{
"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\""
]
}
],
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