Solving Tension in Hanging Sign: 117 N or Wrong?

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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, and the sign weighs 15.1 kg, with the beam length being 2.78 m. The tension calculation involves balancing the torques from the weights of the beam and sign against the tension in the wire, which is attached 2/3 of the way along the beam at an angle of 30.6°. Despite following the torque balance equation, the calculated tension consistently results in 117 N, which the poster believes is incorrect. The thread seeks clarification on potential errors in the torque equation setup or calculations.
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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?

Replace '/' by 'times'
 
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