Chapter 28:Motion Along a Circular Path

Example 28.1, Page no.574

In [1]:
#variable declaration
m=5     #mass of body in kg
r=1.5   #Radius of circle in m
omega=2 #angular velocity of the body in rad/s

#calculation
F=m*omega**2*r

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

F= 30 N

Example 28.2, Page no.574

In [2]:
#variable declaration
m=1   #mass of stone in kg
r=1   #Radius of circle in m
v=10  #linear velocity of the stone in m/s

#calculation
F=(m*v**2)/r

#Result
print"The value of centrifugal force acting on the stone, F=",int(F),"N"

The value of centrifugal force acting on the stone, F= 100 N

Example 28.3, Page no.574

In [4]:
import math
#variable declaration
m=0.25   #mass of ball in kg
r=2      #Radius of circle in m
F=25     #maximum tension in the sring in N

#calculation
omega=math.sqrt(F/(m*r))

#Result
print"The maximum angular velocity at which the ball can be rotated, omega=",round(omega,2),"rad/s"

The maximum angular velocity at which the ball can be rotated, omega= 7.07 rad/s

Example 28.6, Page no.576

In [5]:
#variable declaration
m=60   #mass of railway engine in t
r=200  #Radius of circular path in m
v=10   #velocity of engine in m/s

#calculation
P_c=(m*v**2)/r

#Result
print"The force exerted on the rails towards the centre of the circle, P_c=",int(P_c),"kN"

The force exerted on the rails towards the centre of the circle, P_c= 30 kN

Example 28.7, Page no.576

In [6]:
#variable declaration
m=1.5  #mass of automobile in t
v=15   #velocity of automobile in m/s
r=25   #radius of the sag in m
g=9.8  #gravity in m/s**2

#calculation
R=((m*v**2)/r)+(m*g)

#Result
print"The reaction between the automobile and road while travelling at the lowest part of the sag is",round(R,1),"kN"

The reaction between the automobile and road while travelling at the lowest part of the sag is 28.2 kN

Example 28.13, Page no.583

In [11]:
import math
#variable declaration
r=50     #Radius of level track in m
Mu=0.45  #Coefficient of friction
g=9.8    #gravity in m/s**2

#calculation
v_max=(math.sqrt(Mu*g*r))*3.6  #Multiplying by 3.6 to convert m/s to km.p.h.

#Result
print"Maximum speed,v_max=",round(v_max,1),"km.p.h."

Maximum speed,v_max= 53.5 km.p.h.
In [ ]: