In [1]:

```
import math
#Initilization of Variables
P=100 #N #effort applied
W=900 #N #Lad applied
y=100 #cm #Distance moved by effort
x=10 #cm #Distance moved by load
#Calculations
#Mechanical Advantage
MA=W*P**-1
#Velocity ratio
VR=y*x**-1
#Efficiency
rho=MA*VR**-1*100
#Result
print"Mechanical Advantage is",round(MA,2)
print"velocity ratio is",round(VR,2)
print"Efficiency is",round(rho,2)
```

In [2]:

```
import math
#Initilization of Variables
P=500 #N #Effort applied
y=5 #m #Distance moved by effort
x=0.5 #cm #Distance moved by load
rho=0.8 #Efficiency
#Calculations
#Load Lifted by machine
W=P*y*rho*(x)**-1 #N
#Mechanical Advantage
MA=W*P**-1
#Velocity ratio
VR=y*x**-1
#Result
print"Load Lifted by the machine is",round(W,2),"N"
print"Mechanical Advantage is",round(MA,2)
print"Velocity ratio is",round(VR,2)
```

In [3]:

```
import math
#Initilization of Variables
P=20 #N #Actual Effort
W=900 #N #Load Lifted
y=2.40 #m #Distance moved by effort
x=0.04 #m #Distance moved by load
#Calculations
#Mechanical Advantage
MA=W*P**-1
#Velocity ratio
VR=y*x**-1
#Efficiency
rho=MA*VR**-1
#Ideal Effort required
P1=rho*P
#Result
print"Mechanical Advantage is",round(MA,2)
print"Velocity ratio is",round(VR,2)
print"Efficiency is",round(rho,2)
print"Ideal Effort is",round(P1,2)
```

In [4]:

```
import math
#Initilization of Variables
rho=0.7 #eifficiency
P=10 #N #Effort
W=500 #N #Load
#Calculations
#Mechanical Advantage
MA=W*P**-1
#Velocity ratio
VR=MA*rho**-1
#Result
print"Mechanical Advantage is",round(MA,2)
print"Velocity ratio is",round(VR,2)
```

In [5]:

```
import math
#Initilization of Variables
P1=15 #N #Effort
W1=770 # #Load
rho=0.60 #Efficiency
P2=25 #N
W2=1320
P=15 #N
W=500 #N
#Calculations
#First Case
#Mechanical Advantage
MA=W1*P1**-1
#Velocity ratio
VR=MA*rho**-1
#Second case
#Mechanical Advantage
MA2=W2*P2**-1
#Efficiency
rho2=MA2*VR**-1*100
#Third case
#from LAw of machine
#P=m*W+C ................1
#Equation 2
#P2=W2*m+C ...............2
#Subtracting equation 2 from 1 we get
m=10*550**-1
#Constacnt value
C=P2-W2*m
#Sub value C in equation 1 we get
P3=m*W+C #N
#MAx Mechanical advantage
MA_max=1*m**-1
#MAx Efficiency
rho_max=1*(m*VR)**-1*100
#Result
print"Mechanical Advantage is",round(MA,2)
print"Velocity Ratio is",round(VR,2)
print"Efficiency is",round(rho2,2),"%"
print"Effort Required to raise the Load 500 N",round(P3,2),"N"
print"MAx Mechanical Advantage is",round(MA_max,2)
print"MAx Efficiency is",round(rho_max,2)
```

In [6]:

```
import math
#Initilization of Variables
#Effort
P1=15.5 #N
P2=19.5 #N
#Loads
W1=100 #N
W2=90 #N
m=0.2
#Calculations
#Law of machine equation
#P=m*W+C
#Equations
#P1=m*W1+C ................1
#P2=m*W2+C ....................2
#sub value of m in equation 1 weget
C=P1-m*W1
#Effort required to lift a Load
P1=m*W1+C
#MEchanical advantage
MA=1*m**-1
#Result
print"Effort required to Lift a Load of 100 N",round(P1,2),"N"
print"MAx MEchanical Advantage is",round(MA,2)
```

In [7]:

```
import math
#Initilization of Variables
rho=0.8 #Efficiency
P=15 #N #Effort
W=130 #N #Load
#Calculations
#Velocity ratio
VR=W*(P*rho)**-1
#Frictional force in terms of machine in tems of effort
Fp=P-W*VR**-1 #N
#Frictional Force of the machine in terms of Load
Fw=P*VR-W #N
#Result
print"Velocity ratio is",round(VR,2)
print"Frictional force in terms of machine in tems of effort",round(Fp,2),"N"
print"Frictional Force of the machine in terms of Load is",round(Fw,2),"N"
```

