This document discusses calculating forces on a hinged structure with a hanging weight. It finds that (1) the tension in the wire is equal to the weight divided by the sine of the angle, (2) the horizontal component of the hinge force is equal to the weight divided by the tangent of the angle, and (3) the vertical component of the hinge force is equal to the weight multiplied by 1 minus the ratio of the weight position to the length of the structure.

1. 28. (a) Computing torques about the hinge, we find the tension in the wire:
Wx
T L sin θ − W x = 0 =⇒ T = .
L sin θ
(b) The horizontal component of the tension is T cos θ, so equilibrium of horizontal forces requires that
the horizontal component of the hinge force is
Wx Wx
Fx = cos θ = .
L sin θ L tan θ
(c) The vertical component of the tension is T sin θ, so equilibrium of vertical forces requires that the
vertical component of the hinge force is
Wx x
Fy = W − sin θ = W 1 − .
L sin θ L