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Homework Help: Gravitional potential energy

  1. May 9, 2010 #1

    jwu

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    1. The problem statement, all variables and given/known data
    A satellite of mass M is in a circular orbit of radius R around the earth.

    (a) what is its total mechanical energy (where Ugrav is considered zero as R approaches infinity)?

    (b) How much work wouldbe required to move the satellite into a new orbit, with radius 2R?

    2. Relevant equations
    (a)
    mv²/R=GMm/R² →→ mv²=GMm/R →→ K=1/2mv²=GMm/(2R),
    therefore, E=K+U=GMm/(2R)+(-GMm/R)=-GMm/(2R)

    (b)
    Here's where I got stuck :
    This is the correct answer on the book:
    From the equation Ki+Ui+W=Kf+Uf,
    W=(Kf+Uf)-(Ki+Ui)
    =Ef-Ei
    =-GMm/(2(2R))-(-GMm/(2R))
    =GMm/(4R)

    Here's what I did, instead of using the equation above, Ki+Ui+W=Kf+Uf, I used the WORK-ENERGY THEOREM. But it came out the different answer.

    W=Kf-Ki=GMm/(4R)-GMm/(2R)=-GMm/(4R) , the same magnitude but different sign.

    What's wrong with using WORK-ENERGY THEOREM?




    3. The attempt at a solution
    As above.
     
  2. jcsd
  3. May 9, 2010 #2

    tiny-tim

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    Hi jwu! :smile:

    Have I understood this correctly …

    instead of using W = Kf - Ki + Uf - Ui,

    you just used the "work-energy theorem", W = Kf - Ki ?​

    ok, for the work-energy theorem, you have to include the work done by all the forces, and that includes the force of gravity, so you would have Wrocket + Wgravity = Kf - Ki … the same as the book's answer.

    The only trick is that the book has replaced Wgravity by -PE.

    You see, PE is just another name for (minus) work done by a conservative force (such as gravity) … you can either use work done, or you can use (minus) PE. :wink:

    (btw, you have to be careful about what you regard as "energy" …

    from the PF Library on potential energy …

    Is potential energy energy?

    There is confusion over whether "energy" includes "potential energy".

    On the one hand, in the work-energy equation, potential energy is part of the work done.

    On the other hand, in the conservation-of-energy equation (and conservation of course only applies to conservative forces), potential energy is part of the energy.)​
     
  4. May 9, 2010 #3
    think of it:
    if the distance increases how the P.E., K.E., and T.E varies?
     
  5. May 9, 2010 #4

    jwu

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    So basically you mean the work-energy theorem and the conservation of energy equation are interchangable at some point?
     
  6. May 9, 2010 #5

    tiny-tim

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    For conserved forces (such as gravity), yes.

    But for most applied forces (such as rockets, bits of string, etc), no … conservation of energy can't apply to them because, with them, energy isn't conserved. :wink:
     
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