An ideal rope is massless and inextensible. The whole mechanics of ropes and pulleys rests on this idealisation, because three fundamental properties follow from it.
Principle — Properties of the ideal rope
- Pulls only: like a stretched spring, it cannot push. The tension is always directed along the rope, towards the rope.
- Same tension: the tension is equal in magnitude at the two ends.
- Same acceleration: the ends move with the same speed and the same acceleration (in magnitude).
The first property is the one most often forgotten: a rope can never push a body, exactly as you cannot “push” something by pulling a string. If a setup required a negative tension, it means the rope goes slack and the model needs revisiting.
An ideal pulley (also massless) merely redirects the rope: it transmits the tension unchanged from one side to the other. It changes the direction of the rope, not the magnitude of the tension. This is what allows the tension to be treated as a single common unknown in two-body systems.
Historical context
The most famous application of these principles is the Atwood machine, invented in 1784 precisely to tame free fall and measure in the laboratory (see The Atwood machine).
Links
Topics: Dinamica Concepts: Tensione Objects: Fune ideale · Puleggia
Related exercises: Inclined plane with pulley and hanging mass · The Atwood pulley: the force on the axle · Speed of a conical pendulum