{
 "metadata": {
  "name": "chapter3.ipynb"
 },
 "nbformat": 3,
 "nbformat_minor": 0,
 "worksheets": [
  {
   "cells": [
    {
     "cell_type": "heading",
     "level": 1,
     "metadata": {},
     "source": [
      "Chapter 3: Resultants of Coplanar Force Systems"
     ]
    },
    {
     "cell_type": "heading",
     "level": 1,
     "metadata": {},
     "source": [
      "Example 3.3-1, Page no: 32"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "import math\n",
      "\n",
      "#Initilization of variables\n",
      "\n",
      "F1=150 #lb\n",
      "F2=200 #lb\n",
      "F3=80 #lb\n",
      "F4=180 #lb\n",
      "theta1=((30*pi)/180) #radians\n",
      "theta2=((150*pi)/180) #radians\n",
      "theta3=((240*pi)/180) #radians\n",
      "theta4=((315*pi)/180) #radians\n",
      "\n",
      "#Calculations\n",
      "\n",
      "F1x=F1*cos(theta1) #lb\n",
      "F1y=F1*sin(theta1) #lb\n",
      "F2x=F2*cos(theta2) #lb\n",
      "F2y=F2*sin(theta2) #lb\n",
      "F3x=F3*cos(theta3) #lb\n",
      "F3y=F3*sin(theta3) #lb\n",
      "F4x=F4*cos(theta4) #lb\n",
      "F4y=F4*sin(theta4) #lb\n",
      "Fx=F1x+F2x+F3x+F4x #lb\n",
      "Fy=F1y+F2y+F3y+F4y #lb\n",
      "R=sqrt(Fx**2+Fy**2) #lb\n",
      "theta=((arctan(Fy/Fx))*180)/pi #degrees\n",
      "theta_R=360+theta #degrees\n",
      "\n",
      "#Result\n",
      "\n",
      "print'The resultant of the force system is',round(R),\"lb\"\n",
      "print'The resultant is at',round(theta_R),\"degrees\"\n"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "The resultant of the force system is 49.0 lb\n",
        "The resultant is at 334.0 degrees\n"
       ]
      }
     ],
     "prompt_number": 1
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Example 3.3-2, Page no: 33"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "import math\n",
      "\n",
      "#Initilization of variables\n",
      "\n",
      "F1=50 #N\n",
      "F2=100 #N\n",
      "F3=30 #N\n",
      "\n",
      "#Calculation\n",
      "\n",
      "#The book has a misprint for squareroot of 1**2\n",
      "F1x=F1/sqrt(2) #N \n",
      "F1y=F1/sqrt(2) #N\n",
      "F2x=-(F2*3)/sqrt(10) #N\n",
      "F2y=(-F2)/sqrt(10) #N\n",
      "F3x=F3/sqrt(5) #N\n",
      "F3y=(-F3*2)/sqrt(5) #N\n",
      "Fx=F1x+F2x+F3x #N\n",
      "Fy=F1y+F2y+F3y #N\n",
      "R=sqrt(Fx**2+Fy**2) #N\n",
      "theta=arctan(Fy/Fx) #radians\n",
      "theta_x=180+(theta*180)/pi #degrees\n",
      "\n",
      "#Result\n",
      "\n",
      "print'The resultant is',round(R,1),\"N\"\n",
      "print'The resultant makes an angle of',round(theta_x),\"degrees\"\n"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "The resultant is 51.6 N\n",
        "The resultant makes an angle of 207.0 degrees\n"
       ]
      }
     ],
     "prompt_number": 2
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Example 3.3-3, Page no: 33"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "import math\n",
      "\n",
      "#Initilization of variables\n",
      "\n",
      "F1=70 #lb\n",
      "F2=100 #lb\n",
      "F3=125 #lb\n",
      "theta1=0 #radians\n",
      "theta2=((10*pi)/180) #radians\n",
      "theta3=((30*pi)/180) #radians\n",
      "\n",
      "#Calculations\n",
      "\n",
      "Fx=F1-(F2*cos(theta3))-(125*sin(theta2)) #lb\n",
      "Fy=125*cos(theta2)-(100*sin(theta3)) #lb\n",
      "R=sqrt(Fx**2+Fy**2) #lb\n",
      "theta=arctan(Fy/Fx) #radians\n",
      "theta_x=180+(theta*180)/pi #degrees\n",
      "\n",
      "#Result\n",
      "\n",
      "print'The resultant of the force system is',round(R,1),\"lb\"\n",
