{
"metadata": {
"name": "",
"signature": "sha256:184281d9efd5e0a993226e7e376baf4131b3afd17d002bdb4997678ec13c9170"
},
"nbformat": 3,
"nbformat_minor": 0,
"worksheets": [
{
"cells": [
{
"cell_type": "heading",
"level": 1,
"metadata": {},
"source": [
"Chapter 11:Simple Lifting Machines"
]
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example 11.1, Page no.187"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"#variable declaration\n",
"D=300.0 #Diameter of wheel in mm\n",
"d=30.0 #Diameter of axle in mm\n",
"W=900.0 #Load in N\n",
"P=100.0 #Effort applied in N\n",
"\n",
"#calculation\n",
"VR=D/d\n",
"MA=W/P\n",
"Eta=MA/VR\n",
"\n",
"#Result\n",
"print\"Efficiency, Eta =\",int(Eta*100),\"%\"\n",
"\n",
"\n"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"Efficiency, Eta = 90 %\n"
]
}
],
"prompt_number": 9
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example 11.2, Page no.187"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"#variable declaration\n",
"W=480.0 #Load in N\n",
"P=120.0 #effort in N\n",
"D=500.0 #Diameter of wheel in mm\n",
"d=100.0 #Diameter of axle in mm\n",
"\n",
"#calculation\n",
"MA=W/P\n",
"VR=D/d\n",
"Eta=MA/VR\n",
"\n",
"#Result\n",
"print\"(i)Mechanical Advantage=\",int(MA)\n",
"print\"(ii)Velocity ratio=\",int(VR)\n",
"print\"(iii)Efficiency of machine=\",int(Eta*100),\"%\"\n",
"\n",
"\n"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"(i)Mechanical Advantage= 4\n",
"(ii)Velocity ratio= 5\n",
"(iii)Efficiency of machine= 80 %\n"
]
}
],
"prompt_number": 4
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example 11.3, Page no.189"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"#variable declaration\n",
"d1=80 #larger diameter of wheel in mm\n",
"d2=70 #Smaller diamter of wheel in mm\n",
"D=250 #Diameter of effort wheel in mm\n",
"W=1050.0 #Load lifted in N\n",
"P=25.0 #Effort in N\n",
"\n",
"\n",
"#calculation\n",
"VR=2*D/(d1-d2)\n",
"MA=W/P\n",
"Eta=MA/VR\n",
"F_effort=P-(W/VR)\n",
"\n",
"\n",
"#Result\n",
"print\"Velocity Ratio, VR=\",int(VR) #Answer given wrongly in book. 50 is correct answer\n",
"print\"Efficiency, Eta=\",int(Eta*100),\"%\"\n",
"print\"Frictional effort lost, F_effort=\",int(F_effort),\"N\""
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"Velocity Ratio, VR= 50\n",
"Efficiency, Eta= 84 %\n",
"Frictional effort lost, F_effort= 4 N\n"
]
}
],
"prompt_number": 8
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example 11.5, Page no.190"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"#variable declaration\n",
"D=410.0 #Effective diameter of wheel in mm\n",
"d1=310.0 #Effective diameter of axle in mm\n",
"d2=210.0 #Effective diameter of axle in mm\n",
"P=25.0 #Effort in N\n",
"Eta=84.0/100#Efficiency\n",
"\n",
"#calculation\n",
"VR=2*D/(d1-d2)\n",
"W=Eta*P*VR\n",
"\n",
"#Result\n",
"print\"W=\",round(W,1),\"N\"\n",
"\n"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"W= 172.2 N\n"
]
}
],
"prompt_number": 17
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example 11.6, Page no.191"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"#variable declaration\n",
"R=125 #Radius of larger groove in mm\n",
"r=115 #Radius of smaller groove in mm\n",
"Eta=80.0/100 #Efficiency\n",
"W=1500 #Load in N\n",
"\n",
"#calculation\n",
"VR=2*R/(R-r)\n",
"P=W/(Eta*VR)\n",
"\n",
"#Result\n",
"print\"P=\",int(P),\"N\""
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"P= 75 N\n"
]
}
],
"prompt_number": 18
