# Conservation of Momentum

Law of conservation of momentum is a very important law of science. According to this law, if two or more objects collide with each other, their total momentum remains conserved before and after the collision provided there is no external force acting on them.

From the Newton's laws of motion, the rate of change of momentum is equal to the force.

If p1 = initial momentum and p2 = final momentum after time t, then

F = (p2 - p1)/t

Now, if F = 0, then p1 = p2.

This shows that the momentum of a system remains unchanged (or conserved) if no force is acting on it.

Example 1: A bullet of mass 0.03 kg is fired with a velocity of 100 ms–1 from a rifle of mass 3 kg. Calculate the recoil velocity of the rifle.

Mass of the rifle, m1 = 3 kg

Mass of the bullet, m2 = 0.03 kg

Initial velocity of the riffle, u1 = 0

Initial velocity of the bullet, u2 = 0

Final velocity of the rifle = v1

Final velocity of the bullet, v2 = 100 ms–1

According to the law of conservation of momentum,

m1u1 + m2u2 = m1v1 + m2v2

0 + 0 = 3 × v1 + (0.03) × 100

v1 = - 1.0 ms–1

Recoil velocity of the rifle = –1.0 ms–1

Negative sign indicates that the rifle would move in the direction opposite to that bullet.

Example 2: A rifle having a mass of 5 kg fires a bullet at a speed of 250 ms–1. If the rifle recoil with a velocity of 1 ms–1 then find the mass of the bullet.

M = 5 kg; m = ?

V = –1 ms–1; v = 250 ms–1

U = 0 u = 0

According to the law of conservation of momentum

MU + mu = MV + mv

0 = MV + mv

m = 0.02 kg

So, Mass of the bullet = 0.02 kg or 20 g

Negative sign indicates that the rifle would move in the direction opposite to that of bullet.