$3-59$ A power$-$take$-$off $($PTO$)$ shaft to provide power from a tractor to an implement $($e$.$g$.,$ a mower$)$ is made of two parts that can slide with respect to each other to

provide a variable length. The inner part is a solid bar with a rectangular cross section with dimensions $1\mathrm{.}52\mathrm{.}0$ in$.$ The outer part is a tube with a rectangular

cross section with nominal dimensions to loosely fit over the solid bar, and has a wall thickness of $\frac{1}{8}$ in$.$ The material for both parts is $1035$ CD steel. The

maximum operating speed of the shaft is $540re\frac{v}{m}in.$ Assume the yield strength in shear is $S_{sy}=0\mathrm{.}5S_y.$

$($a$)$ Determine the maximum power $($in hp$)$ that the solid bar can deliver. Use a factor of safety of $2.$

$($b$)$ Determine the maximum power that the hollow tube can deliver, using the closed thin$-$walled method. Use a factor of safety of $2.$