A $342.$ A winding drum raises a cage of mass $500$ kg through a height of $120$ m $.$ The

winding drum has a mass of $250$ kg $,$ an effective radius of $0\mathrm{.}5$ m $,$ and a radius of gyration

of $0\mathrm{.}36$ m $.$ The mass of the rope is $3$k$($g$)/($m$).$ The cage has at first an acceleration of $1\mathrm{.}5($m$)/($s$^(2))$

until a velocity of $9($m$)/($s$)$ is reached, after which the velocity is constant until the cage

nears the top, when the final retardation is $6($m$)/($s$^(2)).$

Find: $($a$)$ the time taken for the cage to reach the tope $($b$)$ the torgue which must be

applied to the drum at starting, and $($c$)$ the power

ceases.

NR$17\mathrm{.}08$s;$4961$Nm;$82\mathrm{.}2$kW