SAT Subject Physics Practice Question 223: Answer and Explanation

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Question: 223


A block is attached to the end of a linear spring, the other end of which is anchored to a wall. The block is oscillating between extreme positions X and Y on a frictionless table, and when the block is at Point O, the spring is at its natural length. The value of the spring’s force constant, k, is known, but the mass of the block, m, is unknown.

If ω = , and the distance between O and Y is d, what is the speed of the block at point O ?

B. dω
C. 2dω
D. d2ω
E. dω2

Correct Answer: B


When the block is at Point Y, all its energy is due to the potential energy of the stretched spring, which is kd2. At the moment the block passes through the equilibrium position, O, this energy has been converted entirely to kinetic. By setting mv2 equal to kd2, we find that

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