", + "# Using +ΣF_y(upward) = 0\n", + "C_y = round(FBC*math.sin(math.pi*45/180),1) #[Newton]\n", + "\n", + "# Joint A\n", + "# # Using +ΣF_x(right) = 0\n", + "A_x = 500 #[Newton]\n", + "A_y = 500 #[Newton]\n", + "\n", + "# Result\n", + "print\"FBC = \",(FBC),\"N\"\n", + "print\"FBA = \",(FBA),\"N\"\n", + "print\"FCA = \",(FCA),\"N\"\n", + "print\"C_y = \",(C_y),\"N\"\n", + "print\"A_x = \",(A_x),\"N\"\n", + "print\"A_y = \",(A_y),\"N\"\n", + "\n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Ex 6.2 Page No 213" + ] + }, + { + "cell_type": "code", + "execution_count": 8, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "FCB = 5.02 kN\n", + "FCD = 4.1 kN\n", + "FDA = 4.1 kN\n", + "FDB = 4.1 kN\n" + ] + } + ], + "source": [ + "# Example 6.2\n", + "import math\n", + "import numpy as np\n", + "\n", + "# Calculation\n", + "# Joint C\n", + "# Using +ΣF_x(right) = 0 and +ΣF_y(upward) = 0\n", + "a = np.array([[-math.cos(math.pi*30/180),math.sin(math.pi*45/180)],[math.sin(math.pi*30/180),-math.cos(math.pi*45/180)]])\n", + "b = np.array([0,-1.5])\n", + "x = np.linalg.solve(a, b)\n", + "FCD = round(x[0],2) #[kilo Newton]\n", + "FCB = round(x[1],2) #[kilo Newton]\n", + "\n", + "# Calculation\n", + "# Joint D\n", + "# Using +ΣF_x(right) = 0\n", + "FDA = round(FCD*math.cos(math.pi*30/180)/math.cos(math.pi*30/180),2) #[kilo Newton]\n", + "# Using +ΣF_y(upward) = 0\n", + "FDB = round(2*FCD*math.sin(math.pi*30/180),2) #[kilo Newton]\n", + "\n", + "# Result\n", + "print\"FCB = \",(FCB),\"kN\"\n", + "print\"FCD = \",(FCD),\"kN\"\n", + "print\"FDA = \",(FDA),\"kN\"\n", + "print\"FDB = \",(FDB),\"kN\"\n", + "\n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Ex 6.3 Page No 214" + ] + }, + { + "cell_type": "code", + "execution_count": 24, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "FAB = 750.0 N\n", + "FAD = 450.0 N\n", + "FDB = -250.0 N\n", + "FDC = 200.0 N\n", + "FCB = 600 N\n" + ] + } + ], + "source": [ + "# Example 6.3\n", + "from __future__ import division\n", + "\n", + "# Calculation\n", + "# Using +ΣF_x(right) = 0\n", + "C_x = 600 #[Newton]\n", + "# Using +ΣMC(counterclockwise) = 0\n", + "A_y = (400*3+600*4)/6 #[Newton]\n", + "# Using +ΣF_y(upward) = 0\n", + "C_y = A_y - 400 #[Newton]\n", + "\n", + "# Joint A\n", + "# Using +ΣF_y(upward) = 0\n", + "FAB = 600*(5/4) #[Newton]\n", + "# Using +ΣF_x(right) = 0\n", + "FAD = (3/5)*FAB #[Newton]\n", + "\n", + "# Joint D\n", + "# Using +ΣF_x(right) = 0\n", + "FDB = (450-600)*(5/3) #[Newton]\n", + "# Using +ΣF_y(upward) = 0\n", + "FDC = (-4/5)*(FDB) #[Newton]\n", + "\n", + "# Joint C\n", + "# Using +ΣF_x(right) = 0\n", + "FCB = 600 #[Newton]\n", + "\n", + "# Result\n", + "print\"FAB = \",(FAB),\"N\"\n", + "print\"FAD = \",(FAD),\"N\"\n", + "print\"FDB = \",(FDB),\"N\"\n", + "print\"FDC = \",(FDC),\"N\"\n", + "print\"FCB = \",(FCB),\"N\"\n" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "collapsed": true + }, + "source": [ + "## Ex 6.4 Page No 218" + ] + }, + { + "cell_type": "code", + "execution_count": 1, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "FGC = 0 N\n", + "FDF= 0 N\n" + ] + } + ], + "source": [ + "# Example 6.4\n", + "\n", + "# Calculation\n", + "# Using +ΣF_y(upward) = 0 at joint G\n", + "FGC = 0 #[Newton]\n", + "\n", + "# GC is a zero force menber means that 5-kN load at C must be supported by members CB,CH,CF and CD\n", + "# Using +ΣF_y(upward) = 0 at joint F\n", + "FDF = 0 #[Newton]\n", + "\n", + "# Result\n", + "print\"FGC = \",(FGC),\"N\"\n", + "print\"FDF= \",(FDF),\"N\"\n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Ex 6.5 Page No 225" + ] + }, + { + "cell_type": "code", + "execution_count": 25, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "FBC = 800.0 N\n", + "FGE = 800.0 N\n", + "FGC = 500.0 N\n" + ] + } + ], + "source": [ + "# Example 6.5\n", + "from __future__ import division\n", + "\n", + "# Calculation\n", + "# Applying equations of equilibrium\n", + "# Using +ΣF_x(right) = 0\n", + "A_x = 400 #[Newton]\n", + "\n", + "# Using +ΣMA(counterclockwise) = 0\n", + "D_y = (400*3+1200*8)/12 #[Newton]\n", + "\n", + "# Using +ΣF_y(upward) = 0\n", + "A_y = 1200-900 #[Newton]\n", + "\n", + "# Using +ΣMG(counterclockwise) = 0\n", + "FBC = (400*3+300*4)/3 #[Newton]\n", + "\n", + "# Using +ΣMC(counterclockwise) = 0\n", + "FGE = (300*8)/3 #[Newton]\n", + "\n", + "# Using +ΣF_y(upward) = 0\n", + "FGC = (300*5)/3 #[Newton]\n", + "\n", + "# Result\n", + "print\"FBC = \",(FBC),\"N\"\n", + "print\"FGE = \",(FGE),\"N\"\n", + "print\"FGC = \",(FGC),\"N\"" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Ex 6.6 Page No 226" + ] + }, + { + "cell_type": "code", + "execution_count": 12, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "FCF = 0.589 kN\n" + ] + } + ], + "source": [ + "# Example 6.6\n", + "import math\n", + "from __future__ import division\n", + "\n", + "# Calculation\n", + "# Using +ΣMO(counterclockwise) = 0\n", + "FCF = round((3*8-4.75*4)/(12*math.sin(math.pi*45/180)),3) #[kilo Newton]\n", + "\n", + "# Result\n", + "print\"FCF = \",(FCF),\"kN\"\n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Ex 6.7 Page No 227" + ] + }, + { + "cell_type": "code", + "execution_count": 13, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "FEB = 2000.0 N\n" + ] + } + ], + "source": [ + "# Example 6.7\n", + "import math\n", + "\n", + "# Calculation\n", + "# Using +ΣMB(counterclockwise) = 0\n", + "FED = (-1000*4-3000*2+4000*4)/(math.sin(math.pi*30/180)*4) #[Newton]\n", + "\n", + "# Using +ΣF_x(right) = 0 for section bb Fig 6-18c\n", + "FEF = 3000*math.cos(math.pi*30/180)/math.cos(math.pi*30/180) #[Newton]\n", + "\n", + "# Using +ΣF_y(upward) = 0\n", + "FEB = 2*3000*math.sin(math.pi*30/180)-1000 #[Newton]\n", + "\n", + "# Result\n", + "print\"FEB = \",(FEB),\"N\"" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Ex 6.8 Page No 231" + ] + }, + { + "cell_type": "code", + "execution_count": 14, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "FAE = 0.0 kN\n", + "FAB = 4.0 kN\n", + "FAC = 0.0 kN\n", + "RB = 5.66 kN\n", + "FBE = 5.66 kN\n", + "FBD = 2.0 kN\n", + "FDE = 0 kN\n", + "FDC = 0 kN\n", + "FCE = 0 kN\n" + ] + } + ], + "source": [ + "# Example 6.8\n", + "import numpy as np\n", + "import math\n", + "\n", + "# Calculation\n", + "# At joint A, ΣF_x = 0, ΣF_y = 0, ΣF_z = 0\n", + "a = np.array([[0.577,0,0],[0.577,1,0],[-0.577,0,-1]])\n", + "b = np.array([0,4,0])\n", + "x = np.linalg.solve(a, b)\n", + "FAE = round(x[0],2) #[kilo Newton]\n", + "FAB = round(x[1],2) #[kilo Newton]\n", + "FAC = round(x[2],2) #[kilo Newton]\n", + "\n", + "# At joint B, ΣF_x = 0, ΣF_y = 0, ΣF_z = 0\n", + "a = np.array([[-math.cos(math.pi*45/180),0.707,0],[math.sin(math.pi*45/180),0,0],[0,-0.707,1]])\n", + "b = np.array([0,4,-2])\n", + "x = np.linalg.solve(a, b)\n", + "RB = round(x[0],2) #[kilo Newton]\n", + "FBE = round(x[1],2) #[kilo Newton]\n", + "FBD = round(x[2],2) #[kilo Newton]\n", + "\n", + "# The scalar equation of equilibrium can be applied at joints D and C\n", + "FDE = FDC = FCE = 0 #[kilo Newton]\n", + "\n", + "# Result\n", + "print\"FAE = \",(FAE),\"kN\"\n", + "print\"FAB = \",(FAB),\"kN\"\n", + "print\"FAC = \",(-FAC),\"kN\"\n", + "print\"RB = \",(RB),\"kN\"\n", + "print\"FBE = \",(FBE),\"kN\"\n", + "print\"FBD = \",(FBD),\"kN\"\n", + "print\"FDE = \",(FDE),\"kN\"\n", + "print\"FDC = \",(FDC),\"kN\"\n", + "print\"FCE = \",(FCE),\"kN\"" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Ex 6.14 Page No 241" + ] + }, + { + "cell_type": "code", + "execution_count": 18, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "C_x = 577.4 N\n", + "C_y = 1000.0 N\n" + ] + } + ], + "source": [ + "# Example 6.14\n", + "import math\n", + "from __future__ import division\n", + "\n", + "# Calculation\n", + "\n", + "# Solution 1\n", + "# Applying equations of equilibrium to member CB\n", + "# Using +ΣMC(counterclockwise) = 0\n", + "FAB = round((2000*2)/(math.sin(math.pi*60/180)*4),1) #[Newton meter]\n", + "# Using +ΣF_x(right) = 0\n", + "C_x = round(FAB*math.cos(math.pi*60/180),1) #[Newton]\n", + "# Using +ΣF_y(upward) = 0\n", + "C_y = round(-FAB*math.sin(math.pi*60/180)+2000,1) #[Newton]\n", + "\n", + "# Solution 2 \n", + "# Using +ΣMC(counterclockwise) = 0 at Member BC\n", + "B_y = (2000*2)/4 #[Newton]\n", + "# Using +ΣMA(counterclockwise) = 0 at Member AB\n", + "B_x = round(B_y*3*math.cos(math.pi*60/180)/(3*math.sin(math.pi*60/180)),1) #[Newton]\n", + "# Using +ΣF_y(upward) = 0 at member BC\n", + "C_x = B_x #[Newton]\n", + "C_y = 2000-B_y #[Newton]\n", + "# Result\n", + "print\"C_x = \",(C_x),\"N\"\n", + "print\"C_y = \",(C_y),\"N\"" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Ex 6.15 Page No 242" + ] + }, + { + "cell_type": "code", + "execution_count": 20, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "A_x = 6.0 kN\n", + "A_y = 12.0 kN\n", + "MA = 32.0 kN.m\n", + "B_x = 0 kN\n", + "B_y = 4.0 kN\n", + "C_y = 4.0 kN\n" + ] + } + ], + "source": [ + "# Example 6.15\n", + "from __future__ import division\n", + "\n", + "# Calculation\n", + "# Using +ΣF_x(right) = 0 at member BC\n", + "B_x = 0 #[kilo Newton]\n", + "# Using +ΣMB(counterclockwise) = 0 at member BC\n", + "C_y = (8*1)/2 #[kilo Newton]\n", + "# Using +ΣF_y(upward) = 0 at member BC\n", + "B_y = 8-C_y #[kilo Newton]\n", + "# Using +ΣF_x(right) = 0 at member AB\n", + "A_x = 10*(3/5)-B_x #[kilo Newton]\n", + "# Using +ΣMA(counterclockwise) = 0 at member AB\n", + "MA = 10*(4/5)*2+B_y*4 #[kilo Newton meter]\n", + "# Using +ΣF_y(upward) = 0 at member AB\n", + "A_y = 10*(4/5)+B_y #[kilo Newton]\n", + "\n", + "# Result\n", + "print\"A_x = \",(A_x),\"kN\"\n", + "print\"A_y = \",(A_y),\"kN\"\n", + "print\"MA = \",(MA),\"kN.m\"\n", + "print\"B_x = \",(B_x),\"kN\"\n", + "print\"B_y = \",(B_y),\"kN\"\n", + "print\"C_y = \",(C_y),\"kN\"\n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Ex 6.16 Page No 243" + ] + }, + { + "cell_type": "code", + "execution_count": 21, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "C_x = 1226.3 N\n", + "C_y = -245.3 N\n" + ] + } + ], + "source": [ + "# Example 6.16\n", + "import math\n", + "\n", + "# Calculation\n", + "# Using +ΣMA(counterclockwise) = 0\n", + "D_x = (981*2)/2.8 #[Newton]\n", + "# Using +ΣF_x(right) = 0\n", + "A_x = D_x #[Newton]\n", + "# Using +ΣF_y(upward) = 0\n", + "A_y = 981 #[Newton]\n", + "\n", + "# Consider member CEF\n", + "# Using +ΣMC(counterclockwise) = 0\n", + "FB = round((-981*2)/(math.sin(math.pi*45/180)*1.6),1) #[Newton]\n", + "# Using +ΣF_x(right) = 0\n", + "C_x = round(-FB*math.cos(math.pi*45/180),1) #[Newton]\n", + "# Using +ΣF_y(upward) = 0\n", + "C_y = round(FB*math.sin(math.pi*45/180)+981,1) #[Newton]\n", + "\n", + "# Result\n", + "print\"C_x = \",(C_x),\"N\"\n", + "print\"C_y = \",(C_y),\"N\"" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "collapsed": true + }, + "source": [ + "## Ex 6.17 Page No 243" + ] + }, + { + "cell_type": "code", + "execution_count": 22, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "B_x = 18.2 N\n", + "B_y = 20 N\n", + "D_x = 0 N\n", + "D_y = 20 N\n" + ] + } + ], + "source": [ + "# Example 6.17\n", + "\n", + "# Calculation\n", + "# Consider entire frame\n", + "# Using +ΣMA(counterclockwise) = 0\n", + "C_x = (20*1)/1.1 #[Newton]\n", + "# Using +ΣF_x(right) = 0\n", + "A_x = 18.2 #[Newton]\n", + "A_y = 20 #[Newton]\n", + "\n", + "# Consider member AB\n", + "# Using +ΣF_x(right) = 0\n", + "B_x= 18.2 #[Newton]\n", + "# Using +ΣMB(counterclockwise) = 0\n", + "ND = (20*2)/1 #[Newton]\n", + "# Using +ΣF_y(upward) = 0\n", + "B_y = 40-20 #[Newton]\n", + "\n", + "# Consider Disk\n", + "# Using +ΣF_x(right) = 0\n", + "D_x = 0 #[Newton]\n", + "# Using +ΣF_y(upward) = 0\n", + "D_y = 40-20 #[Newton]\n", + "\n", + "# Result\n", + "print\"B_x = \",(B_x),\"N\"\n", + "print\"B_y = \",(B_y),\"N\"\n", + "print\"D_x = \",(D_x),\"N\"\n", + "print\"D_y = \",(D_y),\"N\"" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Ex 6.18 Page No 245" + ] + }, + { + "cell_type": "code", + "execution_count": 3, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "P = 200 N\n", + "T = 400 N\n", + "R = 800 N\n" + ] + } + ], + "source": [ + "# Example 6.18\n", + "\n", + "# Calculation\n", + "# Using equations of equilibrium\n", + "\n", + "# Pulley A\n", + "# Using +ΣF_y(upward) = 0\n", + "P = 600/3 #[Newton]\n", + "\n", + "# Pulley B\n", + "# Using +ΣF_y(upward) = 0\n", + "T = 2*P #[Newton]\n", + "\n", + "# Pulley C\n", + "# Using +ΣF_y(upward) = 0\n", + "R = 2*P+T #[Newton]\n", + "\n", + "# Result\n", + "print\"P = \",(P),\"N\"\n", + "print\"T = \",(T),\"N\"\n", + "print\"R = \",(R),\"N\"\n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Ex 6.19 Page No 246" + ] + }, + { + "cell_type": "code", + "execution_count": 23, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "B_x = 346.8 N\n", + "B_y = 837.3 N\n", + "FCB = 1659.8 N\n", + "FAB = 1342.7 N\n" + ] + } + ], + "source": [ + "# Example 6.19\n", + "import math\n", + "from __future__ import division\n", + "\n", + "# Calculation\n", + "# Applying equations of equilibrium to pulley B\n", + "# Using +ΣF_x(right) = 0\n", + "B_x = round(490.5*math.cos(math.pi*45/180),1) #[Newton]\n", + "# Using +ΣF_y(upward) = 0\n", + "B_y = round(490.5*math.sin(math.pi*45/180)+490.5,1) #[Newton]\n", + "\n", + "# Applying equations of equilibrium to pin\n", + "# Using +ΣF_y(upward) = 0\n", + "FCB = round((B_y+490.5)*(5/4),1) #[Newton]\n", + "# Using +ΣF_x(right) = 0\n", + "FAB = round((3/5)*FCB+B_x,1) #[Newton]\n", + "\n", + "# Result\n", + "print\"B_x = \",(B_x),\"N\"\n", + "print\"B_y = \",(B_y),\"N\"\n", + "print\"FCB = \",(FCB),\"N\"\n", + "print\"FAB = \",(FAB),\"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 +} diff --git a/Engineering_Mechanics_Statics_and_Dynamics_by_Hibler_and_Gupta/Chapter_7_Internal_Forces.ipynb b/Engineering_Mechanics_Statics_and_Dynamics_by_Hibler_and_Gupta/Chapter_7_Internal_Forces.ipynb index 3ef7d79a..013e54d4 100644 --- a/Engineering_Mechanics_Statics_and_Dynamics_by_Hibler_and_Gupta/Chapter_7_Internal_Forces.ipynb +++ b/Engineering_Mechanics_Statics_and_Dynamics_by_Hibler_and_Gupta/Chapter_7_Internal_Forces.ipynb @@ -1,747 +1,391 @@ - - - - - - - - - - - - - - - - - - - - - - - Python-Textbook-Companions/Chapter_7_Internal_Forces.ipynb at 1b1bb67e9ea912be5c8591523c8b328766e3680f · 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- - - - - - +{ + "cells": [ + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# Chapter 7 Internal Forces" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Ex 7.1 Page no 261" + ] + }, + { + "cell_type": "code", + "execution_count": 16, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "A_y = 8 kN\n", + "NC = 4 kN\n" + ] + } + ], + "source": [ + "# Example 7.1\n", + "\n", + "# Calculation\n", + "# Applying +ΣF_y(upward) = 0 Refer fig 7-4b\n", + "A_y = 16+4-12 #[kilo Newton]\n", + "\n", + "# Applying +ΣF_y(upward) = 0 to segment AB\n", + "NB = 8 #[kilo Newton]\n", + "\n", + "# Applying +ΣF_y(upward) = 0 to segment DC\n", + "NC = 4 #[kilo Newton]\n", + "\n", + "# Result\n", + "print\"A_y = \",(A_y),\"kN\"\n", + "print\"NC = \",(NC),\"kN\"\n", + "\n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Ex 7.2 Page no 262" + ] + }, + { + "cell_type": "code", + "execution_count": 5, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "TB = 5 N.m\n", + "TC = 25 N.m\n" + ] + } + ], + "source": [ + "# Example 7.2\n", + "\n", + "# Calculation\n", + "# Applying +ΣM_x = 0 Refer fig 7-5b\n", + "TD = -10+15+20 #[Newton meter]\n", + "\n", + "# Applying +ΣM_x = 0 to segment AB\n", + "TB = -10+15 #[Newton meter]\n", + "\n", + "# Applying +ΣM_x = 0 to segment CD\n", + "TC = 25 #[Newton meter]\n", + "\n", + "# Result\n", + "print\"TB = \",(TB),\"N.m\"\n", + "print\"TC = \",(TC),\"N.m\"\n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Ex 7.3 Page no 263" + ] + }, + { + "cell_type": "code", + "execution_count": 4, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "NB = 0 kN\n", + "VB = 5 kN\n", + "MB = 15 kN.m\n", + "NC = 0 kN\n", + "VC = 1 kN\n", + "MC = 15 kN.m\n" + ] + } + ], + "source": [ + "# Example 7.3\n", + "from __future__ import division\n", + "\n", + "# Calculation\n", + "# Applying +ΣMD(counterclockwise) = 0 Refer fig 7-6b\n", + "A_y = (9+6*6)/9\n", + "\n", + "# Consider segment AB\n", + "# Applying +ΣF_x(right) = 0\n", + "NB = 0 #[kilo Newton]\n", + "# Applying +ΣF_y(upward) = 0\n", + "VB = 5 #[kilo Newton]\n", + "# Applying +ΣMB(counterclockwise) = 0 \n", + "MB = 5*3 #[kilo Newton meter]\n", + "\n", + "# Consider segment AC\n", + "# Applying +ΣF_x(right) = 0\n", + "NC = 0 #[kilo Newton]\n", + "# Applying +ΣF_y(upward) = 0\n", + "VC = 6-5 #[kilo Newton]\n", + "# Applying +ΣMC(counterclockwise) = 0\n", + "MC = 5*3 #[kilo Newton meter]\n", + "\n", + "# Result\n", + "print\"NB = \",(NB),\"kN\"\n", + "print\"VB = \",(VB),\"kN\"\n", + "print\"MB = \",(MB),\"kN.m\"\n", + "print\"NC = \",(NB),\"kN\"\n", + "print\"VC = \",(VC),\"kN\"\n", + "print\"MC = \",(MC),\"kN.m\"" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Ex 7.4 Page no 264" + ] + }, + { + "cell_type": "code", + "execution_count": 15, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "NB = 266.7 N\n", + "VB = 0 N\n", + "MB = 400 N.m\n" + ] + } + ], + "source": [ + "# Example 7.4\n", + "from __future__ import division\n", + "\n", + "# Calculation\n", + "# Refer fig 7-7b\n", + "# Applying +ΣMA(counterclockwise) = 0\n", + "FDC = (400*4)/((3/5)*8) #[Newton]\n", + "# Applying +ΣF_x(right) = 0\n", + "A_x = (4/5)*333.3 #[Newton]\n", + "# Applying +ΣF_y(upward) = 0\n", + "A_y = 400-((3/5)*333.3) #[Newton]\n", + "\n", + "# Applying equations of equilibrium to segment AB\n", + "# Applying +ΣF_x(right) = 0\n", + "NB = 266.7 #[Newton]\n", + "# Applying +ΣF_y(upward) = 0\n", + "VB = 200-200 #[Newton]\n", + "# Applying +ΣMB(counterclockwise) = 0\n", + "MB = 200*4-200*2 #[Newton meter]\n", + "\n", + "# Result\n", + "print\"NB = \",(NB),\"N\"\n", + "print\"VB = \",(VB),\"N\"\n", + "print\"MB = \",(MB),\"N.m\"" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Ex 7.5 Page no 265" + ] + }, + { + "cell_type": "code", + "execution_count": 14, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "VE = 600.0 N\n", + "NE = 600.0 N\n", + "ME = 300.0 N.m\n" + ] + } + ], + "source": [ + "# Example 7.5\n", + "import math\n", + "\n", + "# Calculation\n", + "# Using +ΣF_y(upward) = 0 Refer fig 7-8b\n", + "R = round(600/math.sin(math.pi*45/180),1) #[Newton]\n", + "# Applying equations of equilibrium \n", + "# Applying +ΣF_x(right) = 0\n", + "VE = round(R*math.cos(math.pi*45/180),1) #[Newton]\n", + "# Applying +ΣF_y(upward) = 0\n", + "NE = round(R*math.sin(math.pi*45/180),1) #[Newton]\n", + "# Applying +ΣME(counterclockwise) = 0\n", + "ME = round(R*math.cos(math.pi*45/180)*0.5,1) #[Newton meter]\n", + "\n", + "# Result\n", + "print\"VE = \",(VE),\"N\"\n", + "print\"NE = \",(NE),\"N\"\n", + "print\"ME = \",(ME),\"N.m\"\n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Ex 7.6 Page no 266" + ] + }, + { + "cell_type": "code", + "execution_count": 13, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "MA_x = -19.1 kN.m\n", + "MA_y = 70.9 kN.m\n", + "MA_z = -40.5 kN.m\n" + ] + } + ], + "source": [ + "# Example 7.6\n", + "from __future__ import division\n", + "import numpy as np\n", + "\n", + "# Calculation\n", + "W = 650*9.81 #[kilo Newton]\n", + "Fw = 900/(6*2.5) #[kilo Newton]\n", + "# Using +ΣF_x(right) = 0\n", + "FA_x = 13.5 #[kilo Newton]\n", + "FA_y = 0 #[kilo Newton]\n", + "FA_z = 6.376 #[kilo Newton]\n", + "# Using ΣMA = 0, MA + r X (Fw + W)\n", + "a = np.cross([0,3,5.25],[-13.5,0,6.376])\n", + "MA_x = round(-a[0],1) #[kilo Newton meter]\n", + "MA_y = round(-a[1],1) #[kilo Newton meter]\n", + "MA_z = round(-a[2],1) #[kilo Newton meter]\n", + "\n", + "# Result\n", + "print\"MA_x = \",(MA_x),\"kN.m\"\n", + "print\"MA_y = \",(MA_y),\"kN.m\"\n", + "print\"MA_z = \",(MA_z),\"kN.m\" # Correction in MA_z\n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Ex 7.13 Page no 286" + ] + }, + { + "cell_type": "code", + "execution_count": 30, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "TBC = 10.2 kN\n", + "TAB = 13.6 kN\n", + "TCD = 9.5 kN\n", + "TED = 11.8 kN\n" + ] + } + ], + "source": [ + "# Example 7.13\n", + "from __future__ import division\n", + "import math \n", + "\n", + "# Calculation\n", + "# Consider free body diagram Refer fig 7-21b\n", + "# Using +ΣME(counterclockwise) = 0\n", + "A_y = (4*15+15*10+3*2)/18 #[kilo Newton]\n", + "# Using +ΣF_y(upward) = 0\n", + "E_y = -12+4+15+3 #[kilo Newton]\n", + "\n", + "# Consider leftmost section which cuts cable BC Refer fig 7-21b\n", + "# Using +ΣMC(counterclockwise) = 0\n", + "A_x = (12*8-4*5)/12 #[kilo Newton]\n", + "thetaBC = round(math.degrees(math.atan((12-4)/6.33)),1) #[Degrees]\n", + "# Using +ΣF_x(right) = 