Two indentical balls A and B moving with velocities `u_(A)` and `u_(B)` I the same direction collide. Coefficient of restitution is e.
(a) Deduce expression for velocities of the balls after the collision.
(b) If collision is perfectly elastic, what do you observe?

Explanation

Equation expressing momentum conservation is
`v_(A) + v_(B) = u_(A) + u_(B)` …(A)
Equation of coefficient of restitution is
`v_(B) - v_(A) = e u_(A) - e U_(B)m` …(B)
(a) From the above two equations, velocities `v_(A)` and `v_(B)` are
`v_(A) = ((1-e)/2)u_(A)+((1+e)/2)u_(B)` ...(i)
`v_(B) = ((1+e)/2)u_(A) + ((1-e)/2)u_(B)` ...(ii)
(b) For perfectly elastic impact `e = 1`, velocities `v_(A)` and `v_(B)` are
`v_(A) = u_(B)` ...(iii)
`v_(B) = u_(A)` ...(iv)
Identical bodies exchange their velocities after perfectly elastic impact.