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You will be my hero if you could answer this question. I will rate right away!! Thank you sooo much

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 = 16.3 kg. The length of the beam is L = 2.56 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 ? = 30.9.

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 = 894.0 N.

Explanation / Answer

a)

the angle of the horizontal line = 30.9

angle of the forces = 90 - 30.9

= 59.1°

F = T / cos59.1

mb * g * sin 59.1 * 2.56/2 + ms * g * sin 59.1 * 2.56 = T * 2/3 * 2.56 / cos 59.1

6.5 * 9.81 * sin(59.1°) * 2.56 / 2 + 16.3 * 9.8 * sin(59.1°) * 2.56 = T * 2 * 2.56 * cos(59.1°) / 3
solve forT

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