0\n", + "TBC = round(6.33/math.cos(math.pi*thetaBC/180),1) #[kilo Newton]\n", + "thetaAB = round(math.degrees(math.atan(12/6.33)),1) #[Degrees]\n", + "\n", + "# Applying +ΣF_x(right) = 0 at point A\n", + "TAB = round(12/math.sin(math.pi*thetaAB/180),1) #[kilo Newton]\n", + "thetaCD = round(math.degrees(math.atan((-10.2*math.sin(math.pi*51.6/180)+15)/(10.2*math.cos(math.pi*51.6/180)))),1) #[Degrees]\n", + "\n", + "# Applying +ΣF_x(right) = 0 at point C\n", + "TCD = round((10.2*math.cos(math.pi*51.6/180))/math.cos(math.pi*thetaCD/180),1) #[kilo Newton]\n", + "thetaED = round(math.degrees(math.atan(10/6.33)),1) #[Degrees]\n", + "\n", + "# Applying +ΣF_x(right) = 0 at point E\n", + "TED = round(10/math.sin(math.pi*thetaED/180),1) #[kilo Newton]\n", + "\n", + "print\"TBC = \",(TBC),\"kN\"\n", + "print\"TAB = \",(TAB),\"kN\"\n", + "print\"TCD = \",(TCD),\"kN\"\n", + "print\"TED = \",(TED),\"kN\" " + ] + }, + { + "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 +} diff --git a/Engineering_Mechanics_Statics_and_Dynamics_by_Hibler_and_Gupta/Chapter_8_Friction.ipynb b/Engineering_Mechanics_Statics_and_Dynamics_by_Hibler_and_Gupta/Chapter_8_Friction.ipynb index 6169188d..f2059979 100644 --- a/Engineering_Mechanics_Statics_and_Dynamics_by_Hibler_and_Gupta/Chapter_8_Friction.ipynb +++ b/Engineering_Mechanics_Statics_and_Dynamics_by_Hibler_and_Gupta/Chapter_8_Friction.ipynb @@ -1,747 +1,406 @@ - - - - - - - - - - - - - - - - - - - - - - - Python-Textbook-Companions/Chapter_8_Friction.ipynb at 1b1bb67e9ea912be5c8591523c8b328766e3680f · FOSSEE/Python-Textbook-Companions - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
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- - - - - - +{ + "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 +} diff --git a/Engineering_Mechanics_Statics_and_Dynamics_by_Hibler_and_Gupta/Chapter_9_Center_of_Gravity_and_Centroid.ipynb b/Engineering_Mechanics_Statics_and_Dynamics_by_Hibler_and_Gupta/Chapter_9_Center_of_Gravity_and_Centroid.ipynb index fc33d098..92c855af 100644 --- a/Engineering_Mechanics_Statics_and_Dynamics_by_Hibler_and_Gupta/Chapter_9_Center_of_Gravity_and_Centroid.ipynb +++ b/Engineering_Mechanics_Statics_and_Dynamics_by_Hibler_and_Gupta/Chapter_9_Center_of_Gravity_and_Centroid.ipynb @@ -1,747 +1,537 @@ - - - - - - - - - - - - - - - - - - - - - - - Python-Textbook-Companions/Chapter_9_Center_of_Gravity_and_Centroid.ipynb at 1b1bb67e9ea912be5c8591523c8b328766e3680f · FOSSEE/Python-Textbook-Companions - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
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- - - - - - +{ + "cells": [ + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# Chapter 9 Center of Gravity and Centroid" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Ex 9.1 Page No 337" + ] + }, + { + "cell_type": "code", + "execution_count": 12, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "xbar = 0.41 m\n", + "ybar = 0.574 m\n" + ] + } + ], + "source": [ + "# Example 9.1\n", + "from scipy import integrate\n", + "import math\n", + "\n", + "# Calculation\n", + "a = lambda y: y**(2)*math.sqrt(4*y**(2)+1)\n", + "b = lambda y: math.sqrt(4*y**(2)+1)\n", + "xbar = integrate.quad(a, 0, 1)[0]/integrate.quad(b, 0, 1)[0] #[meter]\n", + "\n", + "c = lambda y: y*math.sqrt(4*y**(2)+1)\n", + "d = lambda y: math.sqrt(4*y**(2)+1)\n", + "ybar = integrate.quad(c, 0, 1)[0]/integrate.quad(d, 0, 1)[0] #[meter]\n", + "\n", + "# Result\n", + "print\"xbar = \",round(xbar,3),\"m\"\n", + "print\"ybar = \",round(ybar,3),\"m\"" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Ex 9.5 Page No 342" + ] + }, + { + "cell_type": "code", + "execution_count": 18, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Solution 1\n", + "xbar = 0.75 m\n", + "ybar = 0.3 m\n", + "\n", + "Solution 2\n", + "xbar = 0.75 m\n", + "ybar = 0.3 m\n" + ] + } + ], + "source": [ + "# Example 9.5\n", + "from scipy import integrate\n", + "import math\n", + "from __future__ import division\n", + "\n", + "# Calculation\n", + "# Solution 1\n", + "a = lambda x: x**(3)\n", + "b = lambda x: x**(2)\n", + "xbar = integrate.quad(a, 0, 1)[0]/integrate.quad(b, 0, 