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 331 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.

Explanation / Answer

At the equilibrium, the sum of the vertical and the sum of the horizontal forces on the beam is zero.

For horizontal forces: Pcos-H = 0

For the vertical forces: Psin+V-W = 0

Also the sum of the torques about the axis of rotation are zero

W(L/2)-VL = 0     (L is the length of the beam)

V = W/2

V = 331 N/2

V = 165.5 N

From the equation Psin+V-W = 0

P = (W-V)/sin

P = W/2sin

P = 331 N/2sin42

P = 247.33 N

From the equation Pcos-H = 0

H = Pcos

H = (247.33 N)cos42

H = 183.8 N

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