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+{
+ "cells": [
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "# Chapter 1-INTRODUCTION TO MECHANICS OF SOLIDS "
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "# example1.1 Page number 10\n"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 1,
+ "metadata": {
+ "collapsed": false
+ },
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ " The resultant velocity : 21.54 km/hour\n",
+ "68.2 °\n"
+ ]
+ }
+ ],
+ "source": [
+ "#downstream direction as x\n",
+ "#direction across river as y\n",
+ "\n",
+ "from math import sqrt,atan,pi\n",
+ "\n",
+ "#variable declaration\n",
+ "\n",
+ "Vx= 8 #velocity of stream, km/hour\n",
+ "Vy=float(20) #velocity of boat,km/hour\n",
+ "\n",
+ "V=sqrt(pow(Vx,2)+pow(Vy,2)) #resultant velocity, km/hour\n",
+ "theta=Vy/Vx\n",
+ "\n",
+ "alpha= atan(theta)*180/pi #angle, degrees \n",
+ "\n",
+ "print \" The resultant velocity :\",round(V,2),\"km/hour\"\n",
+ "print round(alpha,2),\"°\"\n",
+ "\n"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "# example 1.2 Page number 10"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 2,
+ "metadata": {
+ "collapsed": false
+ },
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "10.0 KN (to the left)\n",
+ "17.32 KN (downward)\n"
+ ]
+ }
+ ],
+ "source": [
+ "\n",
+ "\n",
+ "\n",
+ "#components of force in horizontal and vertical components. \n",
+ "from math import cos,sin,pi\n",
+ "#variable declaration\n",
+ "\n",
+ "F= 20 #force in wire, KN\n",
+ "\n",
+ "#calculations\n",
+ "Fx= F*cos(60*pi/180) \n",
+ "Fy= F*sin(60*pi/180)\n",
+ "\n",
+ "print round(Fx,2),\"KN\" ,\"(to the left)\"\n",
+ "print round(Fy,2), \"KN\" ,\"(downward)\"\n",
+ "\n",
+ "\n"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "# example 1.3 Page number 11"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 3,
+ "metadata": {
+ "collapsed": false
+ },
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "Component normal to the plane : 9.4 KN\n",
+ "Component parallel to the plane : 3.42 KN\n"
+ ]
+ }
+ ],
+ "source": [
+ "\n",
+ "\n",
+ " #The plane makes an angle of 20° to the horizontal. Hence the normal to the plane makes an angles of 70° to the horizontal i.e., 20° to the vertical\n",
+ "from math import cos,sin,pi\n",
+ "#variable declaration\n",
+ "W= 10 # black weighing, KN\n",
+ "\n",
+ "#calculations\n",
+ "\n",
+ "Nor= W*cos(20*pi/180) #Component normal to the plane\n",
+ "para= W*sin(20*pi/180) #Component parallel to the plane\n",
+ "\n",
+ "print \"Component normal to the plane :\",round(Nor,2),\"KN\"\n",
+ "print \"Component parallel to the plane :\",round(para,2) , \"KN\"\n",
+ "\n",
+ "\n",
+ "\n"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "# example 1.4 Page number 11"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 4,
+ "metadata": {
+ "collapsed": false
+ },
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "F1= 100.0 N\n",
+ "F2= 200.0 N\n",
+ "theta= 63.9 °\n"
+ ]
+ }
+ ],
+ "source": [
+ "\n",
+ "\n",
+ "#Let the magnitude of the smaller force be F. Hence the magnitude of the larger force is 2F\n",
+ "\n",
+ "from math import pi,sqrt, acos\n",
+ "#variable declaration\n",
+ "R1=260 #resultant of two forces,N\n",
+ "R2=float(180) #resultant of two forces if larger force is reversed,N\n",
+ "\n",
+ "\n",
+ "\n",
+ "#calculations\n",
+ "\n",
+ "F=sqrt((pow(R1,2)+pow(R2,2))/10)\n",
+ "F1=F\n",
+ "F2=2*F\n",
+ "theta=acos((pow(R1,2)-pow(F1,2)-pow(F2,2))/(2*F1*F2))*180/pi\n",
+ "\n",
+ "print \"F1=\",F1,\"N\"\n",
+ "print \"F2=\",F2,\"N\"\n",
+ "print \"theta=\",round(theta,1),\"°\"\n",
