What if you could lift a car with a lever?

A car is much too heavy to lift with your hands.

But a lever is a long bar that turns on a bump. What if a long enough lever could lift something as heavy as a car?

A grown-up can lift a heavy bag, but 1,000 kilograms is far too heavy to lift with your arms. That is the load our lab calls 'a small car'.

A lever is one of the oldest helpers people have. It is a stiff bar that turns on a pivot called a fulcrum. Could the right lever let one person lift a load like that? In this lab you can move the fulcrum and find out what a lever can and can't do.

OpenStax defines simple machines as devices that multiply or augment an applied force, often at the expense of the distance through which it is applied. The lever, a rigid bar pivoted at a fulcrum, is one of the simplest.

This lab sets a 1,000 kg load (the model's 'small car' setting) on a lever and asks how far the needed force can be cut by changing the arm lengths, and what it costs in distance and work.

First the bump is right in the middle.

Now the lever does not help at all. You must push as hard as the load is heavy.

Start with the fulcrum in the middle: the load is 1 meter from it on one side, and you push 1 meter from it on the other. This lever is like a seesaw with two children of the same weight.

To hold the load up, your push must be as big as the load's weight: about 9,810 newtons, which feels like lifting the whole 1,000 kilograms. The model's mechanical advantage is 1.0. The lever just changes the direction of your push: you push down, and the load goes up.

With equal arms of 1 m, the balance of moments, F × 1 m = (1,000 kg × 9.81 m/s²) × 1 m, needs an effort of 9,810 N. The mechanical advantage, the ratio of output force to input force, is 1.0, and the effort end moves exactly as far as the load.

In this case a lever only reverses direction: useful, but it gives no help with force.

Now Olly moves the bump very close to the load. Olly's side is long.

Push down gently, and up goes the load! But Olly's end has to move a long way.

Now slide the fulcrum right up to the load: the load is only 0.25 meters from it, and you push 5 meters away on the other side. Your side is twenty times longer.

The push needed drops to about 491 newtons, which feels like lifting 50 kilograms instead of 1,000. The mechanical advantage is 20. But there is a catch: for every centimeter the load rises, your end must move 20 centimeters. To lift the load 1 meter, you would have to push your end down 20 meters.

With a 5 m effort arm and a 0.25 m load arm the mechanical advantage is 5 ÷ 0.25 = 20, so the effort falls to 9,810 ÷ 20 = 491 N, equivalent to holding up 50 kg.

The effort end moves 20 m for every 1 m the load rises. In the model's swing of 15° each side of level, the load rises about 0.13 m while the effort end travels about 2.6 m, and work in equals work out, about 1,270 J. Set friction to 80% efficiency and the push rises to 613 N and the work in to about 1,590 J.

A long side turns the lever more easily than a short side.

But the long end moves farther. A lever swaps a hard push for a long push.

A lever balances when the turning effect on each side is the same. The turning effect is the force times its distance from the fulcrum. So a small push far away can balance a big weight close by.

But a lever can't make energy. The energy you put in is your push times the distance your end moves. A small push has to move a long way to do the same work as lifting the heavy load a short way. Levers trade distance for force; they never give you something for nothing.

For a lever at rest, the torques about the fulcrum cancel: l_in·F_in = l_out·F_out, so MA = l_in ÷ l_out (OpenStax). Because both ends turn through the same angle, the distances they travel are in the same ratio, and work in, F_in·d_in, equals work out, F_out·d_out, for an ideal lever. Friction only makes the work in larger.

The model's limits: a rigid, weightless bar, forces straight down, the load lifted slowly, and friction as a single efficiency. A real 5 m bar would bend and weigh something, and a real car is not a single point load sitting on the end of a bar.

People have used levers for thousands of years.

Long ago, people used a big lever to lift water from rivers. Seesaws are levers too!

Levers are everywhere. Seesaws, crowbars and nail pullers are all levers that turn on a fulcrum. Encyclopaedia Britannica explains that early people used levers to move heavy stones and as digging sticks.

The shaduf is a long lever with a short arm holding a water container. By pulling down on the long arm, a person could lift several times their own weight. Britannica says it is believed to have been used in Egypt and India to raise water as early as 1500 BCE.

Britannica describes a crowbar whose handle is five times as far from the fulcrum as its tip, giving five times the applied force at the tip, and a nutcracker with a 3:1 ratio. The shaduf, a long lever pivoted near one end with counterweights on the long arm, let a person lift several times their own weight, and is said to have been used in Egypt and India by 1500 BCE.

OpenStax analyzes a nail puller the same way: a small force on a long handle balances a large force on the nail close to the pivot. The lab's car-sized lever is a thought experiment: real vehicles are lifted only by trained adults with equipment made for the job.