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Mechanics Question (Please help!!)

A particle P has mass 3m and a particle Q has mass 5m. The particles are moving towards each other in opposite directions along the same straight line on a smooth horizontal surface. The particles collide directly. Immediately before the collision, the speed of P is ku, where k is a constant, and the speed of Q is 2u. Immediately after the collision, the speed of P is u and the speed of Q is 3u. The direction of motion of Q is reversed by the collision.

(a) Find, in terms of m and u, the magnitude of the impulse exerted on Q by P in the collision. (I got 25mu here)

(b) Find the two possible values of k.
(edited 2 years ago)
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Pangol
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Original post by SenThiB
A particle P has mass 3m and a particle Q has mass 5m. The particles are moving towards each other in opposite directions along the same straight line on a smooth horizontal surface. The particles collide directly. Immediately before the collision, the speed of P is ku, where k is a constant, and the speed of Q is 2u. Immediately after the collision, the speed of P is u and the speed of Q is 3u. The direction of motion of Q is reversed by the collision.

(a) Find, in terms of m and u, the magnitude of the impulse exerted on Q by P in the collision. (I got 25mu here)

(b) Find the two possible values of k.


Part (b) is a straightforward conservation of momentum question, but there will be two possible answers because they haven't told you which direction P will be moving in after the collision. You'll get a different answer for k depending on whether P is now moving to the left or to the right. Both are valid, that's why they ask for two answers.

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