In [1]:

```
import math
from math import sin, cos, radians, pi
#Initilization of Variables
W=500 #N #Weight of Body
S=5 #m #Distance
P=250 #N #Force
P2=200 #N #Force 2
theta=30 #Degrees #Angle made by Force with Horizontal
#Calculation
#Part-1
#Work Done
w=P*S #N*m
#Work Done
w2=P2*cos(theta*pi*180**-1)*S #N*m
#Result
print"Work Done when Force 250 N is applied",round(w,2),"N*m"
print"Work Done when Force 200 N is applied",round(w2,2),"N*m"
```

In [2]:

```
import math
#Initilization of Variables
W=1500 #N #Weight of Body
S=500 #m #Distance
P=15 #N #Force
#Calculation
#Work Done by Resistance
w=P*S #N*m
#Result
print"Work Done on body by Resistance is",round(w,2),"N*m"
```

In [2]:

```
import math
from math import sin, cos, radians, pi
#Initilization of Variables
W=800 #N #Weight of Body
theta=30 #Degrees #angle made by Force
S=5 #Distance
#Calculation
#Force apllied on Block
P=W*sin(theta*pi*180**-1) #N
#Work done on body
w=P*S #N*m
#Result
print"Work Done in Pulling up the Body is",round(w,2),"N*m"
```

In [4]:

```
import math
from math import sin, cos, radians, pi
#Initilization of Variables
mu=0.3 #coefficient of Friction
S=5 #m #Distance
W=800 #N #weight of Body
theta=30 #Degrees #Angle made by Weight
#Calculation
#reaction Force
R=W*cos(theta*pi*180**-1) #N
#Force of friction
F=mu*R
#Forces along plane
P=W*sin(theta*pi*180**-1)+F #N*m
#Work done
w=P*S #N*m
#Result
print"Work done in pullint the Body",round(w,2),"N*m"
```

In [5]:

```
import math
from math import sin, cos, radians, pi
#Initilization of Variables
L=50.5 #m #Total Length of chain
R=0.16 #m #Radius of pulley
L_AC=40 #m #Length of chain between A and C
W=505 #N #Weight of chain
w=10 #N #weight of chain per metre length
#Calculation
#Length of BD
L_BD=L-2*pi*R*2**-1-L_AC #m
#Weight of chain
W_AC=w*L_AC #N
#Weight of chain BD
W_BD=w*L_BD #N
#Force applied at D
P=W_AC-W_BD #N
#Length of chain
l=(L_AC-w)*2**-1
#Work Done
W=P*l*2**-1 #N
#Result
print"Work Done by the man",round(W,2),"N"
```

In [6]:

```
import math
#Initilization of Variables
W=2000 #N #Weight of Body
P_o=750 #N #Initial Force
x_o=0 #Initial Force,distance moved is zero
S=25 #m #Distance Moved
#Calculation
#Force after a distance of 25 m
P=P_o+10*S #N
#Work Done
w=(P_o+P)*2**-1*S #N*m
#Result
print"Work Done by applied Force",round(w,2),"N*m"
```

In [7]:

```
import math
from scipy.integrate import *
#Initilization of Variables
L=10 #m #Length of free cable
W=50 #N #weight of cable per m length
#Calculation
#Weight of element
#X=50*dx
#work done on the elemnt
#dw=500-50*x*dx
def f(x) :
return 500-50*x
I,err = quad(f,0,10)
#Result
print"Work done by Electric Motor is",round(I,2),"N*m"
```

In [8]:

```
import math
#Initilization of Variables
W=2000 #KN #Weight of train
v=10 #m/s #speed of train
F=20000 #N #Resistance due to friction
p=F #Net Force in Direction of motion
#Calculation
#Power
P=p*v*10**-3 #KW
#Result
print"Power of the Engine",P,"KW"
```

In [9]:

```
import math
#Initilization of Variables
W=2000 #KN #Weight of train
F=20000 #N #Resistance Force
v=10 #m/s #Velocity
a=0.5 #m/s**2 #Acceleration
g=9.81 #m/s**2 #acceleration due to gravity
#Calculation
#Mass of train
m=W*10**3*g**-1 #Kg
#Net Force
F=m*a+F #N
#Power of the engine
P=F*v*10**-3 #KW
#Result
print"Power of the Engine is",round(P,2),"KW"
```

In [10]:

```
import math
#Initilization of Variables
W=1500*1000 #N #Weight of train
v=10 #m/s #speed
F=7500 #N #Force exerted by engine
#sin(theta)=1*100**-1
#Calculation
#from equation of Net Force
#p=W*sin(theta*pi*180**-1)+F
#After sub values and further simplifying we get
p=15000+7500 #N
#Power Exerted by Engine
P=p*v*10**-3 #KW
#Result
print"Power Exerted by the Engine is",round(P,2),"KW"
```

