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

12mv2=kx2
1 half m v squared is equal to 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 a marble attached to a compressed spring is:

\[ \frac{1}{2}mv^2 = \frac{1}{2}kx^2 \]

This equation states that the kinetic energy (\(\frac{1}{2}mv^2\)) of the marble when it is released is equal to the potential energy stored in the compressed spring (\(\frac{1}{2}kx^2\)) at the point of maximum compression.