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 1.50 m long, has a mass of 20.0 kg , and is hinged to the wall. The sign itself is uniform with a mass of 25.0 kg and over-all length of 1.20 m . The two wires supporting the sign are each 37.0 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

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

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

Explanation / Answer

Here ,

distance betweem cables , d = 85 cm

d = 0.85 m

length , L = 1.5 m

mass of beam , m = 20 Kg

mass of sign , M = 25 Kg

angle between cable and beam , theta = arccos(1.50/2.2)

theta = 47 degree

1) let the tension in the wire is T

balancing the moment abput the hinge

T * sin(47) * L - m * g * (L/2) - M*g * (L - d/2)

T * sin(47) * 1.5 - 20 * 9.8 * (1.5/2) - 25 * 9.8 * (1.5 - 0.85/2) = 0

solving for T

T = 374.1 N

the minimum tension required in the cable is 374.1 N

part 2)

for the minimum vertical force is Fy

Fy + T * sin(theta) - M * g - m * g = 0

Fy + 374.1 * sin(47) - 20 * 9.8 - 25 * 9.8 = 0

Fy = 167.4 N

minimum vertical force must the hinge be able to support without pulling out of the wall is 167.4 N

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