In [8]:

```
import math
#Initilization of Variables
VR=15 #Velocity ratio
rho=0.6 #Efficiency
W=100 #N #Load Lifted
#Calculations
#Power
P=W*(VR*rho)**-1 #N
#Frictional Force
Fp=P-(W*VR**-1) #N
#Let C=Fp
C=Fp
#From law of machine,we get
#P=m*W+C
#After sub values and furter simplifying we get
m=(P-C)*W**-1
#After sub values in above equaion we get law of machine as
#P2=m*W2+c #N
#when W2=140 #N
W2=140 #N
P2=m*W2+C #N
#When W3=0
W3=0 #N
P3=m*W3+C #N
#Result
print"Effort required to run the machine at Load:W2=140 is",round(P2,2),"N"
print"Effort required to run the machine at Load:W3=0 is",round(P3,2),"N"
```

In [9]:

```
import math
#Initilization of Variables
P=12 #N #Effort
VR=18 #Velocity ratio
rho=0.6 #efficiency
#Calculations
#Load lifted
W=rho*P*VR #N
#LEt C=Fp
Fp=P-(W*VR**-1) #N
C=Fp
#From law of machine we get
m=(P-C)*W**-1 #N
#Sub value of m in equation we get
#P2=1*18**-1*W2+C
#Sub W2=90
W2=90
P2=m*W2+C
#Result
print"Effort required to run the machine is",round(P2,2),"N"
```

In [10]:

```
import math
#Initilization of Variables
VR=10 #Velocity ratio
P=100 #N #Effort applied
Fp=20 #N #effort lost in friction
#Calculations
#Load Lifted
W=(P-Fp)*VR #N
#Efficiency
rho=W*P**-1*VR**-1*100
#Result
print"Load Lifted is",round(W,2),"N"
print"Efficiency is",round(rho,2),"%"
```

In [11]:

```
import math
#Initilization of Variables
P=40 #N #Effort applied
W=600 #N #Load Lifted
VR=20 #Velocity ratio
#Calculations
#MAchine Fiction in terms of effort
Fp=P-W*VR**-1 #N
#M/c Friction in terms of Load
Fw=P*VR-W #N
#efficiency
rho=W*P**-1*VR**-1*100
#Result
print"MAchine Fiction in terms of effort is",round(Fp,2),"N"
print"M/c Friction in terms of Load is",round(Fw,2),"N"
print"Ffficiency of the machine is",round(rho,2),"%"
```

In [12]:

```
import math
#Initilization of Variables
P=15 #N #Effort applied
W=200 #N #Load Lifted
VR=40 #Velocity ratio
#Calculations
#Efficiency
rho=W*P**-1*VR**-1 #%
#Friction Load of m/c
Fw=P*VR-W #N
#Result
print"Friction Load of m/c is",round(Fw,2),"N"
```

In [13]:

```
import math
#Initilization of Variables
W=48 #N #Weight
P=16 #N #Force
D=400 #mm #Diameter of wheel
d=100 #mm #Diameter of axle
#Calculations
#Mechanical Advantage
MA=W*P**-1
#Velocity ratio
VR=D*d**-1
#Efficiency of the machine
rho=MA*VR**-1*100 #%
#Result
print"Mechanical Advantage is",round(MA,2)
print"Velocity ratio is",round(VR,2)
print"Efficiency of the machine is",round(rho,2),"%"
```

In [14]:

```
import math
#Initilization of Variables
D=25 #cm #Diameter of wheel
d1=10 #cm #LArge dia. of axle
d2=9 #cm #Small Dia. of axle
P=30 #N #Effort applied
W=900 #N #Load Lifted
#Calculations
#Velocity ratio
VR=2*D*(d1-d2)**-1
#Mechanical advantage
MA=W*P**-1
#Efficiency
rho=MA*VR**-1*100
#Result
print"Velocity ratio is",round(VR,2)
print"Mechanical advantage is",round(MA,2)
print"Efficiency is",round(rho,2),"%"
```

In [15]:

```
import math
#Initilization of Variables
T=60 #No. of teeth on worm wheel
L=12.5 #cm #Radius of effort wheel
r=6.25 #cm #Radius of Load drum
P=20 #N #Effort
W=600 #N #Load
#Calculations
#Velocity ratio
VR=L*T*r**-1
#Efficiency
rho=W*P**-1*VR**-1*100
#Result
print"Velocity ratio for single threaded worm is",round(VR,2)
print"Efficiency of the worm is",round(rho,2),"%"
```

