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Homework Help: I need to know if this exists

  1. Feb 6, 2007 #1
    is there an equation that could be used to determine the energy output of a given weight being pulled by gravity?
     
  2. jcsd
  3. Feb 6, 2007 #2

    AlephZero

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    Yes, it's the same equation as the work done by any other force:

    Work = force * distance.
     
  4. Feb 6, 2007 #3

    Andrew Mason

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    I think you mean power (energy per unit time) of the weight. Since the gravitational force is:

    [tex]F = \frac{GMm}{R^2}[/tex]

    where R is the distance of the object from the centre of mass of the large mass (toward which the weight is gravitating), the change in energy by moving a distance dR closer to the centre would be:

    [tex]dW = \frac{GMm}{R^2}dR[/tex]

    so the power output would be:

    [tex]P = dW/dt = \frac{GMm}{R^2}\frac{dR}{dt} = \frac{GMm}{R^2}\dot r[/tex]

    where [itex]\dot r[/itex] is the radial speed or the speed toward the centre.

    AM
     
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