Question
Conservation of Mechanical Energy Quick Check
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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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Answers
GPT-4o mini
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.
**\(\frac{1}{2} mv^2 = \frac{1}{2} k x^2\)**
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.
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