A purple beam is hinged to a wall to hold up a blue sign. The beam has a mass of
ID: 2201870 • Letter: A
Question
A purple beam is hinged to a wall to hold up a blue sign. The beam has a mass of mb = 6.5 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. What is the maximum mass sign that can be hung from the beam? 4) What else could be done in order to be able to hold a heavier sign? a- while still keeping it horizontal, attach the wire to the end of the beam b-keeping the wire attached at the same location on the beam, make the wire perpendicular to the beam c-attach the sign on the beam closer to the wall d- shorten the length of the wire attaching the box to the beamExplanation / 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.