48.
(a) Computing the torques about the hinge, we have
T L sin 40
◦
= W
L
2
sin 50
◦
where the length of the beam is L = 12 m andthe tension is T = 400 N. Therefore, the weight is
W = 671 N.
(b) Equilibrium of horizontal andvertical forces yields, respectively,
F
hinge x
=
T = 400 N
F
hinge y
=
W
≈ 670 N
where the hinge force components are rightward(for x) andupward(for y).