Pulleys

Pulley systems redirect and can multiply forces. A-Level Mathematics mechanics involves analysing various pulley configurations to find accelerations, tensions, and forces. A smooth, light pulley changes the direction of a string without friction or adding mass. The tension is the same on both sides. Real pulleys may have friction (requiring different tensions) or mass (requiring consideration of the pulley's rotational motion). For a single fixed pulley with masses m₁ and m₂ connected by a string over it, both masses have the same acceleration magnitude. The heavier mass accelerates downward while the lighter accelerates upward. Moveable pulleys create mechanical advantage. If a pulley of mass M is attached to a loop of string with both ends connected to fixed points or other masses, the tension in the string may be different from the weight it supports. Multi-stage pulley problems require careful analysis. Identify all strings and pulleys, note which sections of string have the same tension, and determine the relationship between accelerations (often one mass moves twice as fast as another). The key principle is that inextensible strings have constant length. If one particle moves distance d in one direction, the string length on that side decreases by d, requiring an equal increase elsewhere.