Movement No. 13 presents one of the most fundamental and elegant demonstrations of mechanical advantage in classical mechanics — the single movable pulley with one fixed rope end. The arrangement is deceptively simple: an upper fixed pulley is mounted to a stationary overhead support, and a lower movable pulley is attached directly to the load. A single rope passes over the upper fixed pulley and under the movable lower pulley — one end of the rope is anchored firmly to a fixed point, while the operator pulls upward on the free end. The key physical insight stated by Henry T. Brown is precise and illuminating: because one end of the rope is fixed, the free end must be pulled at twice the speed of the rising load. This velocity relationship is the direct consequence of the mechanical advantage: the load is supported by two rope segments simultaneously — the fixed side and the hauling side — each bearing half the load’s weight. Therefore, the operator need only apply half the force of the load to lift it, achieving a 2:1 mechanical advantage. The price paid for this force reduction is the distance traveled: for every unit the load rises, the rope must be pulled through two units of length. This movement illustrates the universal principle of simple machines — force and distance are always traded against each other — and serves as a foundational building block for understanding the more complex compound pulley systems that follow in Movements 14 through 22. The single movable pulley remains one of the most universally applied mechanical principles in existence, found in everything from flagpoles and window blinds to rock climbing gear and construction cranes.
13. In this the lower pulley is movable. One end of the rope being fixed, the other must move twice as fast as the weight, and a corresponding gain of power is consequently effected.