How Levers and Pulleys Make Work Easier

A lever is a rigid bar that rotates around a pivot called a fulcrum. An effort force acts at one point, while the load acts at another. The turning effect of a force depends on both its size and its perpendicular distance from the pivot.

A small force applied far from the fulcrum can balance a larger force placed close to it. This is why a long handle makes a stubborn lid or bolt easier to turn. The effort moves through a larger distance while the load moves through a smaller one.

Levers are grouped by the relative positions of effort, load and fulcrum. A seesaw has the fulcrum between effort and load. A wheelbarrow places the load between them, while tweezers place the effort between the fulcrum and load. The labels are useful only after you identify the three parts.

A fixed pulley changes the direction of a force. Pulling downward can lift a load upward, which may be more convenient because you can use your body weight. In an ideal fixed pulley, the force size is not reduced.

A movable pulley is supported by more than one section of rope. The load is shared between those supporting sections, so the required pulling force becomes smaller. A block and tackle combines several pulleys to create more supporting rope sections.

The trade-off is distance. If four rope sections support a load, the ideal input force is roughly one quarter of the load's weight, but you must pull about four times as much rope. Machines continue refusing to provide free energy, no matter how persuasively humans arrange the wheels.

In an ideal machine, input work equals useful output work. Real pivots, ropes and pulley bearings create friction, while ropes stretch and components bend. Some input energy becomes heat or sound, so the actual force advantage is smaller than the ideal value.

Use this method when analysing a simple machine:

• •Identify the effort, load and pivot or rope supports.
• •Compare the effort distance with the load distance.
• •Count supporting rope sections for a movable pulley.
• •Remember that smaller force means greater movement distance.
• •Allow for friction in real equipment.

Your own skeleton is full of levers, and many of them do the opposite of a crowbar. When you bend your elbow to lift a cup, the elbow joint is the fulcrum, the cup in your hand is the load and the biceps muscle provides the effort. The biceps attaches to the forearm only a few centimetres from the elbow, while the hand is much further away. Because the effort acts so close to the pivot, the muscle must pull with a force several times greater than the weight of the cup.

That sounds like poor design until you remember the trade-off between force and distance. A small shortening of the biceps moves the hand through a large arc, and it does so quickly. For an animal that needs to reach, throw or swat, speed and range of movement are often more valuable than raw force. Muscles can produce large forces over short distances, so this arrangement suits them well. The same principle explains why a fishing rod or a broom lets a short movement of your hands produce a long sweep at the far end.

A bicycle is a collection of levers and wheels working together. The pedal crank is a lever turning around the axle, and the chain links a front gear, called a chainring, to a smaller gear on the back wheel. The wheel and its axle form another simple machine, in which a small turn near the centre becomes a large movement at the rim. Changing gear changes how far the wheel turns for each push of the pedals.

In a low gear, a small chainring drives a large rear gear, so each turn of the pedals turns the wheel only a little. You need less force, which is why low gears make hills manageable, but you must pedal faster to cover the same ground. In a high gear the arrangement reverses: each pedal turn moves the bike much further but needs more force, which suits flat roads and downhill stretches. The energy rule from pulleys still holds, since changing gear only trades force against distance rather than giving you free work.

Here is how the turning-effect rule works with real numbers. The turning effect, or moment, of a force equals the force multiplied by its perpendicular distance from the pivot. Imagine a child weighing 300 newtons sitting 2 metres from the middle of a seesaw. Their moment is 300 times 2, or 600 newton metres. An adult weighing 600 newtons balances them by sitting only 1 metre from the pivot on the other side, because 600 times 1 is also 600. If the adult shuffles out to 1.5 metres, their moment becomes 900 newton metres, and the child rises into the air.

The same arithmetic shows how much a real machine wastes. Suppose a block and tackle with four supporting rope sections lifts a 400 newton load by 1 metre. Ideally you would pull 4 metres of rope with a force of 100 newtons, doing 400 joules of work, exactly the energy the load gains. In practice friction in the pulleys and stiffness in the rope mean you might need 125 newtons. Your input work is then 125 times 4, or 500 joules, while the useful output is still 400 joules. Dividing output by input gives an efficiency of 80 per cent, with the missing energy lost mostly as heat.

A tower crane on a building site is a giant lever. The horizontal arm, called the jib, pivots on top of the tower, with the load hanging from a trolley that runs out along it. On the short arm, pointing the other way, sit heavy concrete counterweights. Their moment about the tower balances much of the moment of the load and of the long jib itself, so the tower carries mostly a straight downward force rather than a huge turning effect that could bend it or tip it over. Without counterweights, even a modest load far out on the jib would be dangerous.

Because moment depends on distance, a crane cannot lift the same load everywhere. Each crane has a load chart showing the maximum safe load at each distance from the tower. Close to the tower it may lift several tonnes, while out at the tip the limit can be only a fraction of that, since the same weight produces a much larger turning effect there. Modern cranes have sensors that measure the load and its position and stop the operator exceeding the chart. The hook usually hangs from a pulley block with several rope sections, so the winch pulls with less force while winding in more rope.

Levers use distance from a pivot to change turning effects, while pulleys redirect forces or share loads across rope sections. Both can reduce the effort force by increasing the distance through which that force moves. Track force, distance and energy together, and simple machines stop looking like strength from nowhere.