$6-)$ At a construction site, a $65\mathrm{.}0-$kg bucket of concrete hangs from a light $($but strong$)$ cable that passes over a light, friction$-$free pulley and is connected to an $80\mathrm{.}0-kg$ box on a horizontal roof. The cable pulls horizontally on the box, and a $50\mathrm{.}0-kg$ bag of gravel rests on top of the box. The coefficients of friction between the box and roof are shown.

a$-)$ Find the friction force on the bag of gravel and on the box.

b$-)$ Suddenly a worker picks up the bag of gravel. Use energy conservation to find the speed of the bucket after it has descended $2\mathrm{.}00$ m from rest.