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{
"metadata": {
"name": "chapter8.ipynb"
},
"nbformat": 3,
"nbformat_minor": 0,
"worksheets": [
{
"cells": [
{
"cell_type": "heading",
"level": 1,
"metadata": {},
"source": [
"Chapter 8: Simple Lifting Machines"
]
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example 8.8-1,Page No:179"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"import math\n",
"\n",
"# Initilization of variables\n",
"\n",
"VR=6 # Velocity ratio\n",
"P=20 #N # Effort\n",
"W=100 #N # Load lifted\n",
"\n",
"# Calculations\n",
"\n",
"#(a)\n",
"\n",
"P_actual=P #N\n",
"W_actual=W #N\n",
"MA=W/P # where, MA= Mechanical advantage\n",
"E=(0.833)*100 #% # Where MA/VR=0.833 and E= efficiency\n",
"\n",
"#(b)\n",
"# Now ideal effort required is,\n",
"P_ideal=W*VR**-1 #N\n",
"# Effort loss in friction is, (Le)\n",
"Le=P_actual-P_ideal #N # Effort loss in friction\n",
"\n",
"#(c)\n",
"# Ideal load lifted is,(W_ideal)\n",
"W_ideal=P*VR #N \n",
"# Frictional load/resistance,\n",
"F=W_ideal-W_actual # N\n",
"\n",
"# Results\n",
"\n",
"print\"(a) The efficiency of the machine is \",round(E,3),\"percent\"\n",
"print\"(b) The effort loss in friction of the machine is \",round(Le,2),\"N\"\n",
"print\"(c) The Frictional load of the machine is \",round(F),\"N\"\n"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"(a) The efficiency of the machine is 83.3 percent\n",
"(b) The effort loss in friction of the machine is 3.33 N\n",
"(c) The Frictional load of the machine is 20.0 N\n"
]
}
],
"prompt_number": 5
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example 8.8-2, Page No:180"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"import math\n",
"import matplotlib.pyplot as plt\n",
"%matplotlib inline\n",
"\n",
"# Initilization of variables\n",
"V_r=20 # Velocity ratio\n",
"# Values from the table # Variables have been assumed\n",
"# Values of W in N\n",
"W=[30 ,40 ,50 ,60 ,70 ,80 ,90 ,100]\n",
"# P in N\n",
"P=[7 ,8.5 ,10 ,11.5 ,13.5 ,14.5 ,16 ,17.5]\n",
"M_A=[W[0]*P[0]**-1 ,W[1]*P[1]**-1 ,W[2]*P[2]**-1 ,W[3]*P[3]**-1 ,W[4]*P[4]**-1 ,W[5]*P[5]**-1 ,W[6]*P[6]**-1 ,W[7]*P[7]**-1]\n",
"# Efficiency (n)\n",
"n=[(V_r**-1)*M_A[0] ,(V_r**-1)*M_A[1] ,(V_r**-1)*M_A[2] ,(V_r**-1)*M_A[3], (V_r**-1)*M_A[4] ,(V_r**-1)*M_A[5] ,(V_r**-1)*M_A[6] ,(V_r**-1)*M_A[7]]*100 # %\n",
"# Calculations\n",
"# Part (a)- Realtionship between W & P\n",
"# Here part a cannot be solved as it has variables which cannot be defined in Scilab. Ref.textbook for the solution\n",
"# Part (b)- Graph between W & efficiency n(eta)\n",
"x=[0 ,W[0] ,W[1] ,W[2] ,W[3] ,W[4] ,W[5] ,W[6] ,W[7]] # values for W # N\n",
"y=[0 ,n[0] ,n[1] ,n[2] ,n[3] ,n[4] ,n[5] ,n[6] ,n[7]] # values for efficiency n (eta) # %\n",
"d=transpose(x)\n",
"plt.plot(d,y)\n",
"plt.show()\n",
"\n",
"# Results\n",
"\n",
"print\"The graph is the solution\"\n",
"# The value of m is found by drawing straight line on the graph and by taking its slope. Ref textbook for the solution\n",
"# The curve of the graph may differ from textbook because of the graphical calculation.\n"
],
"language": "python",
"metadata": {},
"outputs": [
{
"metadata": {},
"output_type": "display_data",
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T9fWyZ/+114CQENXVEJE/YfD7qYULgdBQYMoU1ZUQkb/hGL8fKi8HkpLkPXQjIlRXQ0Qq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\n/EREGsPgJyLSGAY/EZHG/D+gQLmVwq5uYAAAAABJRU5ErkJggg==\n",
"text": [
"<matplotlib.figure.Figure at 0x4fe1370>"
]
},
{
