Solving for Work Done on Compressing Spring: What Am I Doing Wrong?

AI Thread Summary
The user is trying to calculate the work done on compressing a spring with a force constant of 290.0 N/m over a distance of 12.3 mm but is arriving at an incorrect answer. They initially used the formula F = kx to find the force and then calculated work using W = Fd, but this approach is flawed as the force varies with compression. Instead, the correct method involves using the elastic potential energy formula, Ee = 1/2 kx², to determine the work done. The discussion emphasizes the importance of recognizing that work done on a spring relates to the potential energy stored in it. Understanding these principles is crucial for accurately solving spring compression problems.
dcgirl16
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I have this question
THe work done to compress a spring with a force constant of 290.0 N/m a total of 12.3mm is.. and the answer is .0219J but i can't get this answer
This is what i did
F=kx
F=290(.0123)
F=3.567

W=Fcos0 d
W=3.567(.0123)
.0439J

What am i doing wrong??
 
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Notice the force is different for different distances, thus, Fd doesn't really work here.

Do you know what the potential energy is for a spring with spring constant k compressed a distance of x?
 
do you mean the elastic potential Ee=1/2kx2
and then would i use that in the work equation?
 
It's conservation of energy. Work must have been done against the spring to give the spring that potential energy.
 

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