Drop a cork into the bath and it bobs cheerfully on top. Drop a stone and it plunges straight to the bottom. Gravity is pulling both of them down by their weight — so why does the cork stay up while the stone gives in?

The secret is that water does not just sit there and let things fall through it. The moment you push something into water, the water shoves back — it pushes up on whatever you put in. That upward shove has a name: upthrust (grown-ups sometimes call it buoyancy). Every drop of water in every puddle, pond and ocean is ready to push up like this.

So being in water sets up a tug-of-war between two forces:

• Weight — gravity pulling the object down.
• Upthrust — the water pushing the object up.

Whichever force wins decides everything:

• If the up-push can balance the weight, the object floats.
• If the weight beats the up-push, the object sinks.

A contest you can watch

Here is an object bobbing in a tank of water. Two arrows show the tug-of-war: the down-arrow is its weight, the up-arrow is the upthrust from the water.

Slide How heavy? up and watch the weight arrow stretch. While the object is light, the water pushes up just as hard as gravity pulls down — the arrows match, and it rides near the surface. Load on too much weight and the down-arrow beats the up-arrow: the water can no longer hold it, and it drops to the floor. Now flip the Shape switch from a compact ball to a wide, hollow boat — and watch the very same heavy object suddenly float. Shape is doing something powerful here; the next card explains what.

It is not simply "heavy sinks"

Here is a puzzle that trips everyone up. A little steel nail, no bigger than your finger, sinks the instant it hits the water. Yet a giant steel ship — thousands of times heavier, heavy enough to carry cars and crates and hundreds of people — floats calmly across the ocean. If floating were just about being heavy, that could never happen.

The answer is shape. Upthrust is not fixed — an object gets a bigger upthrust when it pushes more water out of the way. A nail is a tiny, solid lump, so it barely shoves any water aside and gets only a feeble up-push. A ship is spread out wide and hollow, with a huge belly full of air, so it shoves aside an enormous amount of water — and the more water it heaves out of the way, the harder the water pushes back up. Same steel, completely different shape, completely different result.

Try it with plasticine

You can prove the shape idea yourself with a lump of modelling clay. Roll it into a tight ball and drop it in a bowl of water: plop — it sinks. Now fish it out and press exactly the same lump into a wide, hollow boat shape with high sides, and set it down gently: it floats!

Nothing was added or taken away — it is the identical clay, with the identical weight. All you changed was the shape. The boat spreads the clay out so it shoulders aside far more water than the little ball ever could, and that extra shoved-aside water gives a much bigger upthrust — enough, at last, to balance the weight and hold the clay up.

Crowded or roomy: why a stone beats a cork

Shape explains ships and boats — but what about a plain solid lump, like our cork and stone from the start? For solid things, what matters is how tightly the stuff inside is packed. Scientists call this packing density: a thing is dense when a lot of stuff is crammed into a small space, and not dense when the stuff is loose and roomy.

• A stone is packed tight and heavy for its size — it is denser than water. It cannot gather enough upthrust, so it sinks.
• A cork is full of tiny air pockets and feels light for its size — it is less dense than water. The water easily pushes it up, so it floats.

Here is the neat rule for a solid lump: if it is denser than water it sinks; if it is less dense than water it floats. That is why wood, cork, ice and oil all float, while stone, iron, glass and a coin all sink. And it is why a hollow boat wins — by trapping air inside, the whole boat-plus-air becomes roomier and lighter for its size than the water around it.