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Theoretical question

  1. Jan 3, 2008 #1
    This isn't a homework question, just something I was pondering one day.

    W = Fd = mad
    PE = mgh

    m = m, obviously
    g and a are both measurements of acceleration
    h and d are both measurements of distance

    If g = a, and h = d, is it fair to say that W = PE?

    Therefore, W = a change in KE, so PE = Change in KE?
     
  2. jcsd
  3. Jan 3, 2008 #2

    Andrew Mason

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    Science Advisor
    Homework Helper

    Not quite. The work done on an object can result in a change in kinetic and/or potential energy. In order for W to be equal to KE, the accelerating force would have to be at right angles to the direction of the gravitational force.

    The correct equations are:

    PE = mgh
    [tex]W = \vec F \cdot\vec d = m\vec a \cdot\vec d = mad\cos\theta[/tex]

    ie. h would be 0 and [itex]\cos\theta[/itex] would be 1.

    AM
     
  4. Jan 3, 2008 #3

    dynamicsolo

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    Homework Helper

    All you can really show by this argument is that work and energy have the same units; this does not let us conclude anything at a deeper conceptual level by itself. You'll run into a more extreme case of this when you study torque: you'll learn that torque and energy have the same units but are not much related at all.
     
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