An ideal spring is hung vertically from the ceiling.When a 2.0-kg mass hangs at rest from it, the spring is extended 6.0 cm from its relaxed length.A downward external force is now applied to the mass to extend the spring an additional 10 cm.While the spring is being extended by the force, the work done by the spring is:

Question

Quizplus · Accepted Answer

The work done by the spring is negative because the spring force is opposite to the direction of the applied force. The work done by the spring can be calculated using the formula $W = -\frac{1}{2}kx^2$, where $x$ is the total extension from the natural length. The spring constant $k$ can be found using $F = kx$, where $F = mg$ for the initial 6.0 cm extension. With $m = 2.0 \, \text{kg}$ and $g = 9.8 \, \text{m/s}^2$, $k = \frac{mg}{x} = \frac{2.0 \times 9.8}{0.06}$. The total extension is $0.06 \, \text{m} + 0.10 \, \text{m} = 0.16 \, \text{m}$. Substituting these values back into the work formula gives a negative value, indicating the work done by the spring is against the direction of force, which matches choice A, -3.6 J.

An Ideal Spring Is Hung Vertically from the Ceiling