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 336 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

Taking moments about the hinge (Force H and V have zero moment about this point)

Clockwise : mg x ½L = Anti-clock : Pv x L

Pv = vert. component of P
Pv = ½ mg

½ x 336N

Pv = 168 N

cos39=Pv/P
P = Pv/cos39

168N/cos39

P = 216.216 N

As the system is in equilibrium .. horizontal forces are balanced
Force H acts INTO the wall = Ph (horiz. component of P to right)

Ph = P sin39

216.216N x sin39

H= 136.07 N

Vertical forces are also in balance .. 336N = Pv + V

V = 336 - Pv

(336 - 168)N

V =168 N

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