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 1.70m long, has a mass of 20.0kg , 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 33.0cm long, are 80.0cm apart, and are equally spaced from the middle of the sign. The cable supporting the beam is 2.10m long. a )What minimum tension must your cable be able to support without having your sign come crashing down? b) What minimum vertical force must the hinge be able to support without pulling out of the wall?

Explanation / Answer

Part A)

By the sum of torques about the hinges

The angle formed from the cable is found using cos (angle) = 1.7/2.1

angle = 35.95 degrees

(0.8m * 20kg * 9.8) + ((1.7m-0.8m) * (27kg/2) * 9.8) + (1.7m *(27kg/2) * 9.8) = F*1.7* sin35.95

F = 495.13 N

Part B

Upward forces must balance downward

Hinge + (495.13)sin (35.95) = (27)(9.8) + (20)(9.8)

Hinge = 169.91 N

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