1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Proof of the equation of gravational potential energy

  1. May 9, 2010 #1

    jwu

    User Avatar

    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

    User Avatar
    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!
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook




Similar Discussions: Proof of the equation of gravational potential energy
Loading...