Law of Conservation of Momentum

Q. Explain the Law of Conservation of Momentum with the help of an example:-

Introduction:

One of the most powerful laws used in Physics is the Law of Conservation of Momentum which is given by Sir Isaac Newton, which states that:

Statement:

The total momentum of an isolated system before collision is always equal to the total momentum after collision.

Explanation:

Consider two bodies A and B, having mass m1 and m2, moving initially with velocities as v1 and v2. When body A collides with body B the velocities produced after collision are taken as u1 and u2 , on observing it is found that the total amount of mass and velocity of both bodies after collision remains same as before collision. This proves that the Momentum between these two bodies remain constant just as the Law of Conservation of Momentum says that momentum before collision is equal to momentum after collision.

Figure 1: Body A and B moving with initial velocities (v₁ & v₂)

Figure 2: Body A collides with body B

Figure 3: After collision their mass and velocity remains same (take u₁ & u₂ as velocity after collision)

Mathematically:

Formula for Momentum :-

m × v

Total Momentum of A and B before collision :-

m₁v₁ + m₂v₂

Total Momentum of A and B after collision :-

m₁u₁ + m₂u₂

Thus the total amount of Momentum before collision is equal to Momentum after collision:
m₁v₁ + m₂v₂ = m₂v₂

Note for students: You must be curious that why v₁ v₂ are used before and u₁ u₂ are used after collision. Well its because the velocity before collision is initial velocity and velocity produced after collision is final velocity, to differentiate between initial and final v & u are used. I hope u understood :)