Question

What do you mean by the conservation of momentum? Briefly, explain the c_ollision between two bodies and the conservation of momentum.

Answer 1

Conservation of momentum in case of a collision between two bodies means the total momentum before and after collision remains unchanged or conserved, provided no net force acts on the system.

Consider two bodies A and 8 having masses m1 and m, and initial velocities u1 and u, respectively. The bodies collide head on with each other and their collision lasts for t seconds. Suppose the velocities of A and 8 after collision are v1 and v, respectively. Assume that no external forces are acting on the bodies.
Rate of change of momentum of ball A = m₁(v₁ - u₁)/t .
Rate of change of momentum of ball 8 = m₁ (v₁ - u₁)/t .
If F_AB is the force exerted by A on 8 and F_BA is the force ex
Rated by 8 on A,  we can write
F_AB= m₁(v₁ - u₁)/t .
F_BA = m₁ (v₁ - u₁)/t .
F_AB = -F_BA 
m₁(v₁ - u₁)/t = - m₂(v₂- u₂)/t .
m₁(v₁ - u₁) = - m₂(v₂- u₂)
m₁v₁ +m₂v₂ = m₁u₁+m₂u₂
So total momentum after collision = total momentum before collision.
This proves conservation of momentum during collision.