What is density? Why a huge ship floats while a small stone sinks

A steel ship carrying thousands of tonnes of cargo floats on water. A pebble that fits in your pocket goes to the bottom when you throw it in. The idea that “heavy things sink” collapses here: a ship is far heavier than a stone, yet it does not sink. Why? The answer lies in the concept of density. In this article we explain what density is, how floating and sinking are determined, and a safe experiment you can do at home.

What is density?

Density tells you how much mass a given volume of a substance holds. The formula is:

Here $\rho$ (rho) is density, $m$ is mass and $V$ is volume. The unit is usually g/cm³ or kg/m³. Density is a measure of “compactness”: of two objects with the same volume, the one with more mass is denser.

Some approximate values (sources may differ slightly):

• Water: about 1 g/cm³ (1000 kg/m³).
• Sea water: a little denser, about 1.03 g/cm³. Dissolved salt adds mass.
• Ice: about 0.92 g/cm³; it floats because it is less dense than water.
• Steel: about 7.8 g/cm³; far denser than water.
• Many kinds of rock: roughly in the range of 2.5-3 g/cm³.

Note: density does not depend on the size of an object. A small iron nail and a large iron block made of the same material have the same density. Density is a characteristic property of a substance.

Why do some things float and others sink?

When you put an object in water, you see that the water pushes the object upward with a buoyant force. Floating and sinking are a contest between this force and the object’s weight. The principle described by the ancient Greek scholar Archimedes in his work On Floating Bodies is summarised like this:

An object immersed in a liquid (or a gas) experiences an upward buoyant force equal to the weight of the fluid it displaces.

Some consequences follow:

• If an object’s average density is less than the liquid’s, it floats. At equilibrium only part of it is submerged; the weight of the water that part displaces equals the object’s weight.
• If its average density is greater than the liquid’s, it sinks.
• If the two are about equal, the object can hang suspended in the liquid.

Remember that ice, with a density of about 0.92 g/cm³, floats in fresh water: roughly nine tenths of its volume is below the surface, because the density ratio is about 0.92/1. You can find the reason for this special case, that water expands as it freezes, in the Why does ice float journey and in our Expansion and contraction lesson.

Why doesn’t a ship sink?

A ship is not a solid block of steel; it is full of empty space. Inside the hull there is air, engine rooms and cargo holds. What matters is the total mass of the whole ship (steel hull, the air inside, cargo, everything) divided by the total volume enclosed by the hull, including the part above the waterline. As long as this average density stays below that of water, the ship floats.

As the ship settles into the water, it reaches equilibrium when the weight of the water it displaces equals the ship’s weight. At equilibrium, the ship’s mass divided by only the submerged volume is exactly equal to the density of water; because part of the total volume stays above the water, the ship’s average density comes out lower than water’s. Add more cargo and the ship sinks a little deeper. The load line marks on a ship’s hull show the safe limit of this depth. The same ship sits a little deeper in fresh water because fresh water is less dense than sea water: it has to displace more water to support the same weight.

If a hole opens in the hull and water floods in, things change: the air inside gives way to water, the average density rises and the ship can sink.

Why does a stone sink?

A stone is solid; it has no large hollow spaces like a ship. Its density is several times that of water, so the weight of the water it displaces cannot match its own weight and it goes to the bottom. It is not weight but the density comparison that decides. An exception: pumice is a volcanic rock with many gas pockets inside; its average density is low, so it can float on water.

You see this in everyday life too: a small nail sinks, but a large hollow tray made of the same steel floats. The steel did not change; the shape, that is, how much water it displaces, did.

Try at home: egg and salt water

A safe, cheap experiment. A glass, an egg, salt and a spoon are enough.

1. Predict: What happens if you put the egg in tap water? What if you add salt?
2. Fill the glass about two thirds. Lower the egg gently into the water with a spoon: a fresh egg usually sinks to the bottom.
3. Take the egg out. Add a few spoonfuls of salt to the water and stir until the salt has completely dissolved.
4. Lower the egg gently again. If there is enough salt, the egg floats or hangs suspended in the water.

Explanation: When salt dissolves, the density of the water increases. The egg’s average density is fixed; once the water is dense enough, the egg is the “less dense” one. How much salt it takes depends on the egg and the water, so adding it little by little and observing is best. If you do this experiment with the predict-observe-explain method, you can write your predictions first and compare afterwards. In the kitchen, liquids separating into layers by themselves is the same idea: oil sits on top because it is less dense than water (you can see this separation in our emulsion lesson).

Common misconceptions

• “Heavy things sink.” Weight alone does not decide; average density does. A ship is heavier than a stone and floats. This is one of the typical examples in our misconceptions article.
• “Light things float.” Even a very light needle (made of dense steel) usually sinks (placed carefully, surface tension can hold it up for a while); it is not being light that matters, but having a density below that of the water.

You can find the basis of the particle model of matter in the States of matter and the particle model lesson; why density differs from material to material is also related to how closely the particles are packed.

Summary

• Density is found with $\rho = m / V$ and is a characteristic property of a substance; it does not depend on the size of the object.
• Archimedes’ principle: an object experiences an upward force equal to the weight of the fluid it displaces.
• An object whose average density is less than the liquid’s floats; one whose is greater sinks.
• A ship, thanks to the empty space inside, is as a whole less dense than water; a stone is solid and dense.
• At home you can see how density changes floating with salt water and an egg.