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One dimension conservative force and potential energy

  1. Oct 25, 2014 #1
    1. The problem statement, all variables and given/known data

    Given a conservative force, how can we obtain the change in potential energy?
    Given a potential energy function, how can we determine the associated conservative force?

    One dimensional.

    2. Relevant equations

    Fx = -du/dx

    ΔU = -∫ F dx

    3. The attempt at a solution

    I know I can use the above expressions, however, how can I arrive at these expressions? My textbook and class notes simply say

    BY DEFINITION: We will say the change in potential energy is equal to negative of the work done by the internal conservative force.

    I know ΔKE = ∫ F ⋅ dr

    I can integrate the right side but I obtain something like G(x1) - G(x2)

    But then we define U(x) = -G(x) ?

    So then to answer the question, should I simply use my equations listed above? Or is there a better way to approach this?
  2. jcsd
  3. Oct 25, 2014 #2


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    Science Advisor
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    Gold Member

    There is not necessarily any KE involved here. That's just one possibility for where the work done has gone. If you generalise this to work done = ∫ F⋅dr then you seem to have all you need.
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