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 mo -6 kg ard the sign has a mass of m_s = 15.9 kg. The length of the beam is L = 2.7 m. The sign is attached a; the very end of the beam, but the horizontal 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 theta = 34.5 degree. What is the tension in the wire? What is the net force the hinge exerts on the beam? The maximum tension the wire can haw without breaking is T = 773 N. What is the maximum mass sign that can be hung from the beam? What else could be cone in order to be able to hole 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

Ans) 1) "Hinged" means it can support no moment; the sum of the moments must be zero or the beam would be rotating.

0=[Tsin(34.5)x(2/3)x2.7]-(6kgx(1/2)+15.9)x2.7x9.8

[Tsin(34.5)x(2/3)x2.7]=(6kgx(1/2)+15.9)x2.7x9.8

T=490.76 N
2) horizontal: Fh = Tcos = 490.76N x cos34.5º = 404.4 N
vertical: 0 = Fv + Tsin - (m + M)xg
0 = Fv +490.76Nxsin34.5º -( (6 + 15.9)kg x 9.8m/s²)
Fv = -63 N (down)
F net = (404.4)² + (-63)²) N

F net = 409.2 N

3) 0 = 773Nxsin34.5ºx(2/3)x2.7m - (6kg x ½ + M)x2.7mx9.8m/s²

0=788N-m-84.3N-m-Mx26.46 m²/s²

M=704N-m/26.46 m²/s²

=26.6kg
4)the three options could be done but the fourth option is wrong

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