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Height of falling object vs. compression of spring

  1. Apr 30, 2017 #1
    1. Question
    Given an idea spring with constant K, a mass of M is dropped onto the spring from a height of H1. The spring compresses D distance.

    We take the mass off, and drop the mass again at a height of H2, where H2 is significantly greater than H1. This time, will the spring compress a greater distance or the same distance?

    2. Relevant Equations
    F = - k x
    and Conservation of energy:
    U = mgh, Es = ½kx2, where Es is elastic potential of spring
    U = Es

    3. Attempt at solution

    So if we think about it only in terms of F = -kx, then no matter how high we drop the mass, it should compress the same distance D, because F (gravity) remains the same.

    But if we consider it from an energy perspective, then U (gravitational protential) would be greater if the height is greater. And thus the compression must also be greater to match this greater potential energy.

    So which one is correct?
  2. jcsd
  3. Apr 30, 2017 #2

    Doc Al

    User Avatar

    Staff: Mentor

    The point of maximum compression is not the equilibrium point!
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