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 ? = 42o by a brace that is attached to a pin. The beam has a weight of 344 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

Clockwise : mg x ½L = Anti-clock : Pv x L .. .. Pv = vert. component of P Pv = ½ mg .. .. ½ x 340N .. .. Pv = 170 N ? Cos40 = Pv/P P = Pv/cos40 .. .. 170N/cos40 .. .. .. ?P = 222.0 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 sin40 .. .. 222.0N x sin40 .. .. .. ?H = 142.70 N • Vertical forces are also in balance .. 340N? = Pv? + V? V = 340 - Pv? .. .. (340 - 170)N .. .. .. ?V = 170 N

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