Question

Question

A marble is attached to a compressed horizontal spring and is then released. Which equation correctly shows the conservation of mechanical energy for this system? (1 point)
Responses

mgh=12kx2
mg h is equal to 1 half k x squared

12mv2=kx2
1 half m v squared is equal to k x squared

12mv2=12kx2
1 half m v squared is equal to 1 half k x squared

mgh=kx2

Answer 1

The correct equation that shows the conservation of mechanical energy for a marble attached to a compressed horizontal spring when released is:

\(\frac{1}{2}mv^2 = \frac{1}{2}kx^2\)

This equation represents the conversion of potential energy stored in the spring (when it is compressed) into kinetic energy of the marble as it is released and starts to move.

Thus, the correct response is:

\(\frac{1}{2}mv^2 = \frac{1}{2}kx^2\).