physics P.E

Question

A conservative is given by F= k/ r , when k is a positive constant. If the potential energy is zero at r = r0 , find the expression for potential energy as a function of r.

Answer 1

Using the definition of potential energy function,

\(U(r) = U(r_0) = - \int \limits_{r_0}^rFdr\)

\(= - k \int \limits_{r_0}^r \frac{dr}{r^2} \)

\(= k \left[\frac 1r\right]_{r_0}^r\)

\(= k[\frac 1 r - \frac 1{r_0}]\)

Since at r = r₀, U(r₀) = 0, therefore,

\(U(r) = \frac kr - \frac k{r_0}\)