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

Question

You open a restaurant and hope to entice customers by hanging out a sign (Figure 1) . The uniform horizontal beam supporting the sign is 1.50 m long, has a mass of 20.0 kg , and is hinged to the wall. The sign itself is uniform with a mass of 30.0 kg and overall length of 1.20 m . The two wires supporting the sign are each 40.0 cm long, are 90.0 cm apart, and are equally spaced from the middle of the sign. The cable supporting the beam is 2.10 m long.

https://session.masteringphysics.com/problemAsset/2037539/5/Young.Ch11.Pr49.Fig.P11.49.eps.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

Angle of Cable --> cos = 1.5m / 2.1m
                                    = 44
Apply equilibrium condition of torques:

Tcw = Tccw
Hinge is the fulcrum
Gravity = 9.8N/kg

Clockwise --> beam, sign1, sign2
Counterclockwise ---> y-component of cable

T sin (1.5)= (20)(9.8)(0.75)+(30/2)(9.8)(1.5+0.60)

T=434 N

Apply equilibrium condition of weights:

Sign + Beam = Cable + Hinge
30*9.8 + 20*9.8 = 434 * sin44 + Hinge
Hinge = 186 N

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