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This comes from an AP review packet. I'm given a potential energy functon, $$U(r)=br^{-3/2} + c,$$ where $b$ and $c$ are constants, and need to find the expression for the force on the particle.

There's a graph of $U(r)$ given with the problem, but I'm not sure if it's needed or not. I'm just looking for how to go about solving this problem.

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up vote 2 down vote accepted

Use $$\vec F =-\dfrac{dU}{dr}$$ where r is the radial direction.

From graph you can see the slope of $\brace {U-r}$ graph will give: $\underbrace{-\vec F}_{\text{ in radial direction.}}$

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