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A Force and Potential-Energy Problem

  1. Mar 20, 2013 #1
    1. The problem statement, all variables and given/known data

    My book says that just because a conservative force is zero with respect to x, doesn't necessarily mean that the potential-energy U has to be zero.

    How can it be possible to have potential energy without a force acting towards the equilibrium?

    2. Relevant equations

    Fx(x) = dU(x)/dx = 0

    3. The attempt at a solution

    Fx(x)*Δx = -U, so 0*Δx = 0
     
  2. jcsd
  3. Mar 20, 2013 #2

    haruspex

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    As your DEs show, it only implies that the change in PE is vanishingly small for small changes in x. Consider e.g. a ball sitting on the top of a hill.
     
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