Question

A purple beam is hinged to a wall to hold up a blue sign. The beam has a mass of m_b = 6.1 kg and the sign has a mass of m_s = 16.6 kg. The length of the beam is L = 2.89 m. The sign is attached at 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 ? = 32°.

1) What is the tension in the wire?

2) What is the net force the hinge exerts on the beam?

3) The maximum tension the wire can have without breaking is T = 967 N. What is the maximum mass sign that can be hung from the beam?

4) What else could be done in order to be able to hold a heavier sign?

Answer 1

Horizontal distance of 6.1 kg from the hinge is 1.445 cos 32 = 1.2254 m

Horizontal distance of 16.6 kg from the hinge is 2.89 cos 32 = 2.45 m

The vertical distance of the tension T from the hinge is (2/3)*2.81*sin 32 = 1.0209 m

1.

Taking moment about the hinge,

1.0209*T = (6.1*1.2254 + 16.6*2.45)*9.8

T = 462.1612 N

2)

sqrt( 462.1612^2 +(6.1*9.8)^2 +( 16.6*9.8)^2 ) = 493.59 N

493.55 N at an angle 32 Above the horizontal.

3) 1.0209*967 = (6.1*1.2254 + m *2.45)*9.8

m = 38.06 kg

(4) -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.