Two particles with masses m and 3m are moving toward each other along the x-axis

Question

Two particles with masses m and 3m are moving toward each other along the x-axis with thesame initial speed vi. Particle m is traveling to the left, and particle 3m is traveling to the right.They undergo an elastic glancing collision such that particle m is moving downward after thecollision at a right angle to its initial direction. (a) Find the final speeds of the two particles. (b)What is the angle ? at which the particle 3m is scattered? All answers should be in terms of m
and vi

Explanation / Answer

The larger mass stops; speed equals zero after the collision. Call the direction of the 3m the positive x-direction. Initial momentum is 3mv - mv = 2mv. Initial kinetic energy = (3/2)mv^2 + (1/2)mv^2 = 2mv^2 Call the final velocity of the 3m mass, w, and of the m mass, u. Then u > w, 3mw + mu = 2mv (3/2)mw^2 + (1/2)mu^2 = 2mv^2 The difference in speeds after the collision is the same as the difference in speeds before the collision by law of restitution. u = w + 2v 3mw + mu = 2mv 3mw + m(w + 2v) = 2mv 4mw = 0 w = 0, u = 2v.

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