You open a restaurant and hope to entice customers by hanging out a sign. The un

Question

You open a restaurant and hope to entice customers by hanging out a sign. The uniform horizontal beam supporting the sign is 1.60m long, has a mass of 15.0kg , and is hinged to the wall. The sign itself is uniform with a mass of 35.0kg and over-all length of 1.20m . The two wires supporting the sign are each 27.0cm long, are 85.0cm apart, and are equally spaced from the middle of the sign. The cable supporting the beam is 2.10m 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?

Explanation / Answer

Here,

cos(theta) = 1.60/2.1

theta = 40.4 degree

let the tension is T ,

banacing the torques about hinge ,

T*1.6 * sin(40.4) - 1.6 * 15 * 9.8/2 - 35 * 9.8 * 1.425 = 0

solving for T

T = 584.744 N

the tension is cable is 584.744 N

B)

for balacing the vertical forces

Fy + T*sin(40.4) - 15g - 35g = 0

Fy = 50 * 9.8 - 584.744 * sin(40.4)

Fy = 111 N

the minimum vertical force must the hinge be able to support without pulling out of the wall is 111 N

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