Example 1: A force of 2000 N acts on a body of mass 20 kg for a time of 0.1 s. What is the change of momentum of the body?
applied force, F= 2000 N
time duration, t = 0.1 s
change of momentum, mv -mu =?
change of momentum = force x time,
mv — mu = Ft
=2000 N x 0.1 s
= 200 kg ms-2 s =200 kg ms-1
Ans: change of momentum = 200 kg ms-1
Mathematical Example 2: A bullet of mass 10 g was shot from a gun with a velocity of 500 ms-1. If the mass of the gun is 2 kg, find the backward velocity of the gun.
Let the direction of the bullet’s velocity i.e. the forward direction be positive. From the conservation of momentum,
mass of the bullet, m1 = 10 g = 10 x 10-3 kg = 10-2 kg
mass of the gun, m2 = 2 kg
initial velocity of the bullet, u1 = 0 ms-1
initial velocity of the gun, u2 = 0 ms-1
final velocity of the bullet, v1 = 500 ms-1
final velocity of the gun, v2 = ?
m1u1 + m2u2 = m1v1 + m2v2
m1 x 0 ms-1 + m2 kg x 0 ms-1 = 10-2 kg x 500 ms-1 + 2 kg x v2
v2 = kg ms-1/ 2kg = -2.5 ms-1
Here, the velocity of the gun is negative, i.e. the gun will move backward.
Ans: backward velocity = 2.5 ms-1