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Negative Force-potential energy relationship?

  1. May 10, 2014 #1
    I've been wondering for a while why force is the negative derivative of potential energy. In our books, they write that F=-dU/dx, and U=-W
    I don't really understand why it should be negative. Doesn't the force need to be positive in order to increase the potential energy? For example, when you apply a positive force to an object (assuming downward is the negative y direction), Ug goes up, right?
    I'm new to this forum, so sorry if I posted this in the wrong section...
     
  2. jcsd
  3. May 10, 2014 #2

    Doc Al

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    When you apply a positive force, that means the force associated with the potential is applying a negative force. Using your example, while you exert a positive force to raise an object, the force of gravity is negative.
     
  4. May 10, 2014 #3
    Oh, I see, so the "F" in the equation is referring to the force that causes the potential energy, not the force that changes it?
     
  5. May 10, 2014 #4

    Doc Al

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    Right. For gravitational PE, the F refers to the gravitational force. Similarly for other conservative forces.
     
  6. May 10, 2014 #5
    Ok, thanks. That cleared up a lot.
     
  7. May 10, 2014 #6

    Doc Al

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    Staff: Mentor

    Welcome to PF! :smile:
     
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