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 1.40m long, has a mass of 15.0kg , and is hinged to the wall. The sign itself is uniform with a mass of 29.0kg and over-all length of 1.20m . The two wires supporting the sign are each 29.0cm long, are 95.0cm apart, and are equally spaced from the middle of the sign. The cable supporting the beam is 2.20m long.

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

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

Please, show your work.

Explanation / Answer

Angle between cable and rod = acos (1.4 / 2.2) = 50.48 deg

Load in each wire = 29/2 = 14.5 kg

Balancing moments about hinge,

(15*9.81)*(1.4/2) + (14.5*9.81)*1.4 + (14.5*9.81)*(1.4 - 0.95) = (T*sin50.48)*1.4

Solving, T = 339.047 N

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