A small winch is used to raise a $120-$lb load. Find $($a$)$ the magnitude of the vertical force P that should be applied at C to maintain equilibrium in the position shown, $($b$)$ the reactions at A and B$,$ assuming that the bearing at B does not exert any axial thrust.

$($c$)$ Draw the shear and moment diagram of the shaft $($hint: replace P by an equivalent load and moment that acts on the end of the shaft$)$