A spring is stretched 10.0 cm when a 0.200-kg mass is hanging at its end. If another 0.200-kg mass is added to the spring, the elastic potential energy of the spring will be
A) the same.
B) two times larger.
C) three times larger.
D) four times larger.

Question

Quizplus · Accepted Answer

The elastic potential energy stored in a spring is given by the formula $U = \frac{1}{2}kx^2$, where $U$ is the elastic potential energy, $k$ is the spring constant, and $x$ is the displacement from the equilibrium position. When the mass is doubled, the force (due to gravity) on the spring doubles, leading to a doubling of the displacement (since $F = kx$). Since the displacement $x$ appears squared in the formula for elastic potential energy, if $x$ doubles, the elastic potential energy becomes four times larger.

A Spring Is Stretched 10