Buoyancy (Archimedes)

How Archimedes' buoyant force works

Drop any object into a fluid, whether it goes all the way under or only part of the way, and the fluid pushes back up on it. Archimedes' principle says that upward push equals the weight of the fluid the object shoves aside: E = ρ_fluid · g · V_submerged. Here ρ_fluid is the fluid density in kg/m³, g ≈ 9.81 m/s² is gravity, and V_submerged is the volume of fluid that actually gets displaced. If an object's average density comes in below the fluid's, it floats. If not, down it goes. The story everyone knows puts Archimedes (~250 BC) in the bath, trying to work out whether king Hieron II's crown was solid gold. He supposedly yelled "Eureka!" the moment he saw that comparing displaced volumes would expose the silver swap.

A few densities show up over and over. Fresh water sits at 1000 kg/m³, sea water at 1025 kg/m³, and the Dead Sea pushes all the way to 1240 kg/m³, which is exactly why people float there without trying. Take an iceberg: ice at 917 kg/m³ bobbing in sea water at 1025 kg/m³ ends up with 917/1025 ≈ 89.5% of its bulk under the surface, so only about 10.5% pokes above the waterline.

Real-world applications

Naval architects lean on the buoyancy equation to figure out displacement. A loaded vessel has to shove aside a volume of water that weighs as much as the ship and everything in it. Helium balloons go up for the same reason in reverse: the air they push out of the way weighs more than the whole balloon setup. Submarines change depth by flooding or pumping out ballast tanks, nudging their average density above or below that of the sea. And a hydrometer reads liquid density straight from how far it sinks, which is how quality gets checked in beer, wine, dairy, and battery electrolyte.

FAQ

Why do some objects float and others sink? It comes down to average density, meaning mass over total volume. Below the fluid's density and the object floats. Above it, the buoyant force simply can't keep up with the object's weight, so it sinks.

Does buoyant force depend on depth? Not in any direct way. What matters is the displaced volume and the fluid density. With an incompressible fluid, both of those hold steady, so you get the same force at 1 m as at 100 m of submersion (assuming the fluid doesn't compress).

Why is it easier to float in the sea than in a pool? Sea water runs roughly 2.5% denser than fresh water. That means the same submerged volume gives you more buoyant force, so less of your body has to go under before things balance out.