Chapter 11:Simple Lifting Machines

Example 11.1, Page no.187

In [9]:
#variable declaration
D=300.0    #Diameter of wheel in mm
d=30.0     #Diameter of axle in mm
W=900.0    #Load in N
P=100.0    #Effort applied in N

#calculation
VR=D/d
MA=W/P
Eta=MA/VR

#Result
print"Efficiency, Eta =",int(Eta*100),"%"

Efficiency, Eta = 90 %

Example 11.2, Page no.187

In [4]:
#variable declaration
W=480.0    #Load in N
P=120.0    #effort in N
D=500.0    #Diameter of wheel in mm
d=100.0    #Diameter of axle in mm

#calculation
MA=W/P
VR=D/d
Eta=MA/VR

#Result
print"(i)Mechanical Advantage=",int(MA)
print"(ii)Velocity ratio=",int(VR)
print"(iii)Efficiency of machine=",int(Eta*100),"%"

(i)Mechanical Advantage= 4
(ii)Velocity ratio= 5
(iii)Efficiency of machine= 80 %

Example 11.3, Page no.189

In [8]:
#variable declaration
d1=80     #larger diameter of wheel in mm
d2=70     #Smaller diamter of wheel in mm
D=250     #Diameter of effort wheel in mm
W=1050.0  #Load lifted in N
P=25.0    #Effort in N


#calculation
VR=2*D/(d1-d2)
MA=W/P
Eta=MA/VR
F_effort=P-(W/VR)


#Result
print"Velocity Ratio, VR=",int(VR)  #Answer given wrongly in book. 50 is correct answer
print"Efficiency, Eta=",int(Eta*100),"%"
print"Frictional effort lost, F_effort=",int(F_effort),"N"

Velocity Ratio, VR= 50
Efficiency, Eta= 84 %
Frictional effort lost, F_effort= 4 N

Example 11.5, Page no.190

In [17]:
#variable declaration
D=410.0     #Effective diameter of wheel in mm
d1=310.0    #Effective diameter of axle in mm
d2=210.0    #Effective diameter of axle in mm
P=25.0      #Effort in N
Eta=84.0/100#Efficiency

#calculation
VR=2*D/(d1-d2)
W=Eta*P*VR

#Result
print"W=",round(W,1),"N"

W= 172.2 N

Example 11.6, Page no.191

In [18]:
#variable declaration
R=125      #Radius of larger groove in mm
r=115      #Radius of smaller groove in mm
Eta=80.0/100 #Efficiency
W=1500     #Load in N

#calculation
VR=2*R/(R-r)
P=W/(Eta*VR)

#Result
print"P=",int(P),"N"

P= 75 N

Example 11.7, Page no.192

In [20]:
#variable declaration
W=1800.0 #Load in N
P=100    #effort in N
T1=12    #number of teeth on larger block
T2=11    #number of teeth on smaller block

#calculation
VR=2*T1/(T1-T2)
MA=W/P
Eta=MA/VR

#Result
print"Velocity Ratio=",int(VR)
print"Mechanical Advantage=",int(MA)
print"Efficiency=",int(Eta*100),"%"

Velocity Ratio= 24
Mechanical Advantage= 18
Efficiency= 75 %

Example 11.8, Page no.193

In [23]:
#variable declaration
T1=90.0        #No. of cogs on the effort wheel
T2=25.0        #No. of cogs on the effort pinion
T3=40.0        #No. of teeth on the spur wheel
T4=8.0         #No. of teeth on the load wheel
P=50.0         #effort in N
Eta=75.0/100   #Efficiency

#calculation
VR=(T1/T2)*(T3/T4)
W=Eta*P*VR

#Result
print"W=",int(W),"N"

W= 675 N

Example 11.9, Page no.195

In [25]:
#variable declaration
T=40.0    #No. of teeth on the worm wheel
D=300.0   #Diameter of effort wheel in mm
r=50.0    #radius of load drum in mm
W=1800.0  #Load in N
P=24.0    #effort in N

#calculation
VR=D*T/(2*r)
MA=W/P
Eta=MA/VR

#Result
print"Efficiency=",round(Eta*100,1),"%"

Efficiency= 62.5 %

Example 11.10, Page no.195

In [27]:
#variable declaration
n=2        #No. of threads
T=60       #No. of teeth on worm wheel
D=250      #Diameter of effort wheel in mm
r=50       #raidus of load drum in mm
Eta=50.0/100 #Efficiency
W=300      #load in N

#calculation
VR=D*T/(2*n*r)
P=W/(Eta*VR)

#Result
print"Velocity ratio of the machine, VR=",int(VR)
print"Effort required,P=",int(P),"N"

Velocity ratio of the machine, VR= 75
Effort required,P= 8 N

Example 11.11, Page no.197

In [28]:
#variable declaration
D=200.0     #Diameter of effort wheel in mm
T=60.0      #No. of teeth in worn wheel
r=40.0      #radius of load drum in mm
W=9000.0    #load in N
P=75.0      #Effort in N

#calculation
VR=(D*T)/r
MA=W/P
Eta=MA/VR

#Result
print"Efficiency=",int(Eta*100),"%"

Efficiency= 40 %

Example 11.12, Page no.197

In [30]:
#variable declaration
n=2          #No. of threads
D=400        #Diameter of effort wheel in mm
r=50         #radius of load drum in mm
Eta=35.0/100 #efficiency
P=80         #Effort in N
T=50         #No. of teeth in worm wheel

#calculation
VR=D*T/(n*r)
W=P*VR*Eta

#Result
print"W=",int(W),"N"

