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 mb = 6.5 kg and the sign has a mass of ms = 16.2 kg. The length of the beam is L = 2.53 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 = 30.5°.

1) What is the tension in the wire? ____N

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

3) The maximum tension the wire can have without breaking is T = 1035 N.

What is the maximum mass sign that can be hung from the beam? _____kg

Explanation / Answer

Horizontal distance of 6.5 kg from the hinge is 1.2 cos 30.5 = 1.033 m
Horizontal distance of 16.2 kg from the hinge is 2.53 cos 30.5 = 2.179 m
The vertical distance of the tension T from the hinge is (2/3)*2.53*sin 30.5 = 0.856 m

1.
Taking moment about the hinge,
0.856*T = (6.5*1.033 + 16.2*2.179)*9.8
T = 481 N
-----------------------------
2
481^2 +(6.5*9.8)^2 +( 16.2*9.8)^2
510.51 N at an angle 30.5°. Above the horizontal.
--------------------------------------...
3.
0.856*1035 = (6.5*1.033 + m *2.179)*9.8

m = 31.56 kg.

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