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Kinetic energy in frames of reference

  1. Mar 11, 2005 #1
    i was just reading, and i saw this question, and i dont know how to explain it....

    how can you describe why when two things go at a velocity v, and one of them accelerates to 2v, the KE gain w/ respect to the earth and the other object are different, but the work done is constant?

    i just dont know how to explain this... it should not be so difficult, no?
     
  2. jcsd
  3. Mar 11, 2005 #2

    SpaceTiger

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    The work, Fx (assuming constant acceleration), isn't constant. The force is the same in both frames, but the distance isn't.

    [tex]x=\int v~dt[/tex]

    Moving frame:

    [tex]v=\int a~dt=at[/tex]
    [tex]x=\frac{1}{2}at^2[/tex]

    Stationary frame:

    [tex]v=v_0+\int a~dt=v_0+at[/tex]
    [tex]x=v_0t+\frac{1}{2}at^2[/tex]

    In your example, this leads to work that's three times larger in the stationary frame, just like the change of kinetic energy.
     
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