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 A  sample_notebooks/AdityaR/Chapter_5.ipynb

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+{
+ "cells": [
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "# Chapter 5 General Case of Forces in a plane"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "metadata": {
+    "collapsed": true
+   },
+   "outputs": [],
+   "source": [
+    "##Example 5.2 Equations of equilibrium"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 1,
+   "metadata": {
+    "collapsed": false
+   },
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "The reaction at P is 5656.85424949238 N\n",
+      "The reaction at Q is  4000.0 N\n"
+     ]
+    }
+   ],
+   "source": [
+    "import math\n",
+    "\n",
+    "#Initialization of Variables\n",
+    "W=2000 #N\n",
+    "Lab=2 #m #length of the member from the vertical to the 1st load of 2000 N\n",
+    "Lac=5 #m #length of the member from the vertical to the 2nd load of 2000 N\n",
+    "Lpq=3.5 #m\n",
+    "\n",
+    "#Calculations\n",
+    "Rq=((W*Lab)+(W*Lac))/Lpq #N #take moment abt. pt P\n",
+    "Xp=Rq #N #sum Fx=0\n",
+    "Yp=2*W #N #sum Fy=0\n",
+    "Rp=math.sqrt(Xp**2+Yp**2) #N\n",
+    "\n",
+    "#Resuts\n",
+    "print('The reaction at P is' ,Rp ,'N')\n",
+    "print('The reaction at Q is ',Rq ,'N')"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "metadata": {
+    "collapsed": true
+   },
+   "outputs": [],
+   "source": [
+    "##Example 5.3 Equations of equilibrium"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 8,
+   "metadata": {
+    "collapsed": false
+   },
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "The reaction at A i.e Ra is  [[ 120.27406887]] N\n",
+      "The reaction at B i.e Rb is  [[ 35.13703443]] N\n",
+      "The required tension in the string is  [[ 40.57275258]] N\n"
+     ]
+    }
+   ],
+   "source": [
+    "import math,numpy\n",
+    "#Initilization of vaiables\n",
+    "W=25 #N # self weight of the ladder\n",
+    "M=75 #N # weight of the man standing o the ladder\n",
+    "theta=63.43 #degree # angle which the ladder makes with the horizontal\n",
+    "alpha=30 #degree # angle made by the string with the horizontal\n",
+    "Loa=2 #m # spacing between the wall and the ladder\n",
+    "Lob=4 #m #length from the horizontal to the top of the ladder touching the wall(vertical)\n",
+    "\n",
+    "#Calculations\n",
+    "#Using matrix to solve the simultaneous eqn's 3 & 4\n",
+    "A=numpy.matrix('2 -4; 1 -0.577')\n",
+    "B=numpy.matrix('100;100')\n",
+    "C=numpy.linalg.inv(A)*B\n",
+    "\n",
+    "#Results\n",
+    "print('The reaction at A i.e Ra is ',C[0] ,'N')\n",
+    "print('The reaction at B i.e Rb is ',C[1] ,'N')\n",
+    "\n",
+    "#Calculations\n",
+    "T=C[1]/math.cos(math.radians(alpha)) #N # from (eqn 1)\n",
+    "\n",
+    "#Results\n",
+    "print('The required tension in the string is ',T, 'N')"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "metadata": {
+    "collapsed": true
+   },
+   "outputs": [],
+   "source": [
+    "##Example 5.4 Equations of Equilibrium"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 9,
+   "metadata": {
+    "collapsed": false
+   },
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "The reaction at B i.e Rb is  25.0 N\n",
+      "The horizontal reaction at A i.e Xa is  21.650635094610966 N\n",
+      "The vertical reaction at A i.e Ya is  112.5 N\n"
+     ]
+    }
+   ],
+   "source": [
+    "import math\n",
+    "#Initilization of variables\n",
+    "W=100 #N\n",
+    "theta=60 #degree angle made by the ladder with the horizontal\n",
+    "alpha=30 #degree angle made by the ladder with the vertical wall\n",
+    "Lob=4 #m  length from the horizontal to the top of the ladder touching the wall(vertical)\n",
+    "Lcd=2 #m  length from the horizontal to the centre of the ladder where the man stands\n",
+    "\n",
+    "#Calculations\n",
+    "Lab=Lob*(1/math.cos(math.radians(alpha))) #m length of the ladder\n",
+    "Lad=Lcd*math.tan(math.radians(alpha)) #m\n",
