A 2 kg particle moving at 8 m/s collides head-on with a 3 kg particle moving in the same direction at 3 m/s. The coefficient of restitution is e = 0.6. If the velocity of the 2 kg particle after collision is N/5 m/s, find N.
Physics · Center of maas , Momentum and Collision · collision and types of collision
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Question

A 2 kg particle moving at 8 m/s collides head-on with a 3 kg particle moving in the same direction at 3 m/s. The coefficient of restitution is e = 0.6. If the velocity of the 2 kg particle after collision is N/5 m/s, find N.

Physics · Center of maas , Momentum and Collision · collision and types of collision

G1 Physics · Accepted Answer

Let the final velocities be v1 and v2 in the original direction. Momentum conservation: 2(8) + 3(3) = 2v1 + 3v2 ⇒ 25 = 2v1 + 3v2. ...(1) Restitution: v2 − v1 = e(u1 − u2) = 0.6(8−3) = 3. ...(2) Thus v2 = v1 + 3. Substitute in (1): 25 = 2v1 + 3(v1+3) = 5v1 + 9. Hence 5v1 = 16 ⇒ v1 = 16/5 m/s. Given v1 = N/5 m/s, N = 16.