$[25]$ A right$-$hand single$-$tooth hardened steel worm meshed with a $40-$tooth cast$-$iron gear. The out$-$ put gear power rating is $2000$ W at $12\mathrm{.}5$ rpm$.$ The axial pitch of the worm is $25$mm$,$ the normal pressure angle is $14\mathrm{.}5\backslash$deg $,$ the pitch diameter of the worm is $75$ mm$.$ Bearings are centered at loca$-$ tions A and B on the gear shaft.

$($a$)$ Find the magnitudes and directions of the forces on the gear. Use Eqn $(15-38)$ to find the friction coefficient.

$($b$)$ Assume the following force magnitudes $($not the true values$),$ then calculate the forces on bearings at A and B$.$ Draw a clear isometric sketch of the layout and forces.

$|$WGt $|=9500$N

$|$WGr$|=10000$N

$|$WGa$|=1500$N