+    "Rb=(W*Lad)/Lab #N take moment at A\n",
+    "Xa=Rb*math.sin(math.radians(theta)) #N  From eq'n 1\n",
+    "Ya=W+Rb*math.cos(math.radians(theta)) #N From eq'n 2\n",
+    "\n",
+    "#Results\n",
+    "print('The reaction at B i.e Rb is ',Rb, 'N')\n",
+    "print('The horizontal reaction at A i.e Xa is ',Xa, 'N')\n",
+    "print('The vertical reaction at A i.e Ya is ',Ya,'N')\n"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "metadata": {
+    "collapsed": true
+   },
+   "outputs": [],
+   "source": [
+    "##Example 5.5 Equations of Equilibrium"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 10,
+   "metadata": {
+    "collapsed": false
+   },
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "The horizontal reaction at A i.e Xa is  28.867513459481287 N\n",
+      "The vertical reaction at A i.e Ya is  100 N\n",
+      "The reaction at B i.e Rb is  28.867513459481287 N\n"
+     ]
+    }
+   ],
+   "source": [
+    "import math\n",
+    "#Initilization of variables\n",
+    "W=100 #N self weight of the man\n",
+    "alpha=30 #degree angle made by the ladder with the wall\n",
+    "Lob=4 #m  length from the horizontal to the top of the ladder touching the wall(vertical)\n",
+    "Lcd=2 #m\n",
+    "\n",
+    "#Calculations\n",
+    "# using the equiblirium equations\n",
+    "Ya=W #N  From eq'n 2\n",
+    "Lad=Lcd*math.tan(math.radians(alpha)) #m Lad is the distance fom pt A to the point where the line from the cg intersects the horizontal\n",
+    "Rb=(W*Lad)/Lob #N  Taking sum of moment abt A\n",
+    "Xa=Rb #N From eq'n 1\n",
+    "\n",
+    "#Results\n",
+    "print('The horizontal reaction at A i.e Xa is ',Xa, 'N')\n",
+    "print('The vertical reaction at A i.e Ya is ',Ya,'N' )\n",
+    "print('The reaction at B i.e Rb is ',Rb ,'N')\n"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "metadata": {
+    "collapsed": true
+   },
+   "outputs": [],
+   "source": [
+    "##Example 5.6 Equations of Equilibrium"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 12,
+   "metadata": {
+    "collapsed": false
+   },
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "The horizontal reaction at A i.e Xa is  3.84 N\n",
+      "The vertical reaction at A i.e Ya is  7.12 N\n",
+      "Therefore the reaction at A i.e Ra is  8.089499366462674 N\n",
+      "The reaction at D i.e Rd is  4.8 N\n"
+     ]
+    }
+   ],
+   "source": [
+    "import math\n",
+    "#Initilization of variables\n",
+    "d=0.09 #m diametre of the right circular cylinder\n",
+    "h=0.12 #m height of the cyinder\n",
+    "W=10 #N  self weight of the bar\n",
+    "l=0.24 #m length of the bar\n",
+    "\n",
+    "#Calculations\n",
+    "theta=math.degrees(math.atan(h/d))  #angle which the bar makes with the horizontal\n",
+    "Lad=math.sqrt(d**2+h**2) #m Lad is the length of the bar from point A to point B\n",
+    "Rd=(W*h*(math.cos(theta*math.pi/180)))/Lad #N  Taking moment at A\n",
+    "Xa=Rd*(math.sin(theta*math.pi/180)) #N  sum Fx=0.... From eq'n 1\n",
+    "Ya=W-(Rd*(math.cos(theta*math.pi/180))) #N  sum Fy=0..... From eq'n 2\n",
+    "Ra=math.sqrt(Xa**2+Ya**2) #resultant of Xa & Ya\n",
+    "\n",
+    "#Results\n",
+    "print('The horizontal reaction at A i.e Xa is ',Xa, 'N')\n",
+    "print('The vertical reaction at A i.e Ya is ',Ya, 'N')\n",
+    "print('Therefore the reaction at A i.e Ra is ',Ra,'N')\n",
+    "print('The reaction at D i.e Rd is ',Rd,'N')"
+   ]
+  }
+ ],
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+   "display_name": "Python 3",
+   "language": "python",
+   "name": "python3"
+  },
+  "language_info": {
+   "codemirror_mode": {
+    "name": "ipython",
+    "version": 3
+   },
+   "file_extension": ".py",
+   "mimetype": "text/x-python",
+   "name": "python",
+   "nbconvert_exporter": "python",
+   "pygments_lexer": "ipython3",
+   "version": "3.5.1"
+  },
+  "widgets": {
+   "state": {},
+   "version": "1.1.2"
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+ },
+ "nbformat": 4,
+ "nbformat_minor": 0
+}