A $2-$hp$,1200-$rpm motor drives a $60-$rpm machine by means of a worm gear reducer with a $5-$in$.$ center distance. The right$-$hand worm has two threads, an axial pitch of $\frac{5}{8}$ in$.,$ and a normal pressure angle of $14\frac{1}{2}.$ The worm is made of steel, hardened and ground, and the gear is made of bronze. Determine $($a$)$ all force components corresponding to rated motor power, $($b$)$ the power delivered to the driven machine, and $($c$)$ whether or not the drive is self$-$locking.

Worm: Steel, hardened and ground

$N_w=2,RH,p=\frac{5}{8}in.,{}_n=14\frac{1}{2}$