A matter of density
Whether something floats depends on how it compares with the fluid around it. The key quantity is density, which is the mass of a material in a given volume. A kilogram of feathers and a kilogram of lead have the same mass, but the lead fits into a far smaller space, so its density is much greater.
Water has a density of about 1,000 kilograms per cubic meter, or about 1 kilogram per liter. An object that is denser than the fluid it is placed in tends to sink, and an object less dense than the fluid tends to float. Wood, most plastics and cork are generally less dense than water. Stone, iron and glass are denser. (Some forms of plastic, as covered in plastic polymers, sink, and others float, depending on the type.)
The upward buoyant force
Density tells you the outcome, but a force produces it. Any object placed in a fluid, a liquid or a gas, is pushed upward by the fluid. This is the upward buoyant force. It arises because pressure in a fluid increases with depth. The bottom of a submerged object is deeper than the top, so the fluid pushes up on the bottom harder than it pushes down on the top. The net result is an upward force.
The ancient Greek scholar Archimedes is credited with the key insight, now known as Archimedes’ principle: the buoyant force on an object equals the weight of the fluid that the object displaces. Displaced fluid is the fluid pushed out of the way to make room for the object.
So an object sinks or floats depending on a contest between two forces: its weight pulling it down, and the buoyant force pushing it up, an application of the ideas in the laws of motion.
- If the buoyant force when fully submerged is less than the object’s weight, the net force is downward and it sinks.
- If it is greater, the object rises until part of it sticks out of the fluid, and as less fluid is displaced the buoyant force drops.
- It then settles at the level where the buoyant force exactly equals its weight, and it floats.
A simple example
Take an object with a mass of 1 kilogram and a volume of 2 liters. Its density is 1 ÷ 2 = 0.5 kilograms per liter, half that of water. If fully submerged, it would displace 2 liters of water, which has a mass of about 2 kilograms, so the upward push would be about twice its weight, and it rises. It floats with enough of its volume below the surface to displace 1 liter, which is water with a mass of 1 kilogram, matching its own weight. So it floats with half of its volume submerged.
For an object denser than water, such as a 1-kilogram block with a volume of 0.5 liters, full submersion displaces only 0.5 kilogram of water, which is not enough to support it, so it sinks.
Why a steel ship floats
Steel is roughly eight times denser than water, so a solid lump of it sinks. A ship floats because it is not a solid lump. The hull is shaped to enclose a large volume of air, so the ship as a whole, steel plus the air inside, has an average density less than water. The hull displaces a large volume of water, and the weight of that water equals the weight of the ship.
This is also why a ship that is flooded can sink: water replaces air and the average density rises. And a heavily loaded ship rides lower in the water, since it needs to displace more water to match the greater weight.
Salt water, ice and temperature
The fluid matters as much as the object. Salt water is denser than fresh water, so it gives a greater buoyant force for the same displaced volume, and objects float slightly higher in the sea than in a lake. Why the oceans contain dissolved salt is discussed in ocean salinity.
Ice is an unusual case. Most substances are denser as solids than as liquids, but ice is less dense than liquid water, by roughly 8 to 10 percent, so it floats. This is a result of how water molecules arrange themselves when they freeze, and it matters for life in cold climates, since lakes freeze from the top and the liquid water beneath stays available. More on changes between solid and liquid is in states of matter.
Buoyancy in gases
Air is a fluid too, so buoyancy works there. A hot air balloon rises because the air inside is heated and becomes less dense than the cooler air outside, and the balloon displaces enough outside air to lift its own weight. The same principle of rising warm air and sinking cool air plays a part in weather systems.
Submarines control their buoyancy deliberately. They take water into ballast tanks to become denser and sink, and they push it out with compressed air to rise. Fish control theirs using gas-filled organs called swim bladders.
Common misconceptions
Heavy does not always mean sinking: a massive ship floats, while a small pebble sinks. Size alone is not the factor either. What counts is density, together with the shape that determines how much fluid is displaced. And objects do not float because something “pulls” them up; the upward push is the result of pressure differences within the fluid.