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Finding x for a spring using energy equations

  1. May 3, 2013 #1
    1. The problem statement, all variables and given/known data

    This isn't a homework question, just something I've been thinking about. If given a situation in which mass m is hung on a spring with constant k, I know you can set the spring force equal to the weight of the mass to find how far it stretches. Is there a way to find how far it stretches using energy equations? It seems like it should be doable, but I can't figure out how.

    2. Relevant equations

    w = mg
    F = -kx
    ΔUg = mgh
    Us = kx2/2

    3. The attempt at a solution

    As I said, setting mg = kx can solve for x. How do I do it with energy though?
    Ug = Us
    mgx = kx2/2

    But now I get a different answer for x. What did I do wrong with the energy equations?
     
  2. jcsd
  3. May 3, 2013 #2
    The energy approach will give you the farthest the mass on the spring will fall. This is not the equilibrium position. Think about it, if I let the mass drop, then when it passes the equilibrium position, it will not have zero velocity.
     
  4. May 3, 2013 #3
    Ah. This makes sense now! Thanks!
     
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