Why Some Objects Float and Others Sink

Pressure in a fluid increases with depth because deeper layers support the weight of more fluid above them. When an object is partly or fully underwater, the fluid pushes on every surface. The pressure on the lower parts is greater than the pressure on the upper parts.

This difference creates a net upward force called buoyant force. The size of that force equals the weight of the fluid displaced by the object. Displaced fluid is simply the water or air that would otherwise occupy the object's space. A larger submerged volume displaces more fluid, so it produces a larger buoyant force in the same fluid.

If the buoyant force is smaller than the object's weight, the object accelerates downward and sinks. If the forces balance, the object can float or remain suspended. If the buoyant force is initially larger, the object rises until less of it is submerged and balance is reached.

Density tells you how much mass is packed into a certain volume. An object with a lower average density than the surrounding fluid can float. An object with a greater average density tends to sink. Average density matters because an object can include empty spaces, trapped air or several materials with different densities.

This explains why a solid block of steel sinks but a steel ship floats. The hull encloses a large volume of air, so the ship's total mass is spread over a much larger volume. Its average density, including the air-filled space, can be lower than the density of water.

Loading a ship deeper increases the amount of water it displaces. That increases the buoyant force until it balances the greater weight. If too much water enters the hull, the average density rises and the ship may no longer displace enough water before the deck sinks below the surface. Submarines control this balance by changing how much water and air their ballast tanks contain, allowing them to sink, rise or stay at a chosen depth.

A bowl of water and a few waterproof objects can turn the idea into something visible. Keep electronics away, because apparently that still needs saying:

• •Compare objects made from the same material but shaped differently.
• •Press a floating cup down and feel the stronger upward push.
• •Add small weights to a foil boat one at a time.
• •Notice how deeply the boat sits as its load grows.
• •Predict each result before testing it.

Seawater is denser than fresh water because it contains dissolved salts. A floating object needs to displace its own weight of water, so in denser seawater it displaces a smaller volume and sits higher. You may notice that swimming in the sea feels slightly more buoyant than swimming in a lake. In extremely salty water, such as the Dead Sea, the effect becomes dramatic, and people can lie back and float with surprising ease.

Ships have to allow for this. A vessel loaded in a salty port will sink deeper when it sails into a freshwater river or harbour, even though its cargo has not changed. Temperature matters too, because warmer water is slightly less dense. For this reason, cargo ships carry load line markings on their hulls, often called Plimsoll lines, showing the safe loading depth for different kinds of water and seasons. Overloading beyond those marks reduces the reserve buoyancy that keeps a ship safe in rough seas.

The principle that buoyant force equals the weight of displaced fluid is named after Archimedes, the Greek mathematician of Syracuse in the third century BCE. A famous story says that a king suspected a goldsmith of mixing silver into a crown, and asked Archimedes to check without damaging it. Getting into a bath, Archimedes noticed the water rising and realised he could compare the crown's volume with that of pure gold, supposedly running through the streets shouting eureka.

The story comes from the Roman writer Vitruvius, writing about two centuries later, and historians treat it with caution. Galileo pointed out that simply measuring the overflowing water would be too imprecise to detect a small amount of silver. He suggested a cleverer method that uses buoyancy directly. Hang the crown and an equal weight of pure gold from opposite ends of a balance, then lower both into water. If the crown contains lighter silver, it has a larger volume, receives a larger upward push and rises, tipping the balance towards the gold.

An object can have plenty of buoyancy and still roll over. Its weight acts through its centre of gravity, while the buoyant force acts through the centre of the displaced water, called the centre of buoyancy. When a well-designed ship tilts, the shape of the submerged part changes and the centre of buoyancy shifts towards the lower side. The upward push and the downward weight then form a turning effect that rolls the ship back. Keeping heavy cargo, engines and ballast low in the hull makes this righting effect stronger, which is why stacking weight high on deck is risky.

The Swedish warship Vasa is a famous lesson. It carried two decks of heavy bronze cannon, and its hull held too little ballast low down to balance that weight. On its maiden voyage in 1628, a gust of wind heeled it over in Stockholm's harbour, water poured in through the open gun ports, and it sank after sailing little more than a kilometre. Because the cold, brackish water of the Baltic is hostile to shipworm, the wooden hull survived largely intact. It was raised in 1961 and is now displayed in a museum in Stockholm, where visitors can see how tall and narrow it is.

A simple rule tells you how much of a floating object sits underwater. The fraction submerged equals the object's average density divided by the density of the fluid. A block of wood with a density of 600 kilograms per cubic metre, floating in fresh water at about 1000, sits with roughly 60 per cent of its volume below the surface. Ice has a density of about 917 and seawater about 1025, so an iceberg floats with close to 90 per cent of its volume hidden. That is the physics behind the phrase the tip of the iceberg.

You can use the same reasoning for a boat. Picture a flat-bottomed barge with a base 5 metres long and 2 metres wide, giving an area of 10 square metres, and a mass of 3000 kilograms. To float, it must displace 3000 kilograms of fresh water, which is 3 cubic metres. Dividing that volume by the base area shows the barge sits 0.3 metres deep. Load another 1000 kilograms of cargo and it must displace 4 cubic metres, so it settles to 0.4 metres. If its sides are 0.5 metres high, a further 1000 kilograms would bring the water level with the top, leaving no safety margin at all.

Objects float when the upward buoyant force can balance their weight. Density and shape decide how much fluid must be displaced to reach that balance. Follow the forces and the displaced volume, and even a giant steel ship stops looking like a physics trick.