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 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 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 the system where a marble is attached to a compressed horizontal spring and is then released is:

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

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

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

is the correct choice for showing the conservation of mechanical energy in this system.