How does a wheel and axle multiply force?
The wheel and the axle are fixed together and turn through the same angle, but their rims travel very different distances. In one revolution a point on the wheel covers 2πR while the axle winds only 2πr of rope. Because the work at each must balance, the force on the rope is larger than the force at the rim in exactly the ratio R divided by r. A windlass with a 40 cm crank on an 8 cm drum therefore lifts with five times the force you apply — while your hand travels five times as far as the bucket rises.
What is a windlass and how does it work?
A windlass is the classic wheel and axle: a horizontal drum turned by a crank or a spoked wheel, with a rope winding onto the drum to raise a load. Well buckets, anchor winches and old quarry hoists are all windlasses. Mechanical advantage is the crank radius divided by the drum radius, so the way to make one lift more is either a longer crank handle or a narrower drum. A narrower drum has a cost, though: it winds less rope per turn, so the same lift takes proportionally longer.
Is a screwdriver a wheel and axle?
Yes, and it is the clearest everyday example. The fat handle is the wheel and the blade is the axle. A handle 40 mm across driving a 5 mm blade gives a mechanical advantage of about 8, which is why a screwdriver with a broad grip turns screws that a narrow one merely rounds off. The same reasoning explains doorknobs, steering wheels, taps, and the difference between a slim spanner and one with a fat cushioned handle.
How does efficiency affect a real winch?
Bearing friction, rope stiffness and the rope bending round the drum all consume effort, so the force you actually need is higher than the ideal calculation suggests. A well-maintained winch on ball bearings might reach 90 to 95 percent; a rusty pin through a wooden frame could be nearer 60. Efficiency also explains why a loaded winch does not always run backwards when released — the friction wasting your effort on the way up is the same friction resisting the load on the way down.
Why do bigger wheels make a cart easier to pull?
For a related but different reason from the mechanical advantage above. A large wheel meets a bump or a rut at a shallower angle, so less of your pulling force is wasted lifting the cart over obstacles and more goes into moving forward. Large wheels also turn more slowly for a given speed, reducing the number of bearing revolutions. It is why hand carts for rough ground have tall thin wheels while warehouse trolleys on smooth floors have small ones.