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 1.60 m long, has a mass of 17.0 kg , and is hinged to the wall. The sign itself is uniform with a mass of 33.0 kg and overall length of 1.20 m . The two wires supporting the sign are each 35.0 cm long, are 90.0 cm apart, and are equally spaced from the middle of the sign. The cable supporting the beam is 2.20 m long.

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

What minimum vertical force must the hinge be able to support without pulling out of the wall?

Cable Hinge GOOD EATS - 1.20 m

Answer 1

K 2.2m - Caso = 16 2.2 < 0.8m -- ko.im sino = = 2.2²-1.62 2.2 = 0.6863 333 2 K 1.6m - & 90cm - int { Fx = 0 Fx - Fx = Toso = 0 8T - 0 EET {t=o obout 1 9 X 0.7 - 'J xo:8 - 333 x16 + Thino x16 = 0 0.8 - 339 x 1.6 t T sinox 1.6 =0 = 1.6 Tsine = sos. 19 та 505. 19 1.68 0.6863 = 460.07 N

F = 8x460.07 = 334.6 N - ③ Now {fy = 0 Tsino + Fy - 339 - 179 = 0 y = So xq.8 - 505. 19 Fy = 490 – 315.74 h = 174.26 N so cable should bear 460.07 N and hinge must apply 174.26 N force