As you can see, both sides pull with the same force, and as a result, the rope doesn't move.
The static equilibrium can be found using a force table. Force tables use vector forces to balance a ring in the center of the table. Someone is able to find the static equilibrium using trigonometry and Pythagorean Theorem given two forces and two angles. A more detailed lab of this procedure could be found here. Anyway, when the ring is not touching the center piece, it has reached static equilibrium.


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