Show that the elastic force exhibited by a bouncing ball of radius (R), assumed perfectly elastic, can

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Show that the elastic force exhibited by a bouncing ball of radius \(R\), assumed perfectly elastic, can be written as \(\mathbf{F}=-k(r-R) b \hat{f} r\) and that it admits potential energy \(V=\frac{1}{2} k(r-R)^{2}\). Make use of Cartesian coordinates.

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