$8.$ In order for an empty elevator with a balancing weight to move up at a constant velocity of $2\mathrm{.}2$m$/$s$,$ the motor has to provide $220$W$.$

$($a$)$ What is the magnitude of the frictional forces that opposes the motion of the elevator?

$($b$)$ Three people, whose total mass is $240$kg$,$ entered the elevator on its way up$.$ What was the power provided by the motor as the elevator was moving at $2\mathrm{.}2$ m$/$s$?$

$($c$)$ If the maximum power that the motor can provide during the cruising phase is $1\mathrm{.}5$ horsepower, what is the maximum load that can be lifted at a speed of $2\mathrm{.}2$m$/$s$?$