      "print'The resultant with respect to X axis is at',round(theta_x),\"degrees\"\n"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "The resultant of the force system is 82.5 lb\n",
        "The resultant with respect to X axis is at 118.0 degrees\n"
       ]
      }
     ],
     "prompt_number": 3
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Example 3.3-4, Page No: 34"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "import math\n",
      "\n",
      "#Initilization of variables\n",
      "\n",
      "F1=-20 #N\n",
      "F2=30 #N\n",
      "F3=5 #N\n",
      "F4=-40 #N\n",
      "#Distances with respect to point O\n",
      "x1=6 #m\n",
      "x2=0 #m\n",
      "x3=8 #m\n",
      "x4=13 #m\n",
      "\n",
      "#Calculations\n",
      "\n",
      "R=F1+F2+F3+F4 #N\n",
      "# Applying moment about point O equal to zero\n",
      "M_O=-(F1*x1)+(F2*x2)+(F3*x3)+(F4*x4) #N-m\n",
      "#Applying moment about point O equal to R*x\n",
      "x=M_O/R #m\n",
      "\n",
      "#Result\n",
      "\n",
      "print'The resultant of force system is',round(R),\"N\"\n",
      "print'The moment about point O is',round(M_O),\"N.m\"\n",
      "print'The resultant of moment acts at',round(x,1),\"m (to the right of O)\"\n",
      "\n",
      "# The answer for M_O & R is correct but x waries due to some discrepancy in python."
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "The resultant of force system is -25.0 N\n",
        "The moment about point O is -360.0 N.m\n",
        "The resultant of moment acts at 14.0 m (to the right of O)\n"
       ]
      }
     ],
     "prompt_number": 7
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Example 3.3-5, Page No: 34"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "import math\n",
      "\n",
      "#Initilization of variables\n",
      "\n",
      "F1=-100 #lb\n",
      "F2=200 #lb\n",
      "F3=-200 #lb\n",
      "F4=400 #lb\n",
      "F5=-300 #lb\n",
      "#Distance with respect to point O\n",
      "x1=0 #ft\n",
      "x2=2 #ft\n",
      "x3=5 #ft\n",
      "x4=9 #ft\n",
      "x5=11 #ft\n",
      "\n",
      "#Calculation\n",
      "\n",
      "R=F1+F2+F3+F4+F5 #lb\n",
      "M_O=(F1*x1)+(F2*x2)+(F3*x3)+(F4*x4)+(F5*x5) #N-m\n",
      "\n",
      "#Result\n",
      "\n",
      "print'The resultant of the force system is',round(R),\"lb\"\n",
      "print'The moment about point O is',round(M_O),\"lb-ft\"\n"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "The resultant of the force system is 0.0 lb\n",
        "The moment about point O is -300.0 lb-ft\n"
       ]
      }
     ],
     "prompt_number": 8
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Example 3.3-6, Page no: 35"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "import math\n",
      "\n",
      "#Initilization of variables\n",
      "\n",
      "F1=20 #lb\n",
      "F2=20 #lb\n",
      "F3=-40 #lb\n",
      "#Distance from point O\n",
      "x1=3 #ft\n",
      "x2=3 #ft\n",
      "\n",
      "#Calculations\n",
      "\n",
      "R=F1+F2+F3 #lb\n",
      "M_O=-(F1*x1)+(F2*x2) #lb-ft\n",
      "\n",
      "#Results\n",
      "\n",
      "print'The resultant of the force system is',round(R),\"lb\"\n",
      "print'The Moment about point O is',round(M_O),\"lb-ft\"\n"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "The resultant of the force system is 0.0 lb\n",
        "The Moment about point O is 0.0 lb-ft\n"
       ]
      }
     ],
     "prompt_number": 9
