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Fluid Statics

Buoyancy & Archimedes' Principle

Drop an object into a fluid and see whether it floats or sinks — and the upward force that decides.
Buoyant force (up) Weight (down)
Weight
0N
Buoyant force
0N
Submerged
0%
Result
F_buoyant = ρ_fluid · g · V_displaced   |   floats if ρ_object < ρ_fluid, with submerged fraction = ρ_object / ρ_fluid
i About this experiment — click to learn the physics

What you're looking at

An object is dropped into a tank of fluid. It bobs and settles, and the two arrows show the forces deciding its fate: gravity pulling it down, and the buoyant force pushing it up. Whether it floats or sinks comes down to a simple comparison of densities.

Archimedes' principle

Over two thousand years ago Archimedes realised that the upward force on a submerged object equals the weight of the fluid it pushes aside:

F_buoyant = ρ_fluid · g · V_displaced weight of displaced fluid

The deeper an object sinks, the more fluid it displaces and the stronger the upward push — until the buoyant force grows enough to balance gravity, or the object is fully submerged.

To float or to sink

Compare the object's weight, ρ_object·V·g, with the most buoyancy it can get when fully submerged, ρ_fluid·V·g. The volume cancels, so it all comes down to density:

  • ρ_object < ρ_fluid → it floats, sinking only far enough that the submerged part displaces its full weight.
  • ρ_object > ρ_fluid → it sinks; even fully submerged, gravity wins.
  • equal → it hovers, neutrally buoyant at any depth.

The floating fraction

For a floating object the fraction sitting below the surface is exactly the ratio of densities:

submerged fraction = ρ_object / ρ_fluid why icebergs hide 90% below water

Ice has about 90% of water's density, so a floating iceberg shows only a tenth of itself above the surface — the rest lurks below.

Things to try

Float wood in water, then switch the fluid to oil (less dense) and watch it ride lower. Drop dense iron into water (it sinks) and then into mercury (ρ ≈ 13600) and watch it bob right back to the top.