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Why is potential energy negative?

  1. Oct 20, 2013 #1
    Total energy is [itex]\frac{1}{2}mv^{2}-mgh=C[/itex] for a classical non-rotating object right? C can be determined based on an arbitrary initial condition that suits the problem, right? How come it's not [itex]\frac{1}{2}mv^{2}+mgh=C[/itex]? This seems like a more suitable definition of "total" energy. I'm sure there's a reason it's minus and not plus, but what is the reason? o_O

    Does it have something to do with the direction of the conservative force field that the object is in?
  2. jcsd
  3. Oct 20, 2013 #2


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    Staff: Mentor

    It just depends on the definition of h. If h is upwards, it is +mgh, otherwise it is -mgh.
  4. Oct 20, 2013 #3


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    According to who? That's not what I see in the textbooks that I've used, which all have a + sign, and define h as increasing in the upwards direction.
  5. Oct 20, 2013 #4
    If you have taken the surface of the earth as the reference point for your potential energy, then the potential energy of a body of mass m at a height h (small compared to earth's radius) is mgh. It is a positive quantity with respect to the reference point. The total energy in such a case is [itex]\frac{1}{2}mv^{2}+mgh[/itex]. The Lagrangian can be [itex]\frac{1}{2}mv^{2}-mgh=L[/itex].
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