Drop a steel nail into a bucket and it sinks in a second. Yet a cargo ship built from thousands of tonnes of steel sits happily on the sea. What is the ship doing that the nail is not?
Start with something you know
Push a beach ball under water and it fights back, shooting up when you let go. Lift a friend in a swimming pool and they suddenly feel light. Water pushes up on anything you put in it. That upward push is the buoyant force.
Try it
Try this
- Choose steel and watch it sink in fresh water. Now switch the liquid to mercury.
- Pick ice in sea water. How much of the block stays under the surface?
- Drag a floating block down to the floor and let go. What pushes it back up?
What is happening
From the last lesson you know pressure grows with depth. The bottom face of a block sits deeper than its top face, so the water pushes up on the bottom harder than it pushes down on the top. The difference is the buoyant force. Around 250 BC, Archimedes worked out how big it is: the buoyant force equals the weight of the liquid the object pushes aside.
- FB
- buoyant force (N)
- ρliquid
- density of the liquid (kg/m³)
- g
- gravity, 9.81 m/s²
- Vunder
- volume of the object below the surface (m³)
Float or sink
Two forces compete. The weight of the object pulls down. The buoyant force pushes up, and it keeps growing as more of the object goes under. If the object is less dense than the liquid, buoyancy catches up with the weight before the object is fully under. It settles with just enough of its volume below the surface to balance its weight:
Ice at 917 kg/m³ in sea water at 1025 kg/m³ floats with about 89% of its volume under the surface. That is where the phrase “the tip of the iceberg” comes from.
So how does the steel ship float?
Steel is almost 8 times denser than water, so a solid block of steel sinks. But a ship is a hollow shell full of air. What matters is the average density of the whole ship, steel and air together. Spread the same steel into a wide bowl and it pushes aside a huge volume of water, enough to weigh as much as the ship long before the deck reaches the waterline. Load more cargo and the ship settles a little deeper, pushing aside more water, until the forces balance again.
Where you see it
- Load lines on shipsMarks painted on the hull show how deep a ship may sit in fresh, salt, warm and cold water, because each has a different density.
- SubmarinesThey flood ballast tanks with sea water to dive and blow the water out with compressed air to rise.
- Hot air balloonsAir is a fluid too. Hot air is less dense than the cool air around it, so the balloon is pushed upward.
- The Dead SeaThe water is so salty and dense that people float on it without any effort.
Easy to mix up
- Heavy things do not always sink. Density decides, not weight. A huge log floats while a small pebble sinks.
- Once an object is fully under water, the buoyant force stops growing as it goes deeper, because it is not pushing aside any more water.
Check your understanding
5 questions.Buoyancy Quiz