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Homework Help: Hookes law: Calculate the work done by compressing a spring

  1. Jun 15, 2013 #1
    1. The problem statement, all variables and given/known data
    Hookes law: Calculate the work done by compressing a spring by x distance

    2. Relevant equations
    W = Fd
    Ee = 1/2 k x^2
    F = kx

    3. The attempt at a solution

    I've found two solutions, but only one is correct. I'm confused why it's the second one.

    First formula I derived:
    W = Fd
    F = kx
    d = x

    Therefore W = kx^2

    However, you can also use the elastic potential energy equation which is a modified version of the equation I made which is

    W = 1/2 k x^2 - 0

    So, why is it the second equation and not the first one? The way I see it, they sort of both are valid. What is wrong with the first one? Work is force * distance, and that's exactly what I'm doing.
  2. jcsd
  3. Jun 15, 2013 #2


    User Avatar
    Gold Member

    The spring force is a function of x, so W = Fd is not valid. You will have to do an integral.
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