Posted by **Hannah** on Saturday, June 9, 2012 at 4:38pm.

A uniform horizontal beam is attached to a vertical wall by a frictionless hinge and supported from below at an angle è = 38o by a brace that is attached to a pin. The beam has a weight of 347 N. Three additional forces keep the beam in equilibrium. The brace applies a force P 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 H and a vertical component V. Find the magnitudes of these three forces.

I do not know how to start this.

- Phsyics(Please respond) -
**Elena**, Sunday, June 10, 2012 at 2:21pm
Net torque about the hinge is

mg(L/2)- P(y) L = 0,

( Forces H and V have zero moment about this point)

P(y) = mg/2 =347/2 =173.5 N.

P(y)/P(x) =tanα.

P(x) = P(y)/tanα=173.5/tan38 =222 N.

P(y)/P =sin α,

P =P(y)/sin α =173.5/sin38 =282 N.

As the system is in equilibrium, horizontal forces are balanced:

Force H acts into the wall (to the left)= P(x) (to the right).

H = P(x) = 222 N.

Vertical forces are also in balance

mg V - P(y) =0

V = mg P(y) =347 173.5 =173.5 N.

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