In [13]:

```
import math
#Initilization of Variables
W=2*10**6 #N
v=5 #m/s velocity
P=35*10**3 #W
#Calculation
#After simplifying Net Force acting on engine in direction of motion, we get
#F=13333.3-F+P ................1
#Power
P2=P*v**-1
#Sub value in equation 1 we get
F=13333.3+P2 #N
#case-2
#frpm Net force in direction of motion after simplifying we get,value of
F2=W*150**-1+F #N
#Power developed by engine
P3=F2*v*10**-3 #KW
#Result
print"Power required to pull the train is",round(P3,2),"KW"
```

In [1]:

```
import math
from math import pi
#Initilization of Variables
P=1800 #N #Force
D=0.01 #m #Diameter
R=0.005 #m #Radius
theta=2*pi #Radians
#Calculation
#Torque
T=P*R #N*m
#Work done
W=T*theta #N*m
#Result
print"Work Done is",round(W,2),"N*m"
```

In [2]:

```
import math
from math import pi
#Initilization of Variables
F=1800 #N #Force
R=0.005 #m #Radius
T=9 #N*m #Torque
N=200 #r.p.m
#Calculation
#Power of the shaft
P=2*pi*N*T*60**-1 #W
#Result
print"Power of the shaft is",round(P,2),"N*m"
```

In [16]:

```
import math
#Initilization of Variables
M=2 #Kg #Mass
v=50 #m/s**2 #Velocity
#Calculation
#Let K.E be E
E=1*2**-1*M*v**2 #N*m
#Result
print"Kinetic Energy is",round(E,2),"N*m"
```

In [17]:

```
import math
#Initilization of Variables
m=0.081 #Kg
u=300 #m/s #Initial Velocity of bullet
#Calculation
#Part-1
S=0.1 #m #Penetration of bullet
v=0 #Final Velocity of bullet
#Kinetic Energy of bullet
KE=(m*v**2-m*u**2)*2**-1 #N*m
#Force of Resistance
P=-KE*S**-1 #N
#Part-2
#Depth of penetration
S2=0.05 #m
#work Done by force of Resistance
W2=-P*S2 #N*m
#velocity of bullet after 5cm penetration
v1=((W2+(m*u**2*2**-1))*2*m**-1)**0.5
#Result
print"Force of Resistance is",round(P,2),"N"
print"Velocity with which bullet will emerge is",round(v1,2),"m/s"
```

In [18]:

```
import math
#Initilization of Variables
m=0.01 #Kg
u=1000 #m/s #Velocity
t=0.002 #s #time taken b bullet to travel
v=0 #Final Velocity
g=9.81 #acceleration due to gravity
#Calculation
#Kinetic energy of bullet
KE=m*u**2*2**-1 #N*m
#acceleration
a=-(v-u)*t**-1 #m/s**2
#Frictional Force
F=m*a #N
#Distance travelled by bullet
S=F*KE**-1 #m
#Part-2
#Probable speed of the car just before brakes are applied
V=(30*2*g)**0.5*1000**-1*3600 #m/s
#Result
print"Average Force acted on the bullet is",round(F,2),"N"
print"Distance penetrated by it",round(S,2),"m"
print"Probable speed of the car just before brakes are applied",round(V,2),"km/hr"
```

In [19]:

```
import math
#Initilization of Variables
W=20*10**3 #N #Weight of Truck
u=45*10**3*(3600)**-1 #speed of truck #m/s
v=0 #Final Velocity of truck
g=9.81 #Acceleration due to gravity
m=W*g**-1 #mass of truck
S=20 #m #DIstance
#Calculation
#Kinetic energy of Truck
KE=-m*(v**2-u**2)*2**-1 #N*m
#Average Force of Resisting acting on the truck
P=KE*S**-1 #N
#Result
print"Average Force of Resisting acting on the truck",round(P,2),"N"
```

In [20]:

```
import math
#Initilization of Variables
W=9810 #N #Weight of train
m=1000 #Kg #Mass of car
u=0 #m/s #Intial Velocity
v=12.5 #m/s #Final by car
S=50 #m #Distance
P=100 #N #Resistance
#Calculation
#Change in Kinetic Energy
KE=m*(v**2-u**2)*2**-1 #N*m
#Average driving Force exerted by engine
P2=KE*S**-1+P #N
#Power Developed by Engine
P3=P2*v*10**-3 #KW
#Result
print"Average driving Force exerted by engine",round(P2,2),"N"
print"Power Developed by Engine",round(P3,2),"N"
```

