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)

Question

Responses

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

mgh=kx2
mg h is equal to k x squared

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

mgh=12kx2

Answer 1

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

\( \frac{1}{2} mv^2 = \frac{1}{2} k x^2 \)

This equation indicates that the kinetic energy of the marble (on release) is equal to the potential energy stored in the compressed spring at maximum compression. Thus, the correct response is:

12mv²=12kx² (1 half mv squared is equal to 1 half k x squared).