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example 11.7, Page no.192"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"#variable declaration\n",
"W=1800.0 #Load in N\n",
"P=100 #effort in N\n",
"T1=12 #number of teeth on larger block\n",
"T2=11 #number of teeth on smaller block\n",
"\n",
"#calculation\n",
"VR=2*T1/(T1-T2)\n",
"MA=W/P\n",
"Eta=MA/VR\n",
"\n",
"#Result\n",
"print\"Velocity Ratio=\",int(VR)\n",
"print\"Mechanical Advantage=\",int(MA)\n",
"print\"Efficiency=\",int(Eta*100),\"%\"\n"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"Velocity Ratio= 24\n",
"Mechanical Advantage= 18\n",
"Efficiency= 75 %\n"
]
}
],
"prompt_number": 20
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example 11.8, Page no.193"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"#variable declaration\n",
"T1=90.0 #No. of cogs on the effort wheel\n",
"T2=25.0 #No. of cogs on the effort pinion\n",
"T3=40.0 #No. of teeth on the spur wheel\n",
"T4=8.0 #No. of teeth on the load wheel\n",
"P=50.0 #effort in N\n",
"Eta=75.0/100 #Efficiency\n",
"\n",
"#calculation\n",
"VR=(T1/T2)*(T3/T4)\n",
"W=Eta*P*VR\n",
"\n",
"#Result\n",
"print\"W=\",int(W),\"N\""
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"W= 675 N\n"
]
}
],
"prompt_number": 23
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example 11.9, Page no.195"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"#variable declaration\n",
"T=40.0 #No. of teeth on the worm wheel\n",
"D=300.0 #Diameter of effort wheel in mm\n",
"r=50.0 #radius of load drum in mm\n",
"W=1800.0 #Load in N\n",
"P=24.0 #effort in N\n",
"\n",
"#calculation\n",
"VR=D*T/(2*r)\n",
"MA=W/P\n",
"Eta=MA/VR\n",
"\n",
"#Result\n",
"print\"Efficiency=\",round(Eta*100,1),\"%\"\n",
"\n"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"Efficiency= 62.5 %\n"
]
}
],
"prompt_number": 25
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example 11.10, Page no.195"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"#variable declaration\n",
"n=2 #No. of threads\n",
"T=60 #No. of teeth on worm wheel\n",
"D=250 #Diameter of effort wheel in mm\n",
"r=50 #raidus of load drum in mm\n",
"Eta=50.0/100 #Efficiency\n",
"W=300 #load in N\n",
"\n",
"#calculation\n",
"VR=D*T/(2*n*r)\n",
"P=W/(Eta*VR)\n",
"\n",
"#Result\n",
"print\"Velocity ratio of the machine, VR=\",int(VR)\n",
"print\"Effort required,P=\",int(P),\"N\""
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"Velocity ratio of the machine, VR= 75\n",
"Effort required,P= 8 N\n"
]
}
],
"prompt_number": 27
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example 11.11, Page no.197"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"#variable declaration\n",
"D=200.0 #Diameter of effort wheel in mm\n",
"T=60.0 #No. of teeth in worn wheel\n",
"r=40.0 #radius of load drum in mm\n",
"W=9000.0 #load in N\n",
"P=75.0 #Effort in N\n",
"\n",
"#calculation\n",
"VR=(D*T)/r\n",
"MA=W/P\n",
"Eta=MA/VR\n",
"\n",
"#Result\n",
"print\"Efficiency=\",int(Eta*100),\"%\"\n"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"Efficiency= 40 %\n"
]
}
],
"prompt_number": 28
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example 11.12, Page no.197"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"#variable declaration\n",
"n=2 #No. of threads\n",
"D=400 #Diameter of effort wheel in mm\n",
"r=50 #radius of load drum in mm\n",
"Eta=35.0/100 #efficiency\n",
"P=80 #Effort in N\n",
"T=50 #No. of teeth in worm wheel\n",
