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Homework Help: Proof of the equation of gravational potential energy

  1. May 9, 2010 #1

    jwu

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    1. The problem statement, all variables and given/known data
    All we know the gravitional potential energy is U=-GMm/r. But when I got confused when I was trying to understand the proof of this equation.



    2. Relevant equations

    Here's what they did:
    W by grativity=GMm(1/r2-1/r1)
    Therefore, since △Ugrav=-W by grav, we get
    U2-U1=-GMm(1/r2-1/r1)
    Let's choose out U=0 reference at infinity.that is , we decide to allow U2→0 as r2→infinity. Then this equation becomes U=-GMm/r


    3. The attempt at a solution
    Here's my question:
    What does it mean by "Let's choose out U=0 reference at infinity.that is , we decide to allow U2→0 as r2→infinity. Then this equation becomes U=-GMm/r"?
    Why the U2 would approach to 0 when r2 approached to infinity? And what ti U=0 reference?
    Thank you!!!
     
  2. jcsd
  3. May 9, 2010 #2

    jack action

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    Science Advisor
    Gold Member

    We can't measure energy, only the difference between two states, just like velocity: Nobody can say "my velocity is 0". But you can say "my velocity is 0 with respect to ..."

    So just like you assume something is at rest when measuring velocity (ex.: the ground, even though the earth is moving w.r.t. the sun), you have to assume a point where energy is 0, no matter the one you choose. You just select the one that makes the equation "cleaner", which in this case is when r2 = infinity.
     
  4. May 10, 2010 #3
    It's a matter of convention.
    When you solve a few problems about gravitational potential energy, you will see this is a good convention to follow.
    You could have set U=0 at Earth's surface, but it will give you some trouble when solving equations.

    The same convention is used in electrostactics, get used to it!
     
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