$17\mathrm{.}9$ The $10-$in$.-$radius brake drum is attached to a larger flywheel which is not shown. The total mass moment of inertia of the flywheel and drum is $16lb*ft*s^2$ and the coefficient of kinetic friction between the drum and the brake shoe is $0\mathrm{.}40.$ Knowing that the initial angular velocity is $240$ rpm clockwise, determine the force that must be exerted by the hydraulic cylinder if the system is to stop in $75$ revolutions.