Conservation of Mechanical Energy Quick Check

Question

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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

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
mg h is equal to k x squared
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Answer 1

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

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

This can also be written as:

\(12mv^2 = 12kx^2\)

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 when it is compressed (\(\frac{1}{2} k x^2\)).

So the second response you mentioned is the appropriate choice.