You open a restaurant and hope to entice customers by hanging out a sign (see th

Question

You open a restaurant and hope to entice customers by hanging out a sign (see the figure (Figure 1) ). The uniform horizontal beam supporting the sign is 1.50m long, has a mass of 19.0kg , and is hinged to the wall. The sign itself is uniform with a mass of 27.0kg and over-all length of 1.20m . The two wires supporting the sign are each 26.0cm long, are 95.0cm apart, and are equally spaced from the middle of the sign. The cable supporting the beam is 2.00m long.

Part A

What minimum tension must your cable be able to support without having your sign come crashing down?

Part B

What minimum vertical force must the hinge be able to support without pulling out of the wall?

Explanation / Answer

Part A)

Pivot point placed at the hinge

By the sum of torques...

The center of mass of the beam is .75 m from the hinge.

Half of the sign weight will be supported at 1.5 and the other half at .55

The angle is found from cos(angle) = 1.5/2... So the angle = 41.4o

Now Tsin41.4(1.5) = (19)(9.8)(.75) + (13.5)(9.8)(1.5) + (13.5)(9.8)(.55)

T = 414.2 N

Part B)

Sum of forces...

(414.2)sin(41.4) + Fv = (27 + 19)(9.8)

Fv = 177 N

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