Answer
The vertical component of the force on the beam from the hinge is $~55.7~N$
Work Step by Step
To find $F_y$, the vertical component of the force on the beam from the hinge, we can consider the vertical forces exerted on the beam.
In part (a), we found that the tension $T$ in the wire is $~~T = 192~N$
We can find $F_y$:
$F_{net,y} = 0$
$F_y+T~cos~30.0^{\circ}-mg = 0$
$F_y = mg- T~cos~30.0^{\circ}$
$F_y = (222~N)-(192~N)~cos~30.0^{\circ}$
$F_y = 55.7~N$
The vertical component of the force on the beam from the hinge is $~55.7~N$.
