Solving Tension in Hanging Sign: 117 N or Wrong?

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SUMMARY

The discussion centers on calculating the tension in a wire supporting a beam and sign system. The beam has a mass of 6.2 kg, the sign has a mass of 15.1 kg, and the beam length is 2.78 m. The tension calculation involves balancing torques from the weights of the beam and sign against the tension in the wire, which is incorrectly yielding a result of 117 N. The correct approach requires careful consideration of the torque equations and the angles involved.

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A purple beam is hinged to a wall to hold up a blue sign. The beam has a mass of mb = 6.2 kg and the sign has a mass of ms = 15.1 kg. The length of the beam is L = 2.78 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 θ = 30.6°.

What is the tension in the wire?

I have set the torques of the beam's weight and the sign's weight equal to the tension torque as follows:
(6.2)(9.8)(.5)(2.78)(cos30.6) + (15.1)(9.8)(2.78)(cos30.6) = (T/sin30.6)(2/3)(2.78)

Solving for T, I keep getting 117 N which is not the right answer...
Could anyone explain where I am going wrong?
 

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iluvcanucksfo said:
(6.2)(9.8)(.5)(2.78)(cos30.6) + (15.1)(9.8)(2.78)(cos30.6) = (T/sin30.6)(2/3)(2.78)
Could anyone explain where I am going wrong?

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