The Runaway Cable Drum

A contractor on a Ngauranga Gorge road project lets a full cable drum roll down a straight grass slope inclined at $\theta = 12.0^\circ$ to the horizontal. The drum is modelled as a uniform solid cylinder of mass $M$ and radius $R$, with rotational inertia $I = \tfrac{1}{2}MR^2$ about its axis. It is released from rest and rolls without slipping. The static friction force between the drum and the grass can have any magnitude up to a maximum of $\mu_s N$, where $N$ is the normal force and $\mu_s$ is the coefficient of static friction. Air resistance and rolling resistance are negligible. The diagram shows the drum at its release point and its position after rolling $15.0\ \text{m}$ down the slope.