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 = 39o by a brace that is attached to a pin. The beam has a weight of 350 N. Three additional forces keep the beam in equilibrium. The brace applies a force Upper P Overscript bar EndScripts 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 Upper H Overscript bar EndScripts and a vertical component Upper V Overscript bar EndScripts. Find the magnitudes of these three forces.

Explanation / Answer

The drawing shows a uniform horizontal beam attached to a vertical wall by a frictionless hinge and supported from below at an angle = 39o by a brace that is attached to a pin. The beam has a weight of 350 N. A freebody diagram will show that:

V + P*sin39° = 350..........................1)

350*(L/2) = L*P*sin39°
P = 350/(2*sin39°)

P = 278.1 N
From (1),

V = 350 - P*sin39° = 175 N

H = P*cos39° = 216.1 N

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