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Example 3.3-7, Page No: 35"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "import math\n",
      "\n",
      "#Initilization of variables\n",
      "\n",
      "F1=500 #N\n",
      "F2=-400 #N\n",
      "F3=-200 #N\n",
      "C=1500 #N-m\n",
      "#Distance from point O\n",
      "x1=2 #m\n",
      "x2=4 #m\n",
      "x3=6 #m\n",
      "\n",
      "#Calculations\n",
      "\n",
      "R=F1+F2+F3 #N\n",
      "M_O=(F1*x1)+(F2*x2)+(F3*x3)+C #N-m\n",
      "#Applying Varignons theorem\n",
      "x=M_O/R #m\n",
      "\n",
      "#Result\n",
      "\n",
      "print'The resultant of the force system is',round(R),\"N\"\n",
      "print'The moment about point O is',round(M_O),\"N.m\"\n",
      "print'The resultant acts at',round(x),\"m (from point O)\"\n"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "The resultant of the force system is -100.0 N\n",
        "The moment about point O is -300.0 N.m\n",
        "The resultant acts at 3.0 m (from point O)\n"
       ]
      }
     ],
     "prompt_number": 11
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Example 3.3-8,Page No: 35"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "import math\n",
      "\n",
      "#Initilization of variables\n",
      "\n",
      "F1=50 #lb\n",
      "F2=100 #lb\n",
      "theta1=((45*pi)/180) #radians\n",
      "#Distance from point O\n",
      "x1=5 #ft\n",
      "x2=4 #ft\n",
      "\n",
      "#Calculation\n",
      "\n",
      "F_x=F1-(F2*cos(theta1)) #lb\n",
      "F_y=F1-(F2*sin(theta1)) #lb\n",
      "R=sqrt(F_x**2+F_y**2) #lb\n",
      "M_O=F1*x1-(x2*F1) #lb-ft\n",
      "#Applying Varignons Theorem\n",
      "x=M_O/R #ft\n",
      "\n",
      "#Result\n",
      "\n",
      "print'The resultant of the force system is',round(R,1),\"lb\"\n",
      "print'The Moment about point O is',round(M_O),\"lb-ft\"\n",
      "print'The Resultant acts at',round(x,2),\"ft (from point O)\"\n"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "The resultant of the force system is 29.3 lb\n",
        "The Moment about point O is 50.0 lb-ft\n",
        "The Resultant acts at 1.71 ft (from point O)\n"
       ]
      }
     ],
     "prompt_number": 12
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Example 3.3-9, Page no: 36"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "import math\n",
      "\n",
      "#Initilization of variables\n",
      "\n",
      "A=80 #N\n",
      "B=120 #N\n",
      "C=100 #N\n",
      "D=50 #N\n",
      "thetaA=((90*pi)/180) #radians\n",
      "thetaB=((150*pi)/180) #radians\n",
      "thetaC=((45*pi)/180) #radians\n",
      "thetaD=((340*pi)/180) #radians\n",
      "\n",
      "#Calculations\n",
      "\n",
      "Ax=A*cos(thetaA) #N\n",
      "Ay=A*sin(thetaA) #N\n",
      "Bx=B*cos(thetaB) #N\n",
      "By=B*sin(thetaB) #N\n",
      "Cx=C*cos(thetaC) #N\n",
      "Cy=C*sin(thetaC) #N\n",
      "Dx=D*cos(thetaD) #N\n",
      "Dy=D*sin(thetaD) #N\n",
      "M_Ax=0 #N-m\n",
      "M_Ay=0 #N-m\n",
      "M_Bx=-Bx*5 #N-m\n",
      "M_By=By*8 #N-m\n",
      "M_Cx=-Cx*1 #N-m\n",
      "M_Cy=Cy*1 #N-m\n",
      "M_Dx=-Dx*-1 #N-m\n",
      "M_Dy=Dy*8 #N-m\n",
      "Fx=Ax+Bx+Cx+Dx #N\n",
      "Fy=Ay+By+Cy+Dy #N\n",
      "R=sqrt(Fx**2+Fy**2) #N\n",
      "M_O=M_Dx+M_Dy+M_Cx+M_Cy+M_Bx+M_By+M_Ax+M_Ay #N-m\n",
      "theta=arctan(Fy/Fx) #radians\n",
      "theta_x=(theta*180)/pi #degrees\n",
      "#Appliying Varignons theorem\n",
      "x=M_O/R #m\n",
      "\n",
      "#Result\n",
      "\n",
      "print'The resultant of the force system is',round(R),\"N\"\n",
