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 ). The uniform horizontal beam supporting the sign is 1.80 {m} long, has a mass of 18.0 {kg}, and is hinged to the wall. The sign itself is uniform with a mass of 34.0 {kg} and over-all length of 1.20 {m}. The two wires supporting the sign are each 36.0 {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? You open a restaurant and hope to entice customers by hanging out a sign (see the figure ). The uniform horizontal beam supporting the sign is 1.80 {m} long, has a mass of 18.0 {kg}, and is hinged to the wall. The sign itself is uniform with a mass of 34.0 {kg} and over-all length of 1.20 {m}. The two wires supporting the sign are each 36.0 {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?

Explanation / Answer

angle made by the rope with the beam is        ? = cos-1( 1.8 / 2.2)           =35.1 The tension in the wires of the sign board is         T ' = mg /2 = (34)(9.8) / 2              = 166.6 N the net torque acting on the neam is zero , so       T sin 35.1 ( 1.8) - W (0.9) - T ' (0.6) - T ' (1.8) = 0      T sin 35.1 (1.8) - (18)(9.8)(0.9) - (166.6)(0.6) - (166.6)(1.8) = 0     The tension in the cord is T = = 539.7N   ------------------------------------------------------------------------------------------------------------ minimum vertical force must the hinge be able to support without pulling out of the wall is     F = 2 T ' + W - T sin 35.4        = 2 (166.6) + (18)(9.8) - (539.7)(sin 35.1        = 199.26        = 199.3 N    

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