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 mlong, has a mass of 19.0 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 40.0 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.

(NEED PARTS A-B) PLEASE

PART A:

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

Tmin = ___________ N

PART B:

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

Problem 11.51 You open a restaurant and hope to entice custoners by g the sign is 1.50 m uniform horizontal beam sup long, has a mass of 19.0 kg and is hinged to the wall The sign itself is uniform with a mass of 360 ke and over-all length of 1.20 m The two wires su sign are each 40.0 cm long, are 900 cm apart and are equally spaced from the middle of the sign. The cable the Wha Cable 120m

Explanation / Answer

Assign as the angle between the beam and cable.
Use Pythag.thm. to get: y = 2.2² - 1.5² = 1.609
Then = tan-1{ 1.609/1.5} = 47 deg.

The cable tension: T has horiz & vert. components.

T(vert) = 0, => equilibrium condition for vert. component.

T sin = =13.89(9.81) + 35(9.81)

0.731T = 479.66

T = 656.16 N

What minimum vertical force must the hinge be able to support without pulling out of the wall?
Assign F as the vertical hinge reaction.

The equilibrium conditions for moments:

M = 0,

1.5F = 13.89(9.81)(1.5/2.2) + 27(9.81)(1.2/2.2)

F = 158.25 N

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