BrightKidz Library
Subjects
A hard short push and an easy long push, holding the same amount On the left a tall narrow block standing on the ground: a big push made over a short distance. On the right a low wide block on the same ground: a small push made over a long distance. The two blocks are drawn to cover exactly the same amount of space as each other. Between them sits the triangle a lever balances on, because a simple machine is the thing that turns one of these blocks into the other without any of it going missing.

What a Simple Machine Takes in Return

About 11 minutes

There is a contradiction sitting on the page and it is worth going back for.

You were told that simple machines do not give you extra strength. Then, a few lines later, that moving the fulcrum closer to the heavy thing makes the lever stronger.

Both of those are true. A wheelbarrow really does lift a load your arms could not, and the machine really did not hand you any muscle. So something else must be going on, and it is: the machine takes something from you in exchange. Once you know what, all three machines turn out to be one machine.

Put some numbers on a plank

Take a plank a metre long. Put the fulcrum 20 cm from one end, so the short side is 20 cm and the long side is 80 cm — four times as long.

Rest a heavy box on the short end and push down on the long end.

You can lift a box four times heavier than the push you are making. That is the strength the level was supposed not to be giving you.

Now watch your hand. Push the long end down and it sweeps through a big arc. Watch the box, and it barely creeps upward.

Measure both and the numbers come out clean. Your hand travels 40 cm. The box rises 10 cm.

Four times the force. A quarter of the distance. There it is.

Tipping a lever, and how far each end travels A stiff beam resting on a triangle. The load sits close to the triangle on the short side; the push is made at the far end of the long side. A dotted line marks where each end of the beam started. As the beam tips, the pushing end travels a long way down while the load end lifts only a little, and the pushing end always travels four times as far because its side of the beam is four times as long. the load your push short side long side, four times as long

Tip the beam and watch the two ends. The dotted lines mark where each end started from.

Stop at any point you like — a little tip, a big one, anywhere in between — and compare the two gaps. The pushing end has always moved four times as far as the load has. Not roughly. Exactly, at every position, because its side of the beam is exactly four times as long.

The rule underneath

Multiply the two together and you get the same answer on both sides of the fulcrum.

A quarter of the force, over four times the distance. Four times the force, over a quarter of the distance. Whichever end you stand at, force multiplied by distance comes to the same thing.

That is what a simple machine actually is. Not a source of strength — a way of taking the effort you have and reshaping it. You can have it as a big push over a short way, or a small push over a long way, and the machine will swap one for the other all day. What it will never do is hand you more than you put in.

Move the fulcrum and you are choosing the shape of the deal. You are not changing how much there is.

The ramp was saying this all along

You already had this rule and did not know it. The ramp was explained like this: walking a heavy thing up a slope is easier because you spread the work over a longer distance.

That sentence is the whole law, said once about one machine.

Take a ramp 2 metres long that rises half a metre. The slope is four times the height, so pushing along it needs about a quarter of the force lifting straight up would — and you walk 2 metres to gain 50 centimetres.

The same four. The same trade. A ramp is a lever's deal made with a slope instead of a beam.

A wheel is doing two jobs at once

The wheel and axle is the one worth separating carefully, because it helps in two different ways and they are easy to muddle.

The first job is the trade, the same one as before. Turn a doorknob and your fingers travel right around a wide circle while the little spindle inside turns through a much smaller one. Small force, long way round, on the outside. Big twist, short way round, on the inside. A doorknob is a lever bent into a ring.

The second job is nothing to do with the trade. A box dragged across a floor rubs along its whole underside, and rubbing steals effort and turns it into warmth. Put the box on wheels and almost none of it rubs. That is not a swap of force for distance — it is a leak being closed.

So a wheel can help you twice over, and only one of those two is the deal this article is about.

You move a lever's fulcrum so you now need only a fifth of the force. What happens to the distance your hand has to travel?

The small print: you get a little less back

Everything above is the perfect version. Real machines are slightly worse than that, and always in the same direction.

Some of your effort goes into rubbing — the beam against the fulcrum, the box against the ramp, the axle inside the wheel — and comes out as a faint warmth instead of as lifting. So what you get out is a little less than what you put in.

Never more. Not once, in any machine anybody has ever built.

Go and measure it

You do not have to take any of this on trust, and it is a ten-minute job.

Lay a ruler across a pencil to make a lever. Put something small and heavy on the short end. Now push the long end down and hold a second ruler upright beside each end to see how far each one moved.

Try the pencil in three places. Each time, note how hard you had to push and how far your hand went. You will find you can make either number small, and never both.