Three particles A, B and C of masses m, 2m and m are arranged on a straight frictionless track. B and C are initially at rest. A approaches B with speed 9 m/s. All collisions are perfectly elastic and sufficiently separated. If C finally moves with speed N m/s, find N.
Physics · Center of maas , Momentum and Collision · collision and types of collision
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Question

Three particles A, B and C of masses m, 2m and m are arranged on a straight frictionless track. B and C are initially at rest. A approaches B with speed 9 m/s. All collisions are perfectly elastic and sufficiently separated. If C finally moves with speed N m/s, find N.

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

G1 Physics · Accepted Answer

First collision: A of mass m hits stationary B of mass 2m elastically. For an elastic head-on collision with target initially at rest: vB = [2mA/(mA+mB)]uA = [2m/(3m)](9) = 6 m/s. A rebounds with speed 3 m/s, but it moves away and does not affect the next collision. Second collision: B of mass 2m moving at 6 m/s hits stationary C of mass m elastically. Velocity of C: vC = [2mB/(mB+mC)]uB = [4m/(3m)](6) = 8 m/s. Therefore N = 8.