A purple beam is hinged to a wall to hold up a blue sign. The beam has a mass of

Question

A purple beam is hinged to a wall to hold up a blue sign. The beam has a mass of m_b = 6.7 kg and the sign has a mass of m_ = 17 kg. The length of the beam is L = 2.73 m. The sign is attached at the very end of the beam, but the horizon al wire holding up the beam is attached 2/3 of the way to the end of the beam. The angle the wire makes with the beam is e 33.2". What is the tension in the wire? N What is the net force the hinge exerts on the beam? N The maximum tension the wire can have without breaking is T = 934 N. What is the maximum mass sign that can be hung from the beam? kg What else could be done in order to be able to hold a heavier sign? while still keeping it horizontal, attach the wire to the end of the beam keeping the wire attached at the same location on the beam, make the wire perpendicular to the beam attach the sign on the beam closer to the wall. shorten the length of the wire attaching the box to the beam

Explanation / Answer

Taking moments of all forces about the hinge

Tsin(33.2) *(2L/3) = 17*9.8L*Cos(33.2) + 6.7*9.8(L/2)*Cos(33.2)

T = (3/2)*(20.35*9.8/Tan(33.2)) = 457.17 N , tension in the wire.

Let N be the reaction of the hinge on the beam, resolving the forces along and perpendicular to the beam

N = TCos(33.2) + 17*9.8Sin(33.2) + 6.7*9.8Sin(33.2)

     = 457.17*0.837 + 20.5*9.8*0.548 = 492.66 N

3) if maximum tension T = 934 N then

934 = (3/2)*(17+ms)*9.8/Tan(33.2))

maximum mass fo the sign ms = 24.58 kg

4) making the wire perpendicular to the beam or keeing it horizontal and attaching to the end of the beam would increase the troque and reduce the tension in the wire thus allowing higher mass of the sign.

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