W= 5600 N

Example 11.13, Page no.199

In [31]:
#variable declaration
T_2=25.0     #No. of teeth on pinion
T_1=300.0    #No. of teeth on the spur wheel
r=50.0       #Radius of drum in mm
l=300.0      #Radius of the handle in mm
P=20.0       #Effort in N
W=300.0      #Load lifted in N

#calculation
#To calculate efficiency of the machine
VR=int(((1/r)*(T_1/T_2))*100)
MA=W/P
Eta=MA/VR
#To calculate effect of friction
F_load=(P*VR)-W   #In terms of load 
F_effort=P-(W/VR) #In terms of effort

#Result
print"Efficiency of the machine=",round(Eta*100,3),"%"
print"Effect of friction in terms of load, F_load=",int(F_load),"N"
print"Effect of friction in terms of effort, F_effort=",round(F_effort,1),"N"

Efficiency of the machine= 62.5 %
Effect of friction in terms of load, F_load= 180 N
Effect of friction in terms of effort, F_effort= 7.5 N

Example 11.15, Page no.202

In [34]:
#variable declaration
T_2=20.0      #No. of teeth of pinion
T_4=25.0      #No. of teeth of pinion
T_1=50.0      #No. of teeth on the spur wheel
T_3=60.0      #No. of teeth on the spur wheel
l=0.5         #length of the handle in m
r=0.25        #Radius of load drum in m
Eta=60.0/100  #Efficiency
W=720.0       #Load in N
#Calculation
VR=l/r*((T_1/T_2)*(T_3/T_4))
P=W/(VR*Eta)

#Result
print"P=",int(P),"N"

P= 100 N

Example 11.17, Page no.206

In [35]:
#variable declaration
n=3          #No. of pulleys
P=50.0       #Effort in N
W=320.0      #Weight lifted in N

#calculation
#To calculate efficiency of the machine
VR=2**n
MA=W/P
Eta=MA/VR
#To calculate effect of friction
F_load=(P*VR)-W   #In terms of load 
F_effort=P-(W/VR) #In terms of amount

#Result
print"Efficiency of the machine=",int(round(Eta*100,3)),"%"
print"Amount of friction in terms of load, F_load=",int(F_load),"N"
print"Amount of friction in terms of effort, F_effort=",int(F_effort),"N"

Efficiency of the machine= 80 %
Amount of friction in terms of load, F_load= 80 N
Amount of friction in terms of effort, F_effort= 10 N

Example 11.18, Page no.208

In [36]:
#variable declaration
n=2*5         #No. of pulleys in each block
P=125.0       #Effort in N
W=1000.0      #Weight lifted in N

#calculation
VR=n
F_load=(P*VR)-W   #In terms of load 
F_effort=P-(W/VR) #In terms of effort

#Result
print"Amount of effort wasted in friction, F_effort=",int(F_effort),"N"
print"Amount of friction load, F_load=",int(F_load),"N" #Answer given wrongly in book. 250 is correct answer

Amount of effort wasted in friction, F_effort= 25 N
Amount of friction load, F_load= 250 N

Example 11.19, Page no.209

In [37]:
#variable declaration
n=4           #No. of pulleys 
W=1800        #load lifted in N
Eta=75.0/100  #efficiency

#calculation
VR=(2**n)-1
P=W/(Eta*VR)
F_effort=P-(W/VR)


#Result
print"Effort required to lift the load,P=",int(P),"N"
print"Effort wasted in friction, F_effort=",int(F_effort),"N"

Effort required to lift the load,P= 160 N
Effort wasted in friction, F_effort= 40 N

Example 11.20, Page no.210

In [39]:
import math
#variable declaration
p=10         #Pitch of thread in mm
l=400        #length of the handle in mm
W=2000       #load lifted in N
Eta=45.0/100 #Efficiency

#calculation
VR=(2*math.pi*l)/p
P=W/(Eta*VR)

#Result
print"P=",round(P,1),"N"

P= 17.7 N

Example 11.21, Page no.212

In [40]:
import math
#variable declaration
p_1=12     #Pitch of the screw in mm
p_2=10     #Pitch of the screw in mm
l=300      #Arm length of jack in mm
W=7.5*1000 #Load lifted in N
P=30       #Effort in N

#calculation
VR=int((2*math.pi*l)/(p_1-p_2))
MA=W/P
Eta=MA/VR

#Result
print"Efficiency, Eta=",round(Eta*100,1),"%"

Efficiency, Eta= 26.5 %

Example 11.22, Page no.212

In [41]:
import math
#variable declaration
p_1=10       #Pitch of the screw jack in mm
p_2=7        #Pitch of the screw jack in mm
l=360        #Arm length of screw jack in mm
W=5*1000     #Load lifted in N
Eta=28.0/100 #Efficiency

#calculation
VR=int((2*math.pi*l)/(p_1-p_2))
P=W/(Eta*VR)

#Result
print"P=",round(P,1),"N"

P= 23.7 N

Example 11.23, Page no.214

In [43]:
import math
#variable declaration
l=300.0    #length of handle in mm
T=50.0     #No. of teeth in worm wheel
p=10.0     #Pitch of screw in mm
P=100.0    #Effort applied in N
W=100000.0 #Load lifted in N
n=2        #no. of threads
#calculation
VR=int((2*math.pi*l*T)/(n*p))
MA=W/P
Eta=MA/VR

#Result
print"Efficiency, Eta=",round(Eta*100,1),"%"

Efficiency, Eta= 21.2 %
In [ ]: