A 100,000-ton ship floats and a pebble sinks

Quick answer: An object floats if, on average, it's less dense than the fluid it's sitting in. Density comes from two things: how heavy the atoms are, and how much empty space sits between them. Weight alone tells you nothing.

Start with the water that was there first

Drop a pebble in a pond and a Nimitz-class carrier can displace about 100,000 tons of water. The pebble sinks. The carrier doesn't. So "heavy things sink" is simply false.

Here's the version that works. Picture a chunk of water exactly the size and shape of your object, sitting in the pond before you arrived. It wasn't sinking. The water around it held it up perfectly. Now swap your object into that spot.

If your object weighs more than the water it replaced, the surrounding water can't hold it, and it goes down. If it weighs less, the surrounding water still has the strength to hold up that much, and the leftover push sends your object up. If it's equal, it hangs there, like a diver who's got their weights right.

That's Archimedes' principle, and it fits on a napkin. The molecular story explains why it works.

What the water molecules are doing

Water molecules in a pond are jostling constantly and pressing on everything they touch. Gravity pulls the whole column down, so the deeper you go, the more water is stacked overhead, and the harder the molecules push.

Put an object in and the molecules push on every surface. The bottom sits deeper than the top, so it takes a harder shove from below than the top gets from above. That difference is the buoyant force. It equals the weight of the water your object pushed aside, no more and no less.

So the question was never "is this thing heavy?" It is "does this thing weigh more than the same volume of water?" And that's a question about density.

Why one substance is denser than another

Two knobs set density.

Atomic mass. A lead atom weighs roughly seventeen times what a carbon atom does. Pack the same number of each into the same space and the lead wins easily. Plastics, wood and fat are built mostly from carbon, hydrogen and oxygen, which are light. Metals like iron, lead and gold are built from heavy atoms.

Spacing. Atoms in a solid metal sit shoulder to shoulder in tight, repeating patterns. In liquid water the molecules are close but loose. In air they're far apart, which is why air weighs about a thousandth as much as water per cubic foot.

Water comes in at about 62 pounds per cubic foot. Iron is about 490. Aluminum is roughly 170. Lead is over 700. Gold is above 1,200. Gasoline and cooking oil are lighter than water, around 75 to 92 percent of it, which is why a spill spreads across a puddle instead of mixing in.

Why wood floats: it's mostly nothing

Here's the part that surprises people. The cell wall material in wood, mostly cellulose and lignin, is actually denser than water, about one and a half times as dense. A solid chunk of it would sink.

But wood isn't solid cell wall. It's a honeycomb of tiny hollow cells, and those cells are full of air. Balsa is the extreme case, with thin walls and huge empty chambers. Ebony and ironwood go the other way, with thick walls and little air, and they sink like stones.

Leave a floating log in the water long enough and it'll wallow lower. Water slowly seeps into the cells and replaces the air. The log's average density creeps up toward the water's own.

Why a steel ship floats

Steel is nearly eight times denser than water. A steel ball bearing drops straight down. Hammer that same steel into a bowl and it floats.

The trick is the shape. A hull isn't a block of steel. It's a thin steel shell wrapped around an enormous volume of air. What matters is the average density of the entire ship, steel plus all the air inside it. Make the hull deep enough and wide enough, and the water it displaces weighs more than the whole vessel. That's why a hull that's breached and fills with water goes down. The air that was keeping the average low is gone.

It's the same engineering logic behind a lot of structures, which is how steel gets asked to do jobs its raw density would suggest it can't. What Holds a Bridge Up and What Eventually Takes One Down covers the other side of that coin.

Ice, the exception that matters

Almost every substance gets denser when it freezes. The molecules slow down and pack closer. Water is the oddball.

Each water molecule has bumps of slight positive charge on its hydrogen side and slight negative on its oxygen side. Those charges pull neighboring molecules together, and the pulls are called hydrogen bonds. As water cools toward freezing, the bonds lock each molecule to four neighbors in a rigid, open hexagonal lattice. That lattice has gaps in it. Liquid water, with its molecules tumbling around, crowds closer together than the frozen version does.

The result is that ice takes up about nine percent more room than the water it came from, so it's about nine percent less dense. It floats, with most of the cube below the surface.

Liquid water is densest at about 39°F, just above freezing. So when a lake cools in autumn, the coldest, heaviest water sinks until the whole lake hits that temperature. After that the surface water gets colder, stays on top and freezes first. A skin of ice forms, insulates the water under it, and the lake freezes from the top down instead of the bottom up. Fish ride out the winter in the liquid below. If ice sank, ponds would freeze solid from the bottom.

Try it in your kitchen

Three tests that take ten minutes and cost nothing.

• Foil. Squeeze a sheet of aluminum foil into a tight ball and drop it in a sink. It sinks. Fold a second sheet into a little boat with tall sides. It floats, and it'll carry a surprising number of pennies before the sides go under.
• Soda. Put an unopened can of regular soda and a can of diet in a tub of water. Regular typically sinks and diet floats. The cans are the same size and the contents are different. The sugar dissolved in regular soda adds mass without adding much volume.
• Egg. An egg sinks in plain water. Stir in salt, a lot of it, and it'll lift off the bottom and eventually float. Dissolved salt makes the water itself denser. It's why swimmers float higher in the Dead Sea, where the water is roughly a quarter denser than fresh.

You can also use this for something useful. Sorting plastics? Most milk jugs and detergent bottles are HDPE, which has a density a little under water's, so it floats. Soda bottles are PET, which is roughly one and a third times water's density, so it sinks. Drop a clean scrap in water and you've got a quick check on what you're holding.

The rule works in air too

A helium balloon rises for exactly the same reason a cork does. Air is a fluid, and the balloon weighs less than the air it displaces. The wing story is a different mechanism entirely, and Why Airplanes Fly and Why Turbulence Won't Break One takes it apart.

Next time you watch a steel ship slide out of a harbor, remember it isn't beating gravity. It's just mostly air with a steel coat on. The water below has no problem holding that up.