$(40$ pts $)$ A small winch is used to raise a $120$ lb load. Bearing $A$ is a thrust bearing; bearing $B$ is a journal bearing.

a$.$ Draw the free body diagram.

b$.$ Find the magnitude of the vertical force $P$ that should be applied at $C$ to maintain equilibrium.

c$.$ Find the magnitude of the support reactions at A and $B$ assuming that they are perfectly aligned.

d$.$ Draw the shear and moment diagram of the shaft. $($Hint: you will need to replace P by an equivalant load and moment acting at the end of the shaft$)$