A purple beam is hinged to a wall to hold up a blue sign. The beam has a mass of
ID: 1448581 • 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 kg and the sign has a mass of ms = 16.2 kg. The length of the beam is L = 2.77 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?
2.
What is the net force the hinge exerts on the beam?
3.
The maximum tension the wire can have without breaking is T = 950 N.
What is the maximum mass sign that can be hung from the beam?
Explanation / Answer
Here,
mb = 6 Kg
ms = 16.2 Kg
L = 2.77 m
theta = 30.5 degree
1)
let the tension in the wire is T
Balancing the moment about the wall support
T * sin(theta) * 2L/3 - mb * g *L/2 - ms * g * L = 0
T * sin(30.5) * 2/3 - 6 * 9.8/2 - 16.2 * 9.8 = 0
solving for T
T = 556.1 N
the tension in the wire is 556.1 N
2)
Balaning the vertical and horizotal force on the beam
Fx - T * cos(30.5) = 0
Fx = 556.1 * cos(30.5)
Fx = 479.2 N
in vertical direction
Fy + T * sin(30.5) - 16.2 * 9.8 - 6 * 9.8 = 0
Fy + 556.1 * sin(30.5) - 16.2 * 9.8 - 6 * 9.8 = 0
Fy = 64.7 N
net force on the hinge = sqrt(Fx^2 + Fy^2)
net force on the hinge = sqrt(479.2^2 + 64.7^2)
net force on the hinge = 482.5 N
3)
let the maximum mass of the wire is ms
for Tension , T = 950 N
T * sin(theta) * 2L/3 - mb * g *L/2 - ms * g * L = 0
950 * sin(30.5) * 2/3 - 6 * 9.8/2 - ms * 9.8 = 0
solving for ms
ms = 29.8 Kg
the maximum mass of sign is 29.8 Kg
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