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Phsyics(Please respond)

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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) -

    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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