A particle of mass m moving with speed 6 m/s collides head-on with a particle of mass 2m initially at rest. The coefficient of restitution is e = 1/2. If the speed of the first particle after collision is N m/s, find N.
Physics · Center of maas , Momentum and Collision · collision and types of collision
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Question

A particle of mass m moving with speed 6 m/s collides head-on with a particle of mass 2m initially at rest. The coefficient of restitution is e = 1/2. If the speed of the first particle after collision is N 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. Momentum conservation: m(6) + 2m(0) = mv1 + 2mv2 ⇒ 6 = v1 + 2v2. ...(1) Restitution equation: v2 − v1 = e(u1 − u2) = (1/2)(6 − 0) = 3. ...(2) From (2), v2 = v1 + 3. Substitute in (1): 6 = v1 + 2(v1 + 3) ⇒ 6 = 3v1 + 6 ⇒ v1 = 0. Therefore N = 0.