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How do ropes and drums make a wheel-and-axle system lift heavy weights?

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A diagram displays six types of simple machines with labeled illustrations: inclined plane, wedge, screw, lever, wheel and axle, and pulley, each shown with real-world examples like ramps, axes, screws, seesaws, door handles, and pulleys lifting objects. — simple machine Six simple machines for transforming energy into work.

A wheel-and-axle system functions as a simple machine by amplifying force to lift heavy weights. When configured for this purpose, the system replaces gears with drums of different diameters, around which ropes are wrapped.1

The weight to be lifted is attached to a rope on the small-diameter drum, while the operator pulls a rope on the large-diameter drum. Because the force is applied at the larger radius, it creates a mechanical advantage equal to the ratio of the large drum's radius to the small drum's radius. Essentially, the tendency of the force applied to the large drum to turn the shaft is sufficient to overcome the much larger weight attached to the smaller drum.12

For even greater force amplification, a system can utilize a small drum with two slightly different diameters combined with a pulley block. In this arrangement, the velocity ratio is determined by the radii of the drums, allowing for a very high mechanical advantage when the two drum diameters are nearly equal.1