The drawing shows a uniform horizontal beam attached to a vertical wall by a fri

Question

The drawing shows a uniform horizontal beam attached to a vertical wall by a frictionless hinge and supported from below at an angle ? = 40o by a brace that is attached to a pin. The beam has a weight of 334 N. Three additional forces keep the beam in equilibrium. The brace applies a force to the right end of the beam that is directed upward at the angle ? with respect to the horizontal. The hinge applies a force to the left end of the beam that has a horizontal component and a vertical component . Find the magnitudes of these three forces.

Explanation / Answer

A freebody diagram will show that:

V + P*sin41° = 334..........................1)

334*(L/2) = L*P*sin40°
P = 334/(2*sin40°)

P = 259.80 N
From (1),

V = 334 - P*sin40° = 167 N

H = P*cos40° = 199 N

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