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 1.60m long, has a mass of 20.0kg , and is hinged to the wall. The sign itself is uniform with a mass of 25.0kg and over-all length of 1.20m . The two wires supporting the sign are each 34.0cm long, are 85.0cm apart, and are equally spaced from the middle of the sign. The cable supporting the beam is 2.20m long.

http://session.masteringphysics.com/problemAsset/1260563/3/YF-11-37.jpg

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)

Place the pivot point at the hinge and solve by sum of torques

First, the angle at the cable is found from the cosine function

cos(angle) = 1.6/2.2

angle = 43.34o

Tsin(43.34)(1.6) = (12.5)(9.8)(1.6) + (12.5)(9.8)(.75) + (20)(9.8)(.8)

T = 404.9 N

Part B)

By sum of forces

Fv + 404.9(sin 43.34) = (25 + 20)(9.8)

Fv = 163 N

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