PART$($A$)$Each blade on a wind turbine is engineered to produce an effective force through its center of mass that is perpendicular to its long axis. $($Figure $1)$ The magnitude of the force produced by each blade in a wind of speed vv is F$=(40\mathrm{.}0$kg$/$s$)$vF$=(40\mathrm{.}0$kg$/$s$)$v$.$If the center of mass of each blade is rr $=11\mathrm{.}2$ mm $,$ what is U$1$U$1,$ the total work done by the wind turbine's blades, in a wind of speed vv $=8\mathrm{.}80$ m$/$sm$/$s after $10$ revolutions?

PART$($B$)$A brake system is tested by rotating a tire and measuring the number of rotations required for the brake system to bring the tire to a stop. $($Figure $2)$ The tire's radius is RR $=50\mathrm{.}0$ cmcm and the brake system's radius is rr $=19\mathrm{.}3$ cmcm $.$ A moment of MM $=15\mathrm{.}7$ N$$mN$$m is applied to the tire for $5$ rotations before the brake system is applied. $$The brake system is composed of two pads that are pushed out against the drum with a force that increases as the tire rotates and is described by F$=(10\mathrm{.}0$$)$NF$=(10\mathrm{.}0$$)$N$.$If the coefficient of kinetic friction between the brake pads and the outer ring of the brake system is kk $=0\mathrm{.}550,$ how many rotations, nn$,$ will the tire go through before coming to a stop?