Ropes 3 m and 5 m in length are fastened to a holiday decoration that is suspended over a town square. The decoration has a mass of 5 kg. The ropes, fastened at different heights, make angles of 52 degrees and 40 degrees with the horizontal. Find the tension in each wire and the magnitude of each tension.© BrainMass Inc. brainmass.com October 9, 2019, 9:51 pm ad1c9bdddf
The decoration is under equilibrium under the action of three forces, the two tensions of magnitude T1 and T2 and the weight of the decoration of magnitude mg.
The tensions can be resolved in horizontal and vertical components and the three forces can be written in component form as
(i-hat and j-hat are unit vectors in x (horizontal) and y (vertical) directions respectively)
(see attachment ...
The solution explains how the tension in each wire is found and how to calculate the magnitude of each tension.