Q$\mathrm{.}5)$ A $100$ lb $.$ cylinder is hanging from the drum via a cable as shown below. The coefficient of friction between the steel shaft and the bearing $($drum$)$ is $0\mathrm{.}25,$ and the weight of the drum and cable is $150$ lb $.$ Determine

$($a$)$ the force $P$ required to raise the cylinder, and

$($b$)$ the force P required to lower the cylinder.