Why Things Float

What’s going on

Drop a block of wood into water and it bobs back up. Drop a block of iron and it goes straight to the bottom. Press Drop it above, then try other blocks and other liquids.

Whatever goes into water is pushed up by it. The rule for how hard is two thousand years old, and it is called Archimedes’ principle:

The push up equals the weight of the liquid the object pushes aside.

Watch the water level as the block goes in: it rises, because the block takes up room that water used to fill. That water now sits higher in the tank, and its weight is exactly the push on the block.

Floating or sinking

A block sinks into the water until it has pushed aside its own weight of water. Then the push up and the weight balance, and it stops.

• Pine wood is about half as dense as water, so it floats with half of it under the surface.
• Ice is 92% as dense as water, so 92% of an ice cube is under water. That is why most of an iceberg is hidden.
• Iron is almost eight times as dense as water. Even when it is completely under, the water it pushes aside weighs only an eighth of it. It sinks.

Change the liquid. In Dead Sea water, which is very salty and dense, the same block floats higher. In mercury, a liquid metal, even iron floats. Only gold, denser still, sinks.

A steel ship floats for the same reason a wooden block does. Its hull is mostly air inside, so the whole ship, steel and air together, is lighter than the water it pushes aside.

Where the push comes from

Switch on Pressure. The deeper you go, the harder the water presses, because there is more water on top. The water presses on every face of the block:

• on the sides it presses equally from left and right, so those pushes cancel;
• on the bottom face it presses up, and the bottom is deeper than the top;
• so the push up on the bottom is bigger than the push down on the top. The difference is the push up.

Now press Swap for water. Imagine that the block is replaced by water of exactly the same shape. That water just stays where it is: it does not sink or rise. So the water around it must push it up with exactly its own weight. The surrounding water cannot tell what is inside the shape, so it pushes any object of that shape just as hard. That is Archimedes’ principle, without any formulas.

Weigh it

Press Weigh it. A spring balance lowers the block into the liquid. As the block goes in, the balance shows less and less, because the water takes part of the weight. Once the block is fully under water, the reading stops changing: going deeper adds pressure on the top and the bottom equally.

A strange consequence: if a flat block is pressed tight against the bottom so no water gets underneath, nothing pushes it up at all. Things lying in thick mud can be surprisingly hard to lift for this reason.

Try it yourself

1. The full glass

A glass is filled to the brim with water and an ice cube floats in it. When the ice melts, does the water spill over?

Answer

No, the level stays exactly the same. The floating ice pushes aside its own weight of water. When it melts it becomes exactly that weight of water, which fills exactly the hole the ice used to make.

2. The stone in the boat

You are in a small boat on a pond, with a heavy stone in the boat. You throw the stone into the water. Does the level of the pond go up, go down, or stay the same?

Answer

It goes down. In the boat, the stone makes the boat push aside the stone's whole weight of water, several times the stone's volume because stone is denser than water. On the bottom, the stone pushes aside only its own volume.

3. Is the crown gold?

A crown weighs 1 kg in air. Hung from a balance under water, it shows 0.94 kg. Gold is 19.3 times as dense as water. Is the crown pure gold?

Answer

No. It seems to lose 0.06 kg, so it pushes aside 0.06 kg of water, which is 60 cm³. Its density is 1000 g ÷ 60 cm³ ≈ 16.7 g/cm³, less than gold's 19.3: something lighter has been mixed in. A pure gold crown of 1 kg would lose only about 0.052 kg.

Go deeper

• Archimedes lived in Syracuse, in Sicily, in the third century BC. He wrote the rule down in his book On Floating Bodies.
• The famous story of him jumping out of the bath and shouting “Eureka!” (“I have found it!”) when he realised how to test the king’s crown was told by the Roman writer Vitruvius about two hundred years later. It may be a legend, but the method in puzzle 3 really works.
• Submarines use the rule to dive and surface: they let water into tanks to become heavier than the water they push aside, and blow it out with compressed air to rise.