      "print'The moment about point O is +',round(M_O),\"N.m\"\n",
      "print'The resultant acts at and angle of',round(theta_x),\"degrees (with respect to X axis)\"\n",
      "print'The resultant of the force system acts at',round(x,1),\"m (from point O)\"\n"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "The resultant of the force system is 194.0 N\n",
        "The moment about point O is + 910.0 N.m\n",
        "The resultant acts at and angle of 86.0 degrees (with respect to X axis)\n",
        "The resultant of the force system acts at 4.7 m (from point O)\n"
       ]
      }
     ],
     "prompt_number": 1
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Example 3.3-10, Page No: 37"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "import math\n",
      "\n",
      "#Initilization of variables\n",
      "\n",
      "F1=100 #lb\n",
      "F2=80 #lb\n",
      "F3=120 #lb\n",
      "F4=150 #lb\n",
      "theta1=((60*pi)/180) #radians\n",
      "theta2=((45*pi)/180) #radians\n",
      "theta3=((90*pi)/180) #radians\n",
      "theta4=((75*pi)/180) #radians\n",
      "#Distance from point O\n",
      "x1=-5 #ft\n",
      "y1=20 #ft\n",
      "x2=10 #ft\n",
      "y2=10 #ft\n",
      "x3=25 #ft\n",
      "y3=25 #ft\n",
      "x4=35 #ft\n",
      "y4=15 #ft\n",
      "\n",
      "#Calculations\n",
      "\n",
      "Fx=F1*cos(theta1)+F2*cos(theta2)+F4*cos(theta4) #lb\n",
      "Fy=-F1*sin(theta1)+F2*sin(theta2)-F3-F4*sin(theta4) #lb\n",
      "R=sqrt(Fx**2+Fy**2) #lb\n",
      "theta=arctan(Fy/Fx) #radians\n",
      "theta_x=(theta*180)/pi #degrees\n",
      "M_O=-(F1*cos(theta1)*y1)+(-x1)*(F1*sin(theta1))-(x2)*(F2*cos(theta2))+(y2)*(F2*sin(theta2))-(x3*F3)-(y4*F4*cos(theta4))-(x4*F4*sin(theta4)) #lb-ft\n",
      "#Applying varignons theorem\n",
      "x=M_O/Fy #ft\n",
      "y=-M_O/Fx #ft\n",
      "\n",
      "#Results\n",
      "\n",
      "print'The resultant of the force system is',round(R),\"lb\"\n",
      "print'The resultant acts at',round(theta_x,1),\"degrees(with respect to X axis)\"\n",
      "print'The moment about point O is',round(M_O),\"lb-ft\"\n",
      "print'The x intercept of resultant is',round(x,1),\"ft\"\n",
      "print'The y intercept of resultant is',round(y,1),\"ft\"\n",
      "#Answer for angle should be negative which has not been mentioned in the tectbook but a schematic shows the angle in fourth quadrant to clarify the doubt \n"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "The resultant of the force system is 329.0 lb\n",
        "The resultant acts at -63.8 degrees(with respect to X axis)\n",
        "The moment about point O is -9220.0 lb-ft\n",
        "The x intercept of resultant is 31.3 ft\n",
        "The y intercept of resultant is 63.4 ft\n"
       ]
      }
     ],
     "prompt_number": 16
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Example 3.3-11, Page No: 38"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "import math\n",
      "\n",
      "#Initilization of variables\n",
      "\n",
      "F1=150 #lb\n",
      "F2=80 #lb\n",
      "F3=100 #lb\n",
      "F4=50 #lb\n",
      "theta1=((45*pi)/180) #radians\n",
      "r=3  #units\n",
      "\n",
      "#Calculations\n",
      "\n",
      "Fh=F1-F3*cos(theta1) #lb\n",
      "Fv=F4-F2-F3*sin(theta1) #lb\n",
      "R=sqrt(Fh**2+Fv**2) #lb\n",
      "#Applying the Varignons Theorem\n",
      "a=(F4*r-F1*r+F2*r-F3*r)/R # ft\n",
      "\n",
      "#Result\n",
      "\n",
      "print'The resultant of the force system is',round(R),\"lb\"\n",
