8.5 Exercise 22

A mysterious force acts on all particles along a particular line and always points towards a particular point P on the line. The magnitude of the force on a particle increases as the cube of the distance from that point; that is $F \infty r^{3}$, if the distance from P to the position of the particle is r. Let b be the proportionality constant, and write the magnitude of the force as $F = b r^{3}$. Find the potential energy of a particle subjected to this force when the particle is at a distance D from P, assuming the potential energy to be zero when the particle is at P.