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A conservative force held function is gi...

A conservative force held function is given by `F=k//r^2`, where k is a constant.
a. Determine the potential energy funciton `U(r)` assuming zero potential energy at `r=r_0`.
b. Also, determine the potential energy at `r=oo`.

Text Solution

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a. Using the definition of potential energy function,
`U(r)-U(r_0)=-int_(r_0)^rFdr`
`U(r)-U(r_0)=-kint_(r_0)^r(dr)/(r^2)=k[1/r]_(r_0)^r=k[1/r-1/r_0]`
Since at `r=r_0`, `U(r_0)=0`, therefore, `U(r)=k/r-k/r_0`
b. Potential energy at `r=oo` is `U_(oo)=-k//r_0`
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