A mass is pressed against (but is not attached to) an ideal horizontal spring on a frictionless horizontal surface. After being released from rest, the mass acquires a maximum speed v and a maximum kinetic energy K. If instead the mass initially compresses the spring twice as far:
A) Its maximum speed will be 2v and its maximum kinetic energy will be 2K.
B) Its maximum speed will be 2v and its maximum kinetic energy will be K.
C) Its maximum speed will be v and its maximum kinetic energy will be 2K.
D) Its maximum speed will be 2v and its maximum kinetic energy will be 4K.
E) Its maximum speed will be 4v and its maximum kinetic energy will be 2K.

Question

A mass is pressed against (but is not attached to) an ideal horizontal spring on a frictionless horizontal surface. After being released from rest, the mass acquires a maximum speed v and a maximum kinetic energy K. If instead the mass initially compresses the spring twice as far:
A) Its maximum speed will be 2v and its maximum kinetic energy will be 2K. 
B) Its maximum speed will be 2v and its maximum kinetic energy will be K. 
C) Its maximum speed will be v and its maximum kinetic energy will be 2K. 
D) Its maximum speed will be 2v and its maximum kinetic energy will be 4K. 
E) Its maximum speed will be 4v and its maximum kinetic energy will be 2K.

Quizplus · Accepted Answer

The maximum potential energy stored in a spring is directly proportional to the square of the displacement of the spring from its equilibrium position. Therefore, when the mass is compressed twice as far, the spring stores four times as much potential energy (since the displacement is squared). When the mass is released, this stored energy is converted into kinetic energy. Since the potential energy is doubled, the kinetic energy must also be doubled, so the correct choice is C. The maximum speed will not be affected by the amount of compression of the spring, so choices A, B, D, and E can be eliminated.

A Mass Is Pressed Against (But Is Not Attached To)