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 v
_{b}
with which the large sphere strikes the floor.
Immediately after striking the floor, the large sphere is moving upward with speed v
_{b }
and collides head-on with the small sphere, which is moving downward with identical speed v
_{b}
at that instant. Immediately after the collision, the small sphere moves upward with speed v
_{S}
and the large sphere has speed v
_{L}
.
(b) Derive an equation that relates v
_{b}
, v
_{S}
, and v
_{L}
.
In this particular situation v
_{L}
= 0.
(c) Use your relationship from part (b) to determine the speed of the small sphere in terms of v
_{b}
.
(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.
Topic Formulas
Description
Published Formula
impulse
linear momentum
uniform acceleration - displacement and instantaneous velocity
uniform acceleration - instantaneous position
uniform acceleration - instantaneous velocity
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