PhysicsLAB AP Free Response Question
2012 B2

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A small and a large sphere, of mass M and 3M respectively, are arranged as shown on the left side of the figure below.
The spheres are then simultaneously dropped from rest. When the large sphere strikes the floor, the spheres have fallen a height H. Assume air resistance is negligible. Express all answers in terms of M, H, and fundamental constants, as appropriate.
 (a) Derive an expression for the speed vb with which the large sphere strikes the floor.

Immediately after striking the floor, the large sphere is moving upward with speed vb and collides head-on with the small sphere, which is moving downward with identical speed vb at that instant. Immediately after the collision, the small sphere moves upward with speed vS and the large sphere has speed vL.
 (b) Derive an equation that relates vb , vS , and vL.

In this particular situation vL= 0.
 (c) Use your relationship from part (b) to determine the speed of the small sphere in terms of vb .

 (d) Indicate whether the collision is elastic. Justify your answer using your results from parts (b) and (c).

 (e) Determine the height h that the small sphere rises above its lowest position, in terms of the original height H.

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