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

mgh=kx2mg h is equal to k x squared

12mv2=kx21 half m v squared is equal to k x squared

mgh=12kx2mg h is equal to 1 half k x squared

12mv2=12kx2

Answer 1

The correct equation that shows the conservation of mechanical energy for this system, where a marble is 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 the spring is released is equal to the potential energy stored in the spring (\(\frac{1}{2}kx^2\)) when it was compressed. Hence, the correct response is:

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