Tension
Also called Tension force, String tension
Tension is the force a string, rope, cable or chain exerts along its own length when something pulls on it. It can only pull, never push, and in an ideal string it has the same value at every point along the string.
A string does not store a force. It passes one along, and tension is the name for what it passes. AP Physics 1 essential knowledge 2.3.A.3 defines it as the macroscopic net result of forces that segments of a string, cable, chain, or similar system exert on each other in response to an external force. It is filed under Topic 2.3, Newton's Third Law, because segment pulling on segment is exactly a third-law pair.
No formula on the sheet. The AP Physics 1 equation sheet prints no equation for tension at all. Every tension is found the same way, by writing Newton's second law for one object at a time and solving for the unknown pull.
Ideal string, ideal pulley. 2.3.A.3.i says an ideal string has negligible mass and does not stretch under tension, and 2.3.A.3.ii says the tension in an ideal string is the same at all points within it. That, plus the ideal pulley of 2.3.A.3.iv, negligible mass and negligible axle friction, is what lets a single string over a pulley carry one number instead of two.
Drop the idealisation and the number moves. 2.3.A.3.iii says that in a string with nonnegligible mass, tension may not be the same at all points. The CED puts a boundary on how far that goes: AP Physics 1 only expects students to describe tension qualitatively in a string, cable, chain, or similar system with mass, and the example it gives is that the tension in a hanging chain is greater toward the top.
It is not the weight. The tension in a rope holding a hanging object equals only when that object's acceleration is zero and nothing else pulls on it. Accelerate it upward and the tension rises above ; hang the same object from two ropes tilted away from vertical and each one carries more than half the weight. How to find tension works those cases.