Calculate the magnitude of net force exerted by the hinge on the beam of the
previous example.

Answer:

Let F_{h} be the horizontal component
of the force exerted by the hinge and take it to be positive if the force is
outward from the wall. Then, the vanishing of the horizontal component of the
net force on the beam yields

F_{h} - T sin 30 = 0

Þ F_{h} = T sin 30 = (192.3 N) sin 30 =96.1N

Then, let F_{v} be the vertical
component of the force exerted by the hinge and take it to be positive if it is
upward. Then, the vanishing of the vertical component of the net force on the
beam yields

F_{v} + T cos 30 - W =0

ÞF_{v} = W - T cos 30 = 222 N - (192.3 N) cos
30 = 65.5 N

So, the net force exerted by the hinge on the
beam =