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 1.40 m long, has a mass of 16.0 kg , and is hinged to the wall. The sign itself is uniform with a mass of 27.0 kg and over-all length of 1.20 m . The two wires supporting the sign are each 29.0 cm long, are 85.0 cm apart, and are equally spaced from the middle of the sign. The cable supporting the beam is 2.20 m 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?

I have no clue how to do this. I couldn't follow similar Q&As on here, so please try to be clear.

Explanation / Answer

Solution :


Mass of beam = 16 kg
Length of beam = 1.40 meters
Mass of sign = 27 kg
Length of sign = 1.20 meters
Length of wires = 29 centimeters = 0.29 meter
Distance between wires = 85 centimeters = 0.85 meter
Length of cable = 2.2 meters

Solve for angle between cable & beam :
@ = arc cosine (1.40/2.20)
@ = 50.478 degrees

Solving for "T" (tension) :
Summation of Moment at Hinge = 0
T sine @ = (16kg x 9.81m/sec^2 x 0.70m) + (27kg x 9.81m/se^2 x 1.20m)
T sine 50.478 = 427.716 N
T = 427.716/sine 50.478
T = 554.48 Newtons (Answer)
T = 0.5545 KN (Answer)

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