Problem $3$: $(20\%$ of Assignment Value$)$

A uniform beam of length $L$ and mass $M$ has its lower end pivoted at P on the floor, making an angle $$ with the floor. A horizontal cable is attached at its upper end B to a point A on a wall. A box of mass $M$ is suspended from a rope that is attached to the beam one$-$fourth $L$ from its upper end.

Part $($a$)$

Write an expression for the $y-$component $P_y$ of the force exerted by the pivot on the beam.

$P_y=$