AP Free Response Question
2013 B2
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A 20 kg box on a horizontal frictionless surface is moving to the right at a speed of 4.0 m/s . The box hits and remains attached to one end of a spring of negligible mass whose other end is attached to a wall. As a result, the spring compresses a maximum distance of 0.50 m, and the box then oscillates back and forth.
(a) i. The spring does work on the box from the moment the box first hits the spring to the moment the spring first reaches its maximum compression. Indicate whether the work done by the spring is positive, negative, or zero. Justify your answer.
(a) ii. Calculate the magnitude of the work described in part i.
(b) Calculate the spring constant of the spring.
(c) Calculate the magnitude of the maximum acceleration of the box.
(d) Calculate the frequency of the oscillation of the box.
(e) Let x = 0 be the point where the box makes contact with the spring, with positive x directed toward the right.
i. On the axes below, sketch the kinetic energy K of the oscillating box as a function of position x for the range x = -0.50 m to x = +0.50 m.
ii. On the axes below, sketch the acceleration a of the oscillating box as a function of position x for the range x = -0.50 m to x = +0.50 m.
Topic Formulas
Description
Published Formula
centripetal acceleration
elastic potential energy
Hooke's Law
impulse
kinetic energy
linear momentum
period of a simple pendulum
period of a spring
potential energy
power
power
work
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