# Energy due to central force

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A body of mass 2 kg is moving under the influence of a central force whose potential energy is given by U (r) = 2r$^3$ Joule. If the body is moving in a circular orbit of 5m, we have to then find its energy.

I tried as
$$F(r)=-\frac{dU}{dx}=-6r^2=mv^2/r$$
$$F(5)=150=mv^2/r$$
$$(1/2)mv^2=375J$$

But the energy given as 625J

asked Jan 28, 2017
You have found KE but what about PE?
You mean PE = 2(5)$^3$=250

## 1 Answer

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Best answer

The question is ambiguous. (Perhaps the wording is your own, rather than that of the original question?) It asks for the energy of the body. Is this referring to kinetic energy? It also has potential energy, and the two add up to 625J, the given answer.

However, potential energy only has meaning for a system, not a single body. So perhaps only the KE of the body should be counted. But it can also be argued that kinetic energy depends on the frame of reference, and the question does not indicate what frame of reference is to be used.

answered Jan 29, 2017 by (28,746 points)
selected Jan 29, 2017 by koolman