A mass is attached to a spring with spring constant . The mass moves from position to position . The work done by the spring on the mass is:
A) 15.0 mJ
B) 0 J
C) -90.0 mJ
D) -15.0 mJ
E) 90.0 mJ

Question

Quizplus · Accepted Answer

The work done by a spring is given by the formula:
$W=\frac{1}{2}k(x_f^2-x_i^2)$
where $k$ is the spring constant, $x_f$ is the final position, and $x_i$ is the initial position.
Plugging in the values given:
$W=\frac{1}{2}(20 	ext{ N/m})((0.30 	ext{ m})^2-(0.10 	ext{ m})^2)$
$W=\frac{1}{2}(20 	ext{ N/m})(0.16 	ext{ m}^2)$
$W=1.6 	ext{ J}$
However, since the question asks specifically for the work done by the spring on the mass, we need to take into account the fact that the net work done on the mass is equal to its change in kinetic energy:
$W_{net}=\Delta K$
Since the mass starts and ends at rest, $\Delta K=0$ and therefore $W_{net}=0$. This means that the work done by the spring on the mass is equal and opposite to the work done by any other forces acting on the mass. Since there are no other forces mentioned in the problem, we can conclude that the work done by the spring on the mass is:
$W=-W_{net}=0	ext{ J}$
The correct answer choice is therefore D, -15.0 mJ, since it is the closest to 0 J. However, the answer choices provided are not accurate to the required precision, and the true answer is indeed 0 J.

A Mass Is Attached to a Spring with Spring Constant