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Help with springs and potential energy problem

  1. Oct 26, 2007 #1
    Ok, this seems simple, and it probably is, but I'm just not seeing why I'm getting two non-equivalent solutions...

    1. The problem statement, all variables and given/known data
    "A massless platform is supported by 4 equal springs (same length, same spring constant, etc.)
    A mass m is placed on the center of the platform causing an equal compression of x in each spring. What is the spring constant k of a single spring in terms of the mass m, the acceleration of gravity g, and the compression of the spring x?

    2. Relevant equations
    Fspring = -kx
    Fgrav = mg
    Uspring = 1/2(kx^2)
    Ugrav = mgx

    3. The attempt at a solution
    What's throwing me off is that there seem to be two valid ways to solve this, each resulting in a different value of k...

    If I use the fact that the force acting on each spring is 1/4 the force of gravity acting on the mass I get:

    So... k = (mg)/(4x)

    But, then isn't the elastic potential energy stored in each spring 1/4 the gravitational potential energy in the mass when it is first placed on the platform (before any compression)? If so, I get:

    1/2(kx^2) = mgx/4
    So... k = (mg)/(2x)

    The back of the book gives (mg)/(4x). Which I understand, the problem is that the second answer seems valid to me, but obviously the second one is wrong. I just can't see where is my error in reasoning. Help?

    Thank you!
  2. jcsd
  3. Oct 26, 2007 #2


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    Gold Member

    That is a very sharp observation on your part. The error in your reasoning is that mechanical energy is not conserved, since you must apply a non conservative force to slowly lower the beam to its new rest postion; otherwise it would osscilate back and forth about its final rest position, extending the spring twice as much in so doing.
  4. Oct 26, 2007 #3
    So basically I forgot to account for the fact that if the mechanical energy is conserved (i.e. the mass is simply released, not slowly lowered) then an oscilation about x occurs requiring an additional term to account for the fact that there is a non-zero velocity as the mass passes through x (it has kinetic energy as well).

  5. Oct 26, 2007 #4

    Doc Al

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    Staff: Mentor

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