A pulley is keyed to a shaft of diameter 2.0 inch by means of a rectangular key. The key
with is 0.5 inch and its height is 0.375 inch. The shaft transmits 40 hp at 150 rpm. The
key is made of 1020 CD steel ($S_y = 57$ kpsi), the pulley material is AISI 1045 HR steel,
and the shaft is made of AISI 1045 HR steel ($S_y = 45$ kpsi). For a minimum safety factor
1.5 determine the followings,
a. Key length based on shear of key
b. Key length based on bearing on Key
c. Key length based on bearing on shaft or bearing on Pulley, same materials
d. Recommended key length
$S_{sy} = 0.577 \ S_y$, $T = 63025H/n$, where: $T$= torque (in.lbf), $n$ = rpm, $H$ = horse power