A purple beam is hinged to a wall to hold up a blue sign. The beam has a mass of
ID: 1464573 • Letter: A
Question
A purple beam is hinged to a wall to hold up a blue sign. The beam has a mass of mb = 6.5 kg and the sign has a mass of ms = 16.2 kg. The length of the beam is L = 2.51 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 = 30.3°.
1) What is the tension in the wire?
2) What is the net force the hinge exerts on the beam?
3) The maxiumum tension th ewire can have without breaking is T=1038 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?
[]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
Horizontal distance of 6.5 kg from the hinge is 1.2 cos 30.3 = 1.036 m
Horizontal distance of 16.2 kg from the hinge is 2.51 cos 30.3 = 2.167 m
The vertical distance of the tension T from the hinge is (2/3)*2.51*sin 30.3 = 0.844 m
1.
Taking moment about the hinge,
0.844*T = (6.5*1.036 + 16.2*2.167)*9.8
T = 485.80 N
2
485.80^2 +(6.5*9.8)^2 +( 16.2*9.8)^2
515.03 N at an angle 30.03° Above the horizontal.
3.
0.844*1038 = (6.5*1.036 + m *2.167)*9.8
m = 38.15 kg.
4.
A is true, B is true, C is true, and D is NO