In [3]:

```
import math
from math import cos, pi,sin, radians
#Initilization of Variables
W=196.2 #N #Weight of train
m=20 #Kg #Mass
P=300 #N #force
theta=30 #Degrees #Angle of inclination
mu=0.2 #Coefficient of friction
u=0 #initial Velocity
t=4 #seconds
#Calculation
R=W*cos(theta*pi*180**-1) #N
#Net Force in Direction of motion
F=P-W*sin(theta*pi*180**-1)-mu*R #N
#Acceleration
a=F*m**-1 #m/s**2
#Distance travelled in four seconds
s=u*t+a*t**2*2**-1
#Velocity after 4 seconds
v=u+a*t #m/s
#Kinetic Energy after 4 seconds
KE=m*v**2*2**-1 #N*m
#Work Done on Body
W2=F*s #N*m
#Momentum of the body after four seconds
e=m*v #Kg*m/s
#Impulse applied in four seconds
I=F*t #N*s
#Result
print"Acceleration of Body",round(a,2),"m/s**2"
print"Distance travelled in four seconds",round(s,2),"m"
print"Velocity after 4 seconds",round(v,2),"m/s"
print"Kinetic Energy after 4 seconds",round(KE,2),"N*m"
print"Work Done on Body",round(W2,2),"N*m"
print"Momentum of the body after four seconds",round(e,2),"Kg*m/s"
print"Impulse applied in four seconds",round(I,2),"N*s"
```

In [4]:

```
import math
from math import cos, pi,sin, radians
#Initilization of Variables
W=20 #N #Weight
theta=20 #Degrees #Angle
u=12 #m/s #Initial Velocity
mu=0.15 #Coefficient of friction
g=9.81 #acceleration due to gravity
m=W*g**-1 #Kg
#Calculation
#PArt-1
v=0 #Final Velocity
R=W*cos(theta*pi*180**-1)
F=mu*R
#Net Force
F2=W*sin(theta*pi*180**-1)+mu*R #N
#Change in Kinetic Energy
KE=m*(v**2-u**2)*2**-1 #N*m
S=KE*F2**-1 #Max Distance
#PArt-2
#Net Force in direction of motion is
F3=W*sin(theta*pi*180**-1)-mu*R #N
#Work Done on the body
W2=F3*S #N*m
#Velocity of the body
V1=(-W2*2*g*W**-1)**0.5
#Result
print"MAx Distance that the bodt will move up the inclined plane",round(S,2),"m"
print"Velocity of the body",round(V1,2),"m/s"
```

In [23]:

```
import math
#Initilization of Variables
m1=0.025 #Kg #Mass of bullet
u1=600 #m/s #Initial Veloctiy of Bullet
m2=5 #Kg #Mass of Wooden Block
u2=0 #m/s #Final Velocity of bullet
S=0.9 #m #Distance travelled by block and bullet
g=9.81 #Acceleration due to gravity
#Calculation
#Total mass of bullet
M=m1+m2 #Kg
#common Velocityof bullet and block after impact
V=(m1*u1+m2*u2)*M**-1 #m/s
#Average resistance between block and horizontal surface
#Initial Velocity of Block And Bullet
Vi=V #m/s
#Final Velocity
Vf=0 #m/s
#Change of KE of bullet and Block
KE=M*(Vf**2-Vi**2)*2**-1 #N*m
#Frictional resistance
P=-KE*S**-1 #N
#Coefficient of Friction
W=M*g #N
R=W #N
mu=P*R**-1
#Result
print"Average Resistance between Block and horizontal surface",round(P,2),"N"
print"Coefficient of friction is",round(mu,2)
```

In [24]:

```
import math
#Initilization of Variables
m1=0.01 #Kg #mass of bullet
m2=1 #Kg #Mass of Block
S=1 #m #Distance travelled by block and bullet
mu=0.2 #coefficient of friction
g=9.81 #Acceleration due to gravity
#Calculation
#total mass of buulet and wooden block
M=m1+m2 #Kg
#Friction Force
F=mu*M*g #N
#Work Done by force of friction
W=F*S #N
#Velocity of bullet
u1=(W*2*M**-1)**0.5*M*m1**-1 #m/s
#Result
print"Velocity of bullet is",round(u1,2),"m/s"
```

In [25]:

```
import math
#Initilization of Variables
M=1500 #Kg #Mass of Hammer
h=0.6 #m #Height from which hammer drops
m=750 #kg #Mass of pile
S=0.05 #m #Depth of penetration
g=9.81 #Acceleration due to gravity
#Calculation
#Velocity of hammer after falling through height of 0.6 m from rest
v=(2*g*h)**0.5 #m/s
#Total momentum of hammer and pile just before impact
p=M*v #Kg*m/s
#Common Velocity
V=p*(M+m)**-1 #m/s
#Part-2
#K.E of system
KE=(M+m)*round(V,2)**2*2**-1 #N*m
#Loss of P.E of system
PE=(M+m)*g*S #N*m
#Total Energy loss
E=KE+PE #N*m
#Resistance of ground
R=E*S**-1 #N
#Result
print"Common Velocity after impact",round(V,2),"m/s"
print"Average Resistance of the ground",round(R,2),"N"
```

