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

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

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

mgh=kx2

Answer 1

The correct equation that shows the conservation of mechanical energy for the system of the marble and the compressed spring is:

\[ \frac{1}{2} mv^2 = \frac{1}{2} k x^2 \]

This equation indicates that the kinetic energy \(\frac{1}{2} mv^2\) of the marble when the spring is released is equal to the potential energy stored in the spring \(\frac{1}{2} k x^2\) when it is fully compressed. Therefore, the correct response is:

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