      "print'The resultant acts at',round(a,2),\"ft (from point O)\"\n",
      "#Negative sign indicates a negative moment caused by the resultant\n"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "The resultant of the force system is 128.0 lb\n",
        "The resultant acts at -2.81 ft (from point O)\n"
       ]
      }
     ],
     "prompt_number": 17
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Example 3.3-12, Page no: 39"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "import math\n",
      "\n",
      "#Initilization of variables\n",
      "\n",
      "F1=150 #lb\n",
      "F2=200 #lb\n",
      "F3=200 #lb\n",
      "F4=225 #lb\n",
      "M=900 #lb-ft\n",
      "Theta1=(45*pi)/180 #radians\n",
      "Theta2=(30*pi)/180 #radians\n",
      "x1=3 #ft\n",
      "x2=15 #ft\n",
      "x3=12 #ft\n",
      "x4=6 #ft\n",
      "\n",
      "#Calculations\n",
      "\n",
      "Fx=F1*cos(Theta1)+F2-F4*cos(Theta2) #Applying sum of all forces equal to zero in X direction\n",
      "Fy=F1*sin(Theta1)-F4*sin(Theta2)+F2 #Applying sum of all forces equal to zero in Y direction\n",
      "R=sqrt(Fx**2+Fy**2) #lb\n",
      "theta=(arctan(Fy/Fx))*(180/pi) #degrees\n",
      "M_o=x1*F2-x2*F1*cos(Theta1)+x3*F1*sin(Theta1)-x4*F2+M+x4*F4*cos(Theta2)-x1*F4*sin(Theta2) #Moment about point O\n",
      "x=M_o/Fy # in -Varignons Theorem \n",
      "\n",
      "#Result\n",
      "\n",
      "print'The x intercept of resultant position is',round(x,1),\"in\"\n",
      "print'The Resultant is',round(R),\"lb\"\n",
      "print'The resultant acts at an angle of',round(theta),\"degrees\"\n"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "The x intercept of resultant position is 4.2 in\n",
        "The Resultant is 223.0 lb\n",
        "The resultant acts at an angle of 60.0 degrees\n"
       ]
      }
     ],
     "prompt_number": 18
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Example 3.3-13, Page No: 39"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "import math\n",
      "from scipy.integrate import quad\n",
      "def integrand(x, a, b):\n",
      "    return 20\n",
      "a=1\n",
      "b=1\n",
      "I=quad(integrand, 0, 6, args=(a,b))\n",
      "\n",
      "def integrand(x, a, b):\n",
      "    return 20*x\n",
      "a=1\n",
      "b=1\n",
      "J=quad(integrand, 0, 6, args=(a,b))\n",
      "d=J[0]/I[0]\n",
      "\n",
      "# Results\n",
      "print'The value of R is',round(I[0]),\"lb\"\n",
      "print'The value of d is',round(d),\"ft\"\n"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "The value of R is 120.0 lb\n",
        "The value of d is 3.0 ft\n"
       ]
      }
     ],
     "prompt_number": 2
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Example 3.3-14, Page no: 39"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "import math\n",
      "from scipy.integrate import quad\n",
      "def integrand(x, a, b):\n",
      "    return (x/9)*30\n",
      "a=1\n",
      "b=1\n",
      "I=quad(integrand, 0, 9, args=(a,b))\n",
      "\n",
      "def integrand(y, a, b):\n",
      "    return y*(y/9)*30\n",
      "a=1\n",
      "b=1\n",
      "J=quad(integrand, 0, 9, args=(a,b))\n",
      "d=J[0]/I[0]\n",
      "\n",
      "# Results\n",
      "print'The value of R is',round(I[0]),\"N\"\n",
      "print'The value of d is',round(d),\"m\"\n",
      "\n",
      "\n",
      "\n"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "The value of R is 135.0 N\n",
        "The value of d is 6.0 m\n"
       ]
      }
     ],
     "prompt_number": 4
    }
   ],
   "metadata": {}
  }
 ]
}