1)[0] #[meter]\n", + "c = lambda x: (x**(4))/2\n", + "d = lambda x: x**(2)\n", + "ybar = integrate.quad(c, 0, 1)[0]/integrate.quad(d, 0, 1)[0] #[meter]\n", + "\n", + "# Result Solution 1\n", + "print\"Solution 1\"\n", + "print\"xbar = \",round(xbar,3),\"m\"\n", + "print\"ybar = \",round(ybar,3),\"m\\n\"\n", + "\n", + "# Solution 2\n", + "a = lambda y: (1-y)/2\n", + "b = lambda y: 1-math.sqrt(y)\n", + "xbar = integrate.quad(a, 0, 1)[0]/integrate.quad(b, 0, 1)[0] #[meter]\n", + "c = lambda y: y-y**(3/2)\n", + "d = lambda y: 1-math.sqrt(y)\n", + "ybar = integrate.quad(c, 0, 1)[0]/integrate.quad(d, 0, 1)[0] #[meter]\n", + "\n", + "# Result Solution 2\n", + "print\"Solution 2\"\n", + "print\"xbar = \",round(xbar,3),\"m\"\n", + "print\"ybar = \",round(ybar,3),\"m\"" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Ex 9.6 Page No 343" + ] + }, + { + "cell_type": "code", + "execution_count": 19, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Solution 1\n", + "xbar = 0.5 m\n", + "\n", + "Solution 2\n", + "xbar = 0.5 m\n" + ] + } + ], + "source": [ + "# Example 9.6\n", + "from scipy import integrate\n", + "import math\n", + "from __future__ import division\n", + "\n", + "# Calculation\n", + "# Solution 1\n", + "a = lambda x: x*(x-x**(2))\n", + "b = lambda x: (x-x**(2))\n", + "xbar = integrate.quad(a, 0, 1)[0]/integrate.quad(b, 0, 1)[0] #[meter]\n", + "\n", + "\n", + "# Result Solution 1\n", + "print\"Solution 1\"\n", + "print\"xbar = \",round(xbar,3),\"m\\n\"\n", + "\n", + "\n", + "# Solution 2\n", + "a = lambda y: ((math.sqrt(y)+y)/2)*(math.sqrt(y)-y)\n", + "b = lambda y: math.sqrt(y)-y\n", + "xbar = integrate.quad(a, 0, 1)[0]/integrate.quad(b, 0, 1)[0] #[meter]\n", + "\n", + "\n", + "# Result Solution 2\n", + "print\"Solution 2\"\n", + "print\"xbar = \",round(xbar,3),\"m\"\n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Ex 9.7 Page No 344" + ] + }, + { + "cell_type": "code", + "execution_count": 22, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "ybar = 66.7 mm\n" + ] + } + ], + "source": [ + "# Example 9.7\n", + "from scipy import integrate\n", + "import math\n", + "\n", + "# Calculation\n", + "a = lambda y: 100*math.pi*y**(2)\n", + "b = lambda y: 100*math.pi*y\n", + "ybar = integrate.quad(a, 0, 100)[0]/integrate.quad(b, 0, 100)[0] #[millimeter]\n", + "\n", + "# Result\n", + "print\"ybar = \",round(ybar,1),\"mm\"" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "collapsed": true + }, + "source": [ + "## Ex 9.8 Page No 346" + ] + }, + { + "cell_type": "code", + "execution_count": 3, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "zbar = 0.667 m\n" + ] + } + ], + "source": [ + "# Example 9.8\n", + "from scipy import integrate\n", + "import math\n", + "\n", + "# Calculation\n", + "a = lambda z: z*200*z*math.pi*0.5**(2)\n", + "b = lambda z: 200*z*math.pi*0.5**(2)\n", + "zbar = integrate.quad(a, 0, 1)[0]/integrate.quad(b, 0, 1)[0] #[meter]\n", + "\n", + "# Result\n", + "print\"zbar = \",round(zbar,3),\"m\"" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Ex 9.9 Page No 352" + ] + }, + { + "cell_type": "code", + "execution_count": 7, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "xbar = 45.5 mm\n", + "ybar = -22.5 mm\n", + "zbar = -0.805 mm\n" + ] + } + ], + "source": [ + "# Example 9.9\n", + "import math\n", + "\n", + "# Calculation\n", + "xbar = (60*math.pi*60+0*40+0*20)/(math.pi*60+40+20) #[millimeter]\n", + "ybar = (-38.2*math.pi*60+20*40+40*20)/(math.pi*60+40+20) #[millimeter]\n", + "zbar = (0*math.pi*60+0*40+-10*20)/(math.pi*60+40+20) #[millimeter]\n", + "\n", + "# Result\n", + "print\"xbar = \",round(xbar,1),\"mm\"\n", + "print\"ybar = \",round(ybar,1),\"mm\"\n", + "print\"zbar = \",round(zbar,3),\"mm\"" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Ex 9.10 Page No 353" + ] + }, + { + "cell_type": "code", + "execution_count": 9, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "xbar = -0.348 m\n", + "ybar = 1.22 m\n" + ] + } + ], + "source": [ + "# Example 9.10\n", + "\n", + "# Calculation\n", + "xbar = (1*0.5*3*3+(-1.5)*3*3+(-2.5)*(-2)*1)/(0.5*3*3+3*3+(-2)*1) #[meter]\n", + "ybar = (1*0.5*3*3+1.5*3*3+2*(-2)*1)/(0.5*3*3+3*3+(-2)*1) #[meter]\n", + "\n", + "# Result\n", + "print\"xbar = \",round(xbar,3),\"m\"\n", + "print\"ybar = \",round(ybar,2),\"m\"\n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Ex 9.11 Page No 354" + ] + }, + { + "cell_type": "code", + "execution_count": 2, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "zbar = 14.6 mm\n" + ] + } + ], + "source": [ + "# Example 9.11\n", + "import math\n", + "from __future__ import division\n", + "\n", + "# Variable Declaration\n", + "pc = 8 #[milligram per meter cube]\n", + "ph = 4 #[milligram per meter cube]\n", + "\n", + "# Calculation\n", + "zbar = (50*pc*10**(-6)*(1/3)*math.pi*50**(2)*200 + (-18.75)*ph*10**(-6)*(2/3)*math.pi*50**(3) + 125*(-pc)*10**(-6)*(1/3)*math.pi*25**(2)*100 + 50*(-pc)*10**(-6)*math.pi*25**(2)*100)/(pc*10**(-6)*(1/3)*math.pi*50**(2)*200+ph*10**(-6)*(2/3)*math.pi*50**(3)+(-pc)*10**(-6)*(1/3)*math.pi*25**(2)*100+(-pc)*10**(-6)*math.pi*25**(2)*100) #[millimeter]\n", + "\n", + "# Result\n", + "print\"zbar = \",round(zbar,1),\"mm\"" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Ex 9.13 Page No 368" + ] + }, + { + "cell_type": "code", + "execution_count": 3, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Solutuon 1\n", + "FR = 154.5 kN\n", + "h = 1.3 m\n", + "\n", + "Solutuon 2\n", + "FR = 154.5 kN\n", + "h = 1.3 m\n" + ] + } + ], + "source": [ + "# Example 9.13\n", + "from __future__ import division\n", + "\n", + "# Variable Declaration\n", + "b = 1.5 #[meter]\n", + "pw = 1000 #[kilogram per meter cube]\n", + "# Calculation\n", + "# Solution 1\n", + "# Let water pressure at depth A be pA and water pressure at depth B be pB\n", + "pA = pw*9.81*2/1000 #[kilo Pascal]\n", + "pB = pw*9.81*5/1000 #[kilo Pascal]\n", + "wA = round(b*pA,2) #[kilo Newton per meter]\n", + "wB = round(b*pB,2) #[kilo Newton per meter]\n", + "# let FR be area of trapezoid\n", + "FR = round((1/2)*3*(wA+wB),1) #[kilo Newton]\n", + "# Let h be force acting through centroid\n", + "h = round((1/3)*((2*wA+wB)/(wA+wB))*3,1) #[meter]\n", + "\n", + "# Result Solution 1\n", + "print\"Solutuon 1\"\n", + "print\"FR = \",(FR),\"kN\"\n", + "print\"h = \",(h),\"m\\n\"\n", + "\n", + "# Solution 2\n", + "FRe = round(wA*3,1) #[kilo Newton]\n", + "Ft = round((1/2)*(wB-wA)*3,1) #[kilo Newton]\n", + "FR = FRe + Ft #[kilo Newton]\n", + "# +ΣMRB(clockwise) = ΣMB\n", + "h = round((FRe*1.5+Ft*1)/FR,1) #[meter]\n", + "\n", + "# Result Solution 2\n", + "print\"Solutuon 2\"\n", + "print\"FR = \",(FR),\"kN\" \n", + "print\"h = \",(h),\"m\"" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Ex 9.14 Page No 369" + ] + }, + { + "cell_type": "code", + "execution_count": 4, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "FR = 231.0 kN\n" + ] + } + ], + "source": [ + "# Example 9.14\n", + "from __future__ import division\n", + "\n", + "# Variable Declaration\n", + "b = 5 #[meter]\n", + "pw = 1020 #[kilogram per meter cube]\n", + "\n", + "# Calculation\n", + "pB = round(pw*9.81*3/1000,2) #[kilo Pascal]\n", + "wB = round(b*pB,1) #[kilo Newton per meter]\n", + "F_x = round((1/2)*3*wB,1) #[kilo Newton]\n", + "F_y = round(pw*9.81*5*(1/3)*1*3/1000,1) #[kilo Newton]\n", + "FR = round(math.sqrt(F_x**(2)+F_y**(2)),0) #[kilo Newton]\n", + "\n", + "# Result\n", + "print\"FR = \",(FR),\"kN\"" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Ex 9.15 Page No 370" + ] + }, + { + "cell_type": "code", + "execution_count": 31, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "F = 1.64 kN\n", + "xbar = 0\n", + "zbar = 0.5 m\n" + ] + } + ], + "source": [ + "# Example 9.15\n", + "from scipy import integrate\n", + "from __future__ import division\n", + "\n", + "# Calculation\n", + "a = lambda z: 9810*(z-z**(2))\n", + "F = round(integrate.quad(a, 0, 1)[0],2) #[Newton]\n", + "\n", + "# Resultant passes through centroid of volume\n", + "xbar = 0\n", + "a = lambda z: (9810/1635)*(z**(2)-z**(3))\n", + "zbar = round(integrate.quad(a, 0, 1)[0],1) #[meter]\n", + "\n", + "# Result\n", + "print\"F = \",(round(F/1000,2)),\"kN\"\n", + "print\"xbar = \",(xbar)\n", + "print\"zbar = \",(zbar),\"m\"" + ] + }, + { + "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 +} -- cgit