(a) A 5.4 kg particle and a 3.0 kg particle have a gravitational attraction with
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Question
(a) A 5.4 kg particle and a 3.0 kg particle have a gravitational attraction with a magnitude of 2.9 10-12 N. What is the gravitational potential energy of the two-particle system?(b) If you triple the separation between the particles, how much work is done by the gravitational force between the particles? (c) How much work is done by you? can someone explain how to get part b or c because I keep trying the formula sqrt (F*G*m1*M2)*(1-1/n) But the answer i am getting (-1.2165E-12) Keeps showing up as incorrect. THANKS!!Explanation / Answer
The magnitude of the force of gravity is: F = G m1 m2 / r^2 Solve that for the radius r = sqrt (G m1 m2 / F) Gravitational potential energy is given by: U = - G m1 m2 / r Substituting the r from the force law gives you: U = - sqrt (F G m1 m2) They give you the force and the masses. You can look up Newton's big G. Plugnchug to get your potential energy. Note that it is negative. The potential energy is taken to be zero at infinity and falls as the particles get closer. Potential energy is inversely proportional to r. So if you multiply r by n, you have to divide the potential energy by n. The work you do is the difference between the final and initial potential energies. W = U(nr) - U(r) = U(r)/n - U(r) = U(r) (1/n - 1) = sqrt (F G m1 m2) (1 - 1/n) Remember that the potential energy is negative, so you have to DO work to push the particle further away. Whether or not gravity does work is a bit of a question of semantics. You may choose to approach a problem in one of two ways. 1) Gravity creates a potential energy field, and you don't say that it does work. So your answer would be zero. The total work done is the work you do, which results in a gain of potential energy. 2) Gravity is a force that does work but doesn't contribute potential energy. So your answer would be that gravity does negative the work you do. Which means the total work done on the particle would be zero.
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