AP® Physics C: Mechanics · Unit 2 · Topic 2.3
Tension, Strings and Ideal Pulleys
Tension is the pulling force transmitted through a string, and in an ideal (massless, frictionless) string or pulley it has the same value everywhere along the rope.
A string can only pull, never push. Tension is the name for that pull, measured as a force at any point along the rope. Cut an ideal rope anywhere and look at the two pieces: each one is massless, so by Newton's second law the net force on it must be zero. That means whatever pulls on one end must be balanced by an equal pull from the other end. Chase this logic link by link down the whole rope, and you get the same number everywhere. That is why one tension value describes the entire string.
This matters because tension is the connector in multi-object problems. Once you know the string has a single tension T, you can write a separate F = ma equation for each object attached to it, with T appearing in both, and solve the system together. An ideal pulley does not break this chain: because it is massless and frictionless, it takes zero net force and zero net torque to spin it, so it cannot add or remove any force from the rope. It only changes the rope's direction, letting you turn a vertical pull into a horizontal one, for example, without touching the number T.
Real ropes complicate this. If a rope has mass, each segment needs its own net force to accelerate, so tension actually varies along its length, highest near whatever is pulling hardest. Unit 2 treats this as the idealized case; later work with systems of connected masses, inclined planes, and Atwood machines all lean on the single-tension assumption to keep the algebra manageable.
Key terms
- Tension
- The magnitude of the pulling force transmitted through a string or rope at a given point.
- Ideal string
- A string treated as massless and inextensible, so it has one uniform tension throughout.
- Ideal pulley
- A pulley treated as massless and frictionless, so it changes a rope's direction without changing its tension.
- Free body diagram
- A diagram showing all the forces, including tension, acting on a single object in a system.
Watch it explained
- How it worksHow do the forces between neighboring bits of a rope add up into one number called tension?
- Worked exampleFind the tension in the cable of an elevator carrying 800 kg upward at 2 m/s2.
- Common mistakeWhy doesn't an ideal pulley change how big the tension in the rope is?
- Going furtherWhat changes about the tension when the rope itself has real, non-negligible mass?
Check yourself
End of topic.