"\n",
"#calculation\n",
"VR=D*T/(n*r)\n",
"W=P*VR*Eta\n",
"\n",
"#Result\n",
"print\"W=\",int(W),\"N\"\n"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"W= 5600 N\n"
]
}
],
"prompt_number": 30
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example 11.13, Page no.199"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"#variable declaration\n",
"T_2=25.0 #No. of teeth on pinion\n",
"T_1=300.0 #No. of teeth on the spur wheel\n",
"r=50.0 #Radius of drum in mm\n",
"l=300.0 #Radius of the handle in mm\n",
"P=20.0 #Effort in N\n",
"W=300.0 #Load lifted in N\n",
"\n",
"#calculation\n",
"#To calculate efficiency of the machine\n",
"VR=int(((1/r)*(T_1/T_2))*100)\n",
"MA=W/P\n",
"Eta=MA/VR\n",
"#To calculate effect of friction\n",
"F_load=(P*VR)-W #In terms of load \n",
"F_effort=P-(W/VR) #In terms of effort\n",
"\n",
"#Result\n",
"print\"Efficiency of the machine=\",round(Eta*100,3),\"%\"\n",
"print\"Effect of friction in terms of load, F_load=\",int(F_load),\"N\"\n",
"print\"Effect of friction in terms of effort, F_effort=\",round(F_effort,1),\"N\"\n",
"\n"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"Efficiency of the machine= 62.5 %\n",
"Effect of friction in terms of load, F_load= 180 N\n",
"Effect of friction in terms of effort, F_effort= 7.5 N\n"
]
}
],
"prompt_number": 31
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example 11.15, Page no.202"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"#variable declaration\n",
"T_2=20.0 #No. of teeth of pinion\n",
"T_4=25.0 #No. of teeth of pinion\n",
"T_1=50.0 #No. of teeth on the spur wheel\n",
"T_3=60.0 #No. of teeth on the spur wheel\n",
"l=0.5 #length of the handle in m\n",
"r=0.25 #Radius of load drum in m\n",
"Eta=60.0/100 #Efficiency\n",
"W=720.0 #Load in N\n",
"#Calculation\n",
"VR=l/r*((T_1/T_2)*(T_3/T_4))\n",
"P=W/(VR*Eta)\n",
"\n",
"#Result\n",
"print\"P=\",int(P),\"N\""
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"P= 100 N\n"
]
}
],
"prompt_number": 34
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example 11.17, Page no.206"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"#variable declaration\n",
"n=3 #No. of pulleys\n",
"P=50.0 #Effort in N\n",
"W=320.0 #Weight lifted in N\n",
"\n",
"#calculation\n",
"#To calculate efficiency of the machine\n",
"VR=2**n\n",
"MA=W/P\n",
"Eta=MA/VR\n",
"#To calculate effect of friction\n",
"F_load=(P*VR)-W #In terms of load \n",
"F_effort=P-(W/VR) #In terms of amount\n",
"\n",
"#Result\n",
"print\"Efficiency of the machine=\",int(round(Eta*100,3)),\"%\"\n",
"print\"Amount of friction in terms of load, F_load=\",int(F_load),\"N\"\n",
"print\"Amount of friction in terms of effort, F_effort=\",int(F_effort),\"N\"\n",
"\n",
"\n"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"Efficiency of the machine= 80 %\n",
"Amount of friction in terms of load, F_load= 80 N\n",
"Amount of friction in terms of effort, F_effort= 10 N\n"
]
}
],
"prompt_number": 35
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example 11.18, Page no.208"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"#variable declaration\n",
"n=2*5 #No. of pulleys in each block\n",
"P=125.0 #Effort in N\n",
"W=1000.0 #Weight lifted in N\n",
"\n",
"#calculation\n",
"VR=n\n",
"F_load=(P*VR)-W #In terms of load \n",
"F_effort=P-(W/VR) #In terms of effort\n",
"\n",
"#Result\n",
"print\"Amount of effort wasted in friction, F_effort=\",int(F_effort),\"N\"\n",
"print\"Amount of friction load, F_load=\",int(F_load),\"N\" #Answer given wrongly in book. 250 is correct answer\n",
"\n",
"\n"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"Amount of effort wasted in friction, F_effort= 25 N\n",
"Amount of friction load, F_load= 250 N\n"
]
}
],
"prompt_number": 36
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example 11.19, Page no.209"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"#variable declaration\n",
"n=4 #No. of pulleys \n",
"W=1800 #load lifted in N\n",
"Eta=75.0/100 #efficiency\n",
"\n",
"#calculation\n",
"VR=(2**n)-1\n",
"P=W/(Eta*VR)\n",
"F_effort=P-(W/VR)\n",
"\n",
"\n",
"#Result\n",
"print\"Effort required to lift the load,P=\",int(P),\"N\"\n",
"print\"Effort wasted in friction, F_effort=\",int(F_effort),\"N\""
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"Effort required to lift the load,P= 160 N\n",
"Effort wasted in friction, F_effort= 40 N\n"
]
}
],
"prompt_number": 37
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example 11.20, Page no.210"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"import math\n",
"#variable declaration\n",
"p=10 #Pitch of thread in mm\n",
"l=400 #length of the handle in mm\n",
"W=2000 #load lifted in N\n",
"Eta=45.0/100 #Efficiency\n",
"\n",
"#calculation\n",
"VR=(2*math.pi*l)/p\n",
"P=W/(Eta*VR)\n",
"\n",
"#Result\n",
"print\"P=\",round(P,1),\"N\"\n"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"P= 17.7 N\n"
]
}
],
"prompt_number": 39
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example 11.21, Page no.212"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"import math\n",
"#variable declaration\n",
"p_1=12 #Pitch of the screw in mm\n",
"p_2=10 #Pitch of the screw in mm\n",
"l=300 #Arm length of jack in mm\n",
"W=7.5*1000 #Load lifted in N\n",
"P=30 #Effort in N\n",
"\n",
"#calculation\n",
"VR=int((2*math.pi*l)/(p_1-p_2))\n",
"MA=W/P\n",
"Eta=MA/VR\n",
"\n",
"#Result\n",
"print\"Efficiency, Eta=\",round(Eta*100,1),\"%\"\n",
"\n"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"Efficiency, Eta= 26.5 %\n"
]
}
],
"prompt_number": 40
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example 11.22, Page no.212"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"import math\n",
"#variable declaration\n",
"p_1=10 #Pitch of the screw jack in mm\n",
"p_2=7 #Pitch of the screw jack in mm\n",
"l=360 #Arm length of screw jack in mm\n",
"W=5*1000 #Load lifted in N\n",
"Eta=28.0/100 #Efficiency\n",
"\n",
"#calculation\n",
"VR=int((2*math.pi*l)/(p_1-p_2))\n",
"P=W/(Eta*VR)\n",
"\n",
"#Result\n",
"print\"P=\",round(P,1),\"N\""
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"P= 23.7 N\n"
]
}
],
"prompt_number": 41
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example 11.23, Page no.214"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"import math\n",
"#variable declaration\n",
"l=300.0 #length of handle in mm\n",
"T=50.0 #No. of teeth in worm wheel\n",
"p=10.0 #Pitch of screw in mm\n",
"P=100.0 #Effort applied in N\n",
"W=100000.0 #Load lifted in N\n",
"n=2 #no. of threads\n",
"#calculation\n",
"VR=int((2*math.pi*l*T)/(n*p))\n",
"MA=W/P\n",
"Eta=MA/VR\n",
"\n",
"#Result\n",
"print\"Efficiency, Eta=\",round(Eta*100,1),\"%\"\n"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"Efficiency, Eta= 21.2 %\n"
]
}
],
"prompt_number": 43
},
{
"cell_type": "code",
"collapsed": false,
"input": [],
"language": "python",
"metadata": {},
"outputs": []
}
],
"metadata": {}
}
]
}