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Question

Two particles, A and B, have masses 2m and 3m respectively. The particles are moving in the same direction along the same straight line on a smooth horizontal surface when they collide directly. Immediately after the collision, the speed of A is u, the speed of B is (8/5)u and the particles are both moving in the same direction.

After the collision with A, particle B hits a fixed smooth vertical wall which is perpendicular to the direction of motion of B. Particle B rebounds from the wall so that there is a second collision between A and B.

The first collision between A and B occurs at a distance d from the wall. The second collision between A and B occurs at a distance x from the wall.

Given that the coefficient of restitution between B and the wall is 0.5

(a) find x in terms of d.

Given also that the coefficient of restitution between the particles is 1/3

(b) show that there will not be a third collision between A and B.

Answer 1

a) x= 23/48d

b) The particles after the 2nd collisions will have different speeds yet agin. Although Particle B will have to rebound off the wall once more and it's speed will decrease again. So now Particle A is 5.5 times faster and continually moving to the left where there is no wall, thus no rebound for A to go back and collided a third time.

1st time with a video answer hopefully this is helpful, PM me or comment for any more explanation.