Question

A shop sign weighing 215N is supported by a uniform 130N beam of length L =...

A shop sign weighing 215N is supported by a uniform 130N beam of length L = 1.67m.

1. The guy wire is connected D = 1.20m from the backboard. Find the tension in the guy wire. Assume theta = 42.4o

2. Find the horizontal force exerted by the hinge on the beam.

3. Find the vertical force exerted by the hinge on the beam. Use "up" as the positive direction.

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Homework Answers

Answer #1

T = tension in the wire

L = length of beam

Mg = weight of sign = 215 N

mg = weight of beam = 130 N

using equilibrium of torque about A

T Sin42.4 (D) = mg (L/2) + MgL

T Sin42.4 (1.20) = (130) (1.67/2) + (215) (1.67)

T = 577.88 N

2,

using equilibrium of forces along the horizontal direction

Fx = horizontal force exerted by the hinge on the beam = T Cos42.4 = 577.88 Cos42.4 = 426.74 N

3.

using equilibrium of forces along the vertical direction

Fy = vertical force exerted by the hinge on the beam

using equilibrium of forces in vertical direction

Fy + T sin42.4 = mg + Mg

Fy + 577.88 Sin42.4 = 130 + 215

Fy = - 44.7

negative sign suggest Fy is in down direction

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