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.

***PLEASE NOTE THESE ANSWERS HAVE COME BACK INCORRECTLY ALREADY; ANSWERS ARE NOT 656.16 AND 158.25

(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?

Explanation / Answer

from the diaagram

theta = cos^-1 ( 1.5/2.2) =47

tension

Tw = m2g/2 = 35 ( 9.8)/2 = 171.5 N

(a)

under equibrium condition the net torque is zero

T = 0

T sin thea b- m1g ( b/2) - T b - Tw ( b- 0.90 m) = 0

T = m1g( b/2) + Tw (b) + Tw ( b-0.90 m)/ sin theta (b)

= 19 kg ( 9.8) ( 1.5/2) + 171.5 ( 1.5) + 171.5 ( 1.5-0.9)/ sin47 ( 1.5)

=455.59 N

-----------------------------------------------------------------------------

the vertical forces

F = 2Tw+ m1g - T sin theta

= 2 ( 171.5)+ 19( 9.8) - 455.59 sin47

=195.99 N

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