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AP® Practice Problems 333

Free-Response Questions 2. Students are to conduct a series of experiments in
their physics classroom with two blocks, A and B.
1. Consider a tennis ball of mass m that has been For the first experiment, some students decide to
thrown upward from ground level with an initial use a launcher to give both blocks the same initial
speed 0 v and then rises to a maximum height H velocity, 0 v , and launch them across a table. The
above ground level before falling back down to the coefficient of kinetic friction between the table and
ground. Air resistance can be considered negligible. µ . The blocks are made of the same
In analyzing this situation, we can apply energy each block is k ) is twice the
material, but the mass of block A (m
principles to at least two different systems: the sys- mass of block B (m ). A
tem that includes just the ball, and the ball–Earth B
system. (a) i. Student 1 says block A will slide farther
along the table before coming to rest than
(a) i. Write a sentence that describes the energy block B will. What reasoning would support
conversions within and the energy transfers this prediction? Explain your answer using
into and out of the system consisting of just work and energy concepts and without
the ball as the ball rises to H. using equations.
ii. Write a sentence that describes the energy ii. Student 2 says block B will slide farther
conversions within and the energy transfers along the table than block A will. What
into and out of the system consisting of the reasoning would support this prediction?
ball and Earth as the ball rises to H. Explain your answer using work and energy
(b) Apply the work-energy theorem to the system concepts and without using equations.
consisting of just the ball to derive an expres- (b) What forces are exerted (and by what other
sion for the maximum height H in terms of the objects are they exerted) on block A as it slides
initial speed, 0 v . to rest? Describe and justify their relative mag-
(c) Sketch a graph of kinetic energy of the ball as nitudes and directions and how they compare to
a function of its height above the ground from the forces on block B as it slides to rest.
the time it leaves the ground until the time it (c) Another student in your class derives a mathemat-
reaches its maximum height. ical expression, x∆= 1 0 v 2 / g, for the distance
µ
2
(d) Another tennis ball is thrown vertically upward traveled by block A after it leaves the launcher
with a speed 2 v and it reaches a height 2 =h 2H. and slides to rest. Does the expression support the
Calculate the ratio 2 v v . reasoning you used in part (a) to support either
/ 0
The tennis ball is replaced by a softball that has student 1 or student 2, or both? Explain briefly,
approximately three times the mass of the tennis again using work and energy concepts.
ball (M = 3m). Another student claims that because (d) In a second experiment, students set up a single
the kinetic energy depends on the mass of the ball, launcher, in which a block is placed at the end of
the softball has more kinetic energy if it leaves the a compressed spring. The block is then released
ground with the same speed. Thus it will reach a from rest and loses contact with the spring when
maximum height that is three times the height that the spring reaches its equilibrium length. Explain
the tennis ball reached. why compressing the spring farther might
(e) Do you agree with this student or not? Justify increase the distance the block slides before
your choice by reasoning with the work-energy coming to rest. Include a discussion of how the
theorem. friction force affects the increased slide distance.

Uncorrected proofs have been used in this sample. Copyright © Bedford, Freeman & Worth Publishers.
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