In [16]:

```
import math
#Initilization of Variables
T1=10 #No.of teeth on pinion
T2=100 #No.of teeth on spur wheel
D=30 #cm #Dia. of Load axle
L=30 #cm #Length of lever
P=20 #N #Effort applied
W=360 #N #Load Lifted
#Calculations
#Velocity ratio
VR=2*L*T2*(D*T1)**-1
#Efficiency
rho=W*P**-1*VR**-1*100
#Result
print"Velocity ratio is",round(VR,2)
print"Efficinecy is",round(rho,2),"%"
```

In [17]:

```
import math
#Initilization of Variables
P=40 #N #Effort
rho=0.5 #Efficincy
D=20 #cm #Dia. of load axle
L=80 #cm #Length of Lever
T1=10 #No. of teeth om pinion of effort axle
T2=100 #No. of teeth on spur wheel of intermediate axle
T3=20 #No. of teeth om pinion of Load axle
T4=200 #No. of teeth on spur wheel of load axle
#Calculations
#Velocity ratio
VR=2*L*D**-1*T2*T1**-1*T4*T3**-1
#Mechanical Advatnage
MA=rho*VR
#Load Which can be Lifted
W=MA*P*10**-3 #N
#Result
print"Velocity ratio is",round(VR,2)
print"Load Which can be Lifted is",round(W,2),"KN"
```

In [18]:

```
import math
#Initilization of Variables
rho=0.4 #Efficincy
D=20 #cm #Dia. of load axle
L=40 #cm #Length of Lever
T1=15 #No. of teeth om pinion of effort axle
T2=45 #No. of teeth on spur wheel of intermediate axle
T3=20 #No. of teeth om pinion of Load axle
T4=40 #No. of teeth on spur wheel of load axle
W=250 #N #Load Lifted
#Calculations
#Velocity ratio
VR=VR=2*L*D**-1*T2*T1**-1*T4*T3**-1
#Effort applied
P=W*(rho*VR)**-1 #N
#Result
print"Effort applied at the end is",round(P,2),"N"
```

In [19]:

```
import math
#Initilization of Variables
n=4 #No. of movable pulleys
W=1440 #N #Load
P=100 #N #effort
#Calculations
#Mechanical Advantage
MA=W*P**-1
#Velocity ratio
VR=2**4
#Efficiency
rho=MA*VR**-1*100 #%
#Ideal Effort
P2=W*VR**-1
#Effort wsted in friction
P3=P-P2 #N
#Load WAsted in friction
W2=VR*P
W3=W2-W
#Result
print"Efficiency of the machine is,",round(rho,2),"%"
print"Effort Wasted in friction is",round(P3,2),"N"
print"Load Wasted in friction is",round(W3,2),"N"
```

In [20]:

```
import math
#Initilization of Variables
W=2000 #N #Weight
P=600 #Effort
n=5 #Total No. of pulleys
VR=n
#Calculations
#Mechanical advantage
MA=W*P**-1
#efficiency
rho=MA*VR**-1*100
#Result
print"Efficiency of the system is",round(rho,2),"%"
```

In [21]:

```
import math
#Initilization of Variables
n=4 #No. of pulleys
P=160 #N #Effort
rho=0.75 #efficiency
VR=15 #Velocity ratio
#Calculations
#weight Lifted
W=rho*P*VR
#Result
print"Weight Lifted is",round(W,2),"N"
```

In [22]:

```
import math
#Initilization of Variables
rho=0.5 #Efficency
D=25 #cm #Diameter of Large pulley
d=20 #cm #Dia. of smaller pulley
P=20 #N #Effort applied
#Calculations
#Velocity ratio
VR=2*D*(D-d)**-1
#Load Lifted
W=rho*d*VR #N
#Result
print"Load Lifted by the machine is",round(W,2),"N"
```

In [23]:

```
import math
#Initilization of Variables
W=1500 #Load
L=0.7 #Length of handle
d=0.06 #m #Mean diaof screw jack
p=0.009 #pitch of the screw jack
mu=0.095 #co-efficient of friction
pi=3.14
#Calculations
#Effort required
X=(W*d*(2*L)**-1)*(p+mu*pi*d)*(pi*d-p*mu)**-1 #N
#Effort required at the end of the handle for lowering the load
P2=W*d*(2*L)**-1*(mu*pi*d-p)*(pi*d+mu*p)**-1 #N
#Result
print"Effort required at the end of the handle for Lifting Load 1500 N",round(X,2),"N"
print"Effort required at the end of the handle for lowering the load is",round(P2,2),"N"
```

