# 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 p_{1} = initial momentum and p_{2} = final momentum after time t, then

F = (p_{2} - p_{1})/t

Now, if F = 0, then p_{1} = p_{2}.

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, m_{1} = 3 kg

Mass of the bullet, m_{2} = 0.03 kg

Initial velocity of the riffle, u_{1} = 0

Initial velocity of the bullet, u_{2} = 0

Final velocity of the rifle = v_{1}

Final velocity of the bullet, v_{2} = 100 ms^{–1}

According to the law of conservation of momentum,

m_{1}u_{1} + m_{2}u_{2} = m_{1}v_{1} + m_{2}v_{2}

0 + 0 = 3 × v_{1} + (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.