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 1.60 m long, has a mass of 16.0 kg , and is hinged to the wall. The sign itself is uniform with a mass of 35.0 kg and over-all length of 1.20 m . The two wires supporting the sign are each 33.0 cm long, are 95.0 cm apart, and are equally spaced from the middle of the sign. The cable supporting the beam is 2.10 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?

Explanation / Answer

The net force along x direction is

Fx = 0

the net force along y direction is

Fy = 0

Fy + T sin theta = w1+ w2

Fy + T sin theta = 16(9.8) +35(9.8)

Fy + T sin theta = 499.8 N

theta = cos^-1 ( 1.6/2.10) = 40.36

The net torque is,

T sin theta ( 1.6) = w2( 0.8) + w1( 0.95/2 + 0.8)

T sin (40.36( 1.6) = 16 * 9.8( 0.8) + 35(9.8) (1.275)

T = 543.13 N

(b)

Fy = 499.8- T sin 40.36

= 499.8 - 543.13 sin 40.36

=148 N

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