User:SpartRL/Equilibrant force

Things I want to add or flesh out.

1: How to find the angle of an equilibrant force given the angle of the resultant force.

2: Give a real life example of equilibrant forces like the four people pulling ropes attached to a ring at different angles.

Paragraph I want to add/change:

Suppose that two known forces, which are going to represented as vectors, A and B are pushing an object and an unknown equilibrant force, C, is acting to maintain that object in a fixed position. Force A points to the west (at 180 degrees) and has a magnitude of 10 N and is represented by the vector <-10, 0>N. Force B points to the south (at 270 degrees) and has a magnitude of 8.0 N and is represented by the vector <0, -8>N. Since these forces are vectors, they can be added by using the parallelogram method or vector addition. This addition will look like A + B = <-10, 0>N + <0, -8>N = <-10, -8>N which is the vector representation of the resultant force. By the Pythagorean theorem, the magnitude of the resultant force is [(-10)2 + (-8)2]1/2 ≈ 12.8 N, which is also the magnitude of the equilibrant force. To find the angle of the resultant vector use trigonometry which will yield and angle of 231 degrees. Because the angle of the equilibrant force is opposite of the resultant force, if 180 degrees are added or subtracted to the resultant force's angle, the equilibrant force's angle will be known. Therefor, the equilibrant force's angle will be 231 - 180 = 51 degrees. Multiplying the resultant force vector by a -1 will also give the correct equilibrant force vector: <-10, -8>N x (-1) = <10, 8>N = C.

Sources to add/use:

For parallelogram rule: https://physics.unc.edu/wp-content/uploads/sites/218/2013/05/10-Equilibrium-of-Forces.pdf

For a more in-depth view on equilibrant forces: https://www2.tntech.edu/leap/murdock/books/v2chap3.pdf