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How do I find the maximum compression of a spring?

  1. Oct 30, 2008 #1
    1. The problem statement, all variables and given/known data
    A linear elastic spring can be compressed 0.10m by an applied force of magnitude 5.0N. A 4.5kg crate, moving at 2.0m/s, collides with this spring. What will be the maximum compression of the spring?

    x= 0.10kg
    F= 5.0N
    m= 4.5kg
    v= 2.0m/s


    2. Relevant equations
    I'm not really sure, but I think that this is a law of conservation of energy problem...
    E = E'
    Eg+Ek+Ee=(Eg+Ek+Ee)'

    Ek=0.5(mv)^2


    3. The attempt at a solution
    I'm just really lost. Any help would be greatly appreciated!
     
  2. jcsd
  3. Oct 30, 2008 #2
    This is indeed a problem of conservation of energy.

    As the crate collides with the spring, at some point all the kinetic energy of the crate will have been transferred to the spring. The mathematical expression for energy stored in a spring is E=ky^2/2 where k is the "spring constant" (don't know this in english), and y is the displacement/compression of the spring.

    You can find the spring constant from the first part of the problem, where you are told how much the spring compresses when compressed by a given amount of force. When you have k and have calculated the kinetic energy of the crate, you can solve for y.

    Good luck!
     
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