In [26]:

```
import math
#Initilization of Variables
M=750 #Kg #MAss of hammer
h=1.2 #m #Height through which hammer drops
m=200 #kg #mass of pile
R=79*10**3 #N #Average resistance of ground
g=9.81 #Acceleration due to gravity
#Calculation
#Velocity of hammer after falling through height of 0.6 m from rest
v=(2*g*h)**0.5 #m/s
#Total momentum of hammer and pile just before impact
p=M*v #Kg*m/s
#Common Velocity
V=p*(M+m)**-1 #m/s
#Part-2
#K.E of system
KE=(M+m)*round(V,2)**2*2**-1 #N*m
#Depth of penetration into the ground
S=KE*(R-(M+m)*g)**-1
#Result
print"Depth of penetration into the ground",round(S,2),"m"
```

In [27]:

```
import math
#Initilization of Variables
M=400 #Kg #Mass of Hammer
h=3 #m #Height from which hammer drops
m=0 #kg #Mass of pile
S=1 #m #Depth of penetration
g=9.81 #Acceleration due to gravity
#Calculation
#Velocity of hammer after falling through height of 0.6 m from rest
v=(2*g*h)**0.5 #m/s
#Total momentum of hammer and pile just before impact
p=M*v #Kg*m/s
#Common Velocity
V=p*(M+m)**-1 #m/s
#Part-2
#K.E of system
KE=(M+m)*V**2*2**-1 #N*m
#Loss of P.E of system
PE=(M+m)*g*S #N*m
#Total Energy loss
E=KE+PE #N*m
#Resistance of ground
R=E*S**-1 #N
#Result
print"Resistance of ground for penetration is",round(R,2),"N"
```

In [28]:

```
import math
#Initilization of Variables
M=10 #Kg #Mass of Body
k=100 #N/cm #stiffnes
h=2 #cm #Height through which mass 10 kg is dropped
#Calculation
#For Position 1
#PE+KE=M*g*(x+h) ............1
#For Position 2
#PE of spring=50*x**2 .............2
#Equating equations 1 and 2 we get
#5x**2-9.81*x-19.62=0
a=5
b=-9.81
c=-19.62
X=b**2-4*a*c
#Max Displacement of spring
x1=(-b+X**0.5)*(2*a)**-1
x2=(-b-X**0.5)*(2*a)**-1
#Result
print"Max Displacement of spring",round(x1,2),"m"
```

In [5]:

```
import math
from math import sin, cos, radians, pi
#Initilization of Variables
m=0.01 #kg #Mass of bullet
M=1 #kg #Mass of body
L=1 #m #Length of string
theta=18.2 #degrees
g=9.81 #acceleration due to gravity
L_OA=1 #m #Length of OA
L_OB=1 #m #Length of OB
#Calculation
#From Geometry of figure
h=L_OA-L_OB*cos(theta*pi*180**-1) #m
#Potential Energy of body and bullet at B
PE=(M+m)*g*h
#from Kinetic Energy of body and bullet after impact
V=(PE*2*(M+m)**-1)**0.5 #m/s #Velocity of body and bullet
#Velocity of bullet
u=(M+m)*V*m**-1
#Result
print"Velocity of Bullet is",round(u,2),"m/s"
```

In [2]:

```
import math
from math import sin, cos, radians, pi
import numpy as np
#Initilization of Variables
m=0.03 #kg #Mass of bullet
u=483 #m/s #Velocity of bullet
M=10 #kg #MAss of body
L=0.8 #m #Length of string
g=9.81
#Calculation
#Momentum of bullet and body before impact
p=m*u #Kg*m/s
#from Momentum of bullet and body after impact
V=p*(M+m)**-1 #m/s
#K.E of the bullet and body after impact
KE=(M+m)*V**2*2**-1 #N*m
#Angle through which body swings
theta=np.arccos(-((KE*((M+m)*g)**-1)-L)*L**-1)*(pi**-1*180) #Degrees
#Result
print"Angle through which body swings is",round(theta,2),"Degrees"
```

In [1]:

```
import math
from math import sin, cos, radians, pi
import numpy as np
#Initilization of Variables
m=0.03 #kg #mass of bullet
u=483 #m/s #velocity of bullet
M=10 #Kg #Mass of body
L=0.8 #m #Length of string
v=96.5 #m/s #Velocity of body
g=9.81 #acceleration due to gravity
#Calculation
#Velocity of Body after impact
V=(m*u-m*v)*M**-1 #m/s
#Height
h=V**2*(2*g)**-1 #m
#from geometry
theta=np.arccos((L-h)*L**-1)*(pi**-1*180)
#Result
print"Angle through which the body will swing",round(theta,2),"Degrees"
```