In [1]:

```
import math
from math import sin, cos, tan, radians, pi
#Initilization of Variables
W=3000 #N #Load Lifted
n=2 #No. of square thread
D1=6 #cm #Outer diameter
mu=0.09 #Coefficient offriction
L=0.6 #m #Length
#Calculations
#pitch of screw
p=1.2*n**-1*10**-2 #m
#Thickness of thread
t=0.5*p #
#Diameter at base of screw
D2=D1-2*t
#Mean Diameter
d=(D1+D2)*2**-1*10**-2 #m
#Force
P=W*d*(2*L)**-1*(p+mu*pi*d)*(pi*d-p*mu)**-1 #N
#Result
print"Force required at the end of handle is",round(P,2),"N"
#Answer in textbook is incorrect
```

In [25]:

```
import math
from math import sin, cos, tan, radians, pi
#Initilization of Variables
W=5000 #N #Load
n=2
t=0.003 #m #Thickness
D1=0.06 #m #outer diameter
D2=0.054 #m #Inner diameter
d=0.057 #MEan diameter
mu=0.08 #Coefficient of friction
L=0.6 #m #Length
p=0.006 #m #pitch
#Calculations
#Let tan(alpha)=X
X=p*(pi*d)**-1
#Let tan(phi)=Y
Y=mu
#Force reuired at the end of handle
P=d*(2*L)**-1*W*(X+Y)*(1-X*Y)**-1
#Result
print"Force reuired at the end is",round(P,2),"N"
```

In [26]:

```
import math
from math import sin, cos, tan, radians, pi
#Initilization of Variables
W=2000 #N #Load Lifted
p=1 #mm #pitch
rho=0.5 #efficiency
L=50 #cm #Length of handle
#Calculations
#Velocity ratio
VR=2*pi*L*p**-1
#Effort applied
P=W*(rho*VR)**-1
#Result
print"Effort applied at the end of handle",round(P,2),"N"
```

In [27]:

```
import math
from math import sin, cos, tan, radians, pi
#Initilization of Variables
rho=0.55 #efficiency
W=1500 #N #Load Lifted
L=0.5 #m #Length of handle
p=0.01 #m #Pitch of the screw
#Calculations
#Velocity ratio
VR=2*pi*L*p**-1
#Effort applied
P=W*(VR*rho)**-1 #N
#Result
print"Effort applied is",round(P,2),"N"
```

In [28]:

```
import math
from math import sin, cos, tan, radians, pi
#Initilization of Variables
d=0.075 #m #Mean diameter
p=0.015 #m #Pitch of threads
mu=0.05 #Coefficient of friction
W=600 #N
L=0.36 #m #LEngth
#Calculations
#Tangential Force
P=W*d*(2*L)**-1*(p+mu*pi*d)*(pi*d-p*mu)**-1 #N
#Let Tan(alpha)=X
#tan(phi)=Y
#tan(alpha+phi)=Z
X=p*(pi*d)**-1
Y=mu
Z=(X+Y)*(1-X*Y)**-1
#efficiency
rho=X*Z**-1
#Effort
P2=W*((X-Y)*(1+X*Y)**-1) #N
#Torque required
T=P2*d*2**-1 #N*m
#Result
print"Tangential Force to be qpplied is",round(P,2),"N"
print"Torque necesscary to lower the load is",round(T,2),"Nm"
```

In [29]:

```
import math
from math import sin, cos, tan, radians, pi
#Initilization of Variables
d=0.06 #m #Mean diameter
p=0.008 #m P#itch
mu=0.09
W=3 #Load Lifted
x=0.12 #m
n=15 #No. of turns
#Calculations
#Let Tan(alpha)=X
#tan(phi)=Y
X=p*(pi*d)**-1
Y=mu
P=W*((X+Y)*(1-X*Y)**-1) #N
#Torque required
T=P*d*2**-1 #N*m
#Total Angular displacement
omega=n*2*pi
#Workk done
W2=omega*T #KNm
#efficiency
rho=W*x*W2**-1*100 #%
#Efficiency can also be determined as
rho2=X*(X+Y)**-1*(1-X*Y)*100
#Result
print"Torque required is",round(T,2),"Nm"
print"Work done in lifting the load is",round(W2,3),"KN"
print"Efficiency of the jack is",round(rho2,1),"%"
```

In [3]:

```
import math
from math import sin, cos, tan, radians, pi
#Initilization of Variables
p1=1 #cm #Pitch of Larger screw
p2=0.7 #cm #Pitch of smaller screw
l=36 #cm #Length of handle
rho=0.28 #efficiency
W=5000 #N #Weight
#Calculations
#Velocity ratio
VR=2*pi*l*(p1-p2)**-1
#Effort applied
P=W*(rho*VR)**-1 #N
#Result
print"Effort required to Lift the Load",round(P,2),"N"
```