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B If an object runs an infinite distance in universe...?

  1. Nov 19, 2016 #1
    ...(after infinite distance) falls into earth, would exist infinite potential energy if E=mgh and h is infinite?
  2. jcsd
  3. Nov 19, 2016 #2


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    Since it would take an infinite amount of time, it would never happen.

    If you are asking whether any object at an infinite distance from the Earth has infinite potential energy, the answer is no, absolutely not and it is easy to see why if you study "escape velocity".
  4. Nov 20, 2016 #3


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    Irrelevant, anything at infinity has no influence on the observable universe
  5. Nov 20, 2016 #4
    Everybody remember infinity is a "concept" (a very useful one) but not a physical "thing!"
  6. Nov 20, 2016 #5


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    I think the real answer to your question is that E = mgh is just an approximation for small values of h near the Earth's surface. The full equation for the potential energy of an object of mass m at a distance R from the Earth's center is that E = -GMm/R, where M is the mass of the Earth, and G is Newton's constant of gravitation. Near the Earth's surface, R is approximately constant, so we can write
    R = R0 + h where h <<R. Then the potential energy can be approximated by $$ E=-\frac{GMm}{R0+h} \approx -\frac{GMm}{R0}(1-h/R0) = -\frac{GMm}{R0} +\frac{GM}{R0^2} mh$$ Then, for changes in the potential energy, we ignore the first term, since it doesn't change, and we call the quantity $$\frac{GM}{R0^2}$$ g, and then you have your formula E=mgh. So if you use the full formula, even an object falling from infinity only gains an amount of energy equal to $$\frac{GMm}{R0}$$, which is a finite quantity.
  7. Nov 20, 2016 #6


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    Staff: Mentor

    E=mgh is only an approximation, valid for objects near the earth's surface.
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