+ "\n",
+ "\n"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "# example 1.5 Page number 12"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 5,
+ "metadata": {
+ "collapsed": false
+ },
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "F1= 326.35 N\n",
+ "F2= 223.24 N\n"
+ ]
+ }
+ ],
+ "source": [
+ "\n",
+ "\n",
+ "#Let ?ABC be the triangle of forces drawn to some scale\n",
+ "#Two forces F1 and F2 are acting at point A\n",
+ "#angle in degrees '°'\n",
+ "\n",
+ "from math import sin,pi\n",
+ " \n",
+ "#variabble declaration\n",
+ "cnv=pi/180\n",
+ "\n",
+ "BAC = 20*cnv #Resultant R makes angle with F1 \n",
+ " \n",
+ "ABC = 130*cnv \n",
+ "\n",
+ "ACB = 30*cnv \n",
+ "\n",
+ "R = 500 #resultant force,N\n",
+ "\n",
+ "#calculations\n",
+ "#sinerule\n",
+ "\n",
+ "F1=R*sin(ACB)/sin(ABC)\n",
+ "F2=R*sin(BAC)/sin(ABC)\n",
+ "\n",
+ "print \"F1=\",round(F1,2),\"N\"\n",
+ "print \"F2=\",round(F2,2),\"N\"\n",
+ "\n",
+ "\n"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "# example 1.6 Page number 12"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 6,
+ "metadata": {
+ "collapsed": false
+ },
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "theta= 78.13 °\n",
+ "alpha= 29.29 °\n"
+ ]
+ }
+ ],
+ "source": [
+ "\n",
+ "\n",
+ "#Let ABC be the triangle of forces,'theta' be the angle between F1 and F2, and 'alpha' be the angle between resultant and F1 \n",
+ "\n",
+ "from math import sin,acos,asin,pi\n",
+ "\n",
+ "#variable declaration\n",
+ "cnv= 180/pi\n",
+ "F1=float(400) #all forces are in newtons,'N'\n",
+ "F2=float(260)\n",
+ "R=float(520)\n",
+ "\n",
+ "#calculations\n",
+ "\n",
+ "theta=acos((pow(R,2)-pow(F1,2)-pow(F2,2))/(2*F1*F2))*cnv\n",
+ "\n",
+ "alpha=asin(F2*sin(theta*pi/180)/R)*cnv\n",
+ "\n",
+ "print\"theta=\",round(theta,2),\"°\"\n",
+ "print \"alpha=\",round(alpha,2),\"°\"\n",
+ "\n"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "# example 1.7 Page number 13"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 7,
+ "metadata": {
+ "collapsed": false
+ },
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "horizontal component= 2814.2 N\n",
+ "Vertical component = 1039.2 N\n",
+ "Component along crank = 507.1 N\n",
+ "Component normal to crank= 2956.8 N\n"
+ ]
+ }
+ ],
+ "source": [
+ "\n",
+ "\n",
+ "#The force of 3000 N acts along line AB. Let AB make angle alpha with horizontal.\n",
+ "\n",
+ "from math import cos,sin,pi,asin,acos\n",
+ "\n",
+ "#variable declaration\n",
+ "F=3000 #force in newtons,'N'\n",
+ "BC=80 #length of crank BC, 'mm'\n",
+ "AB=200 #length of connecting rod AB ,'mm'\n",
+ "theta=60*pi/180 #angle b/w BC & AC\n",
+ "\n",
+ "#calculations\n",
+ "\n",
+ "alpha=asin(BC*sin(theta)/200)*180/pi\n",
+ "\n",
+ "HC=F*cos(alpha*pi/180) #Horizontal component \n",
+ "VC= F*sin(alpha*pi/180) #Vertical component \n",
+ "\n",
+ "#Components along and normal to crank\n",
+ "#The force makes angle alpha + 60 with crank.\n",
+ "alpha2=alpha+60\n",
+ "CAC=F*cos(alpha2*pi/180) # Component along crank \n",
+ "CNC= F*sin(alpha2*pi/180) #Component normal to crank \n",
+ "\n",
+ "\n",
+ "print \"horizontal component=\",round(HC,1),\"N\"\n",
+ "print \"Vertical component = \",round(VC,1),\"N\"\n",
+ "print \"Component along crank =\",round(CAC,1),\"N\"\n",
+ "print \"Component normal to crank=\",round(CNC,1),\"N\""
+ ]
+ }
+ ],
+ "metadata": {
+ "anaconda-cloud": {},
+ "kernelspec": {
+ "display_name": "Python [Root]",
+ "language": "python",
+ "name": "Python [Root]"
+ },
+ "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": 0
+}
generated by cgit (git 2.34.1) at 2024-12-20 22:02:30 +0000