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 = 6.3 kg and the sign has a mass of ms = 17.8 kg. The length of the beam is L = 2.68 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 A purple beam is hinged to a wall to hold up a blue sign. The beam has a mass of mb = 6.3 kg and the sign has a mass of ms = 17.8 kg. The length of the beam is L = 2.68 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

Explanation / Answer

1.) To find the tension, you need to make sure that all the torques on the beam add to zero. Consider three torques: one from the wire, another from the weight of the beam (acting about the center of mass of the beam), and one more from the weight of the sign (acting about the end of the beam). Make sure you draw the picture right and use sine terms in the torque expressions. When you do it right, you'll come up with 459.3 N for the tension in the wire.

2.) Come up with a vector sum of the tension force, and two gravity forces. The force from the hinge onto the beam must be equal and opposite to this. When done right, you will get 514.8 N.

3.) Back solve (opposite of part 1) with your torque expression. When done right, you will get 37.4 kg.

4.) A is true, B is true, C is true, and D is NOT.

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