"output_type": "stream",
"stream": "stdout",
"text": [
"The graph is the solution\n"
]
}
],
"prompt_number": 1
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example 8.8-3,Page No:184"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"import math\n",
"\n",
"# Initialization of variables\n",
"\n",
"W_actual=1360 #N #Load lifted\n",
"P_actual=100 #N # Effort\n",
"n=4 # no of pulleys\n",
"\n",
"# Calculations\n",
"\n",
"# for 1st system of pulleys having 4 movable pulleys, Velocity ratio is\n",
"VR=2**(n) # Velocity Ratio\n",
"\n",
"# If the machine were to be ideal(frictionless)\n",
"MA=VR # Here, M.A= mechanical advantage \n",
"\n",
"# For a load of 1360 N, ideal effort required is\n",
"P_ideal=W_actual/VR #N\n",
"\n",
"# Effort loss in friction is,\n",
"P_friction=P_actual-P_ideal #N\n",
"\n",
"# For a effort of 100 N, ideal load lifted is,\n",
"W_ideal=VR*100 #N \n",
"\n",
"# Load lost in friction is,\n",
"W_friction=W_ideal-W_actual # N \n",
"\n",
"# Results\n",
"\n",
"print\"(a) The effort wasted in friction is \",round(P_friction,2),\"N\"\n",
"print\"(b) The load wasted in friction is \",round(W_friction,2),\"N\"\n"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"(a) The effort wasted in friction is 15.0 N\n",
"(b) The load wasted in friction is 240.0 N\n"
]
}
],
"prompt_number": 2
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example 8.8-4,Page No:185"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"import math\n",
"\n",
"# Initilization of variables\n",
"\n",
"W=1000 #N # Load to be lifted\n",
"n=5 # no. of pulleys\n",
"E=75 #% # Efficiency\n",
"\n",
"# Calculations\n",
"\n",
"# Velocity Ratio is given as,\n",
"VR=n \n",
"\n",
"# Mechanical Advantage (MA) is,\n",
"MA=(E*0.01)*VR # from formulae, Efficiency=E=MA/VR\n",
"P=W/MA #N # Effort required\n",
"\n",
"# Results\n",
"\n",
"print\"The effort required to lift the load of 1000 N is \",round(P,2),\"N\"\n"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"The effort required to lift the load of 1000 N is 266.67 N\n"
]
}
],
"prompt_number": 4
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example 8.8-5,Page No:191 "
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"import math\n",
"\n",
"# Initilization of variables\n",
"\n",
"W=2000 #N # Load to be raised\n",
"l=0.70 #m # length of the handle\n",
"d=0.05 #m # diameter of the screw\n",
"p=0.01 #m # pitch of the screw\n",
"mu=0.15 # coefficient of friction at the screw thread\n",
"pie=3.14 #constant\n",
"E=1 # efficiency\n",
"\n",
"# Calculations\n",
"\n",
"phi=arctan(mu)*(180/pi) #degree\n",
"theta=arctan(p/(pie*d))*(180/pi) #degree # where theta is the Helix angle\n",
"\n",
"# Force required at the circumference of the screw is,\n",
"P=W*tan(theta*(pi/180)+phi*(pi/180)) # N //\n",
"\n",
"# Force required at the end of the handle is,\n",
"F=(P*(d*0.5))/l #N # as d/2=d*0.5\n",
"\n",
"# Force required (Ideal case)\n",
"VR=2*pie*l/p\n",
"MA=E*VR # from formulae E=M.A/V,R\n",
"P_ideal=W/MA #N # From formulae, M.A=W/P\n",
"\n",
"# Results\n",
"\n",
"print\"The force required at the end of the handle is \",round(F,2),\"N\"\n",
"print\"The force required if the screw jack is considered to be an ideal machine is \",round(P_ideal,2),\"N\" \n"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"The force required at the end of the handle is 15.41 N\n",
"The force required if the screw jack is considered to be an ideal machine is 4.55 N\n"
]
}
],
"prompt_number": 10
}
],
"metadata": {}
}
]
}
|
