Problem $1(50$ points$).$ A $2-$tooth left$-$hand worm transmits $0\mathrm{.}75$ hp at $600re\frac{v}{m}in$ to a $36-$tooth gear

having a transverse diametral pitch of $8$ teeth$/$in$.$ The worm has a normal pressure angle of $20,$ a pitch

diameter of $1\mathrm{.}5$ in $,$ and a face width of $1\mathrm{.}5$ in $.$ Use a coefficient of friction of $0\mathrm{.}05.$

$($a$)$ Find the force exerted by the gear on the worm and the torque input.

$($b$)$ Bearings are centered at locations A and $B$ on the worm shaft. Determine which bearings should be

the thrust bearing and find the magnitudes and directions of the forces exerted by both bearings.