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 = 43o by a brace that is attached to a pin. The beam has a weight of 338 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. I can't find P.

Explanation / Answer

given data:

angle = 43o.

weight of 338 N

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

from the defination of torque , is forece* distance

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

where Pv is vertical componet of P

Pv = ½ mg=½ *338=169 N

Cos43 = Pv/P
P = Pv/cos43 =169/cos43=231.1 N------------(1)

As the system is in equilibrium . horizontal forces are balanced
Force H acts into the wall = Ph (horizontal component of P to right)
Ph = P sin43

231.1* sin43= 157.61 N

H= 157.61 N

Vertical forces are also in balance

338N = Pv + V
V = 338 - Pv

V=338-169

V=169 N

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