Buoyancy and Archimedes' Principle
A massive steel cargo ship floats while a small steel coin sinks — same material, wildly different outcomes, and the explanation has nothing to do with weight alone. Any object submerged in a fluid pushes some of that fluid out of the way, and the fluid pushes back with an upward force exactly equal to the weight of whatever it displaced — a relationship discovered over two thousand years ago by Archimedes and still taught, unchanged, as one of the oldest quantitative laws in physics. Whether that upward push is enough to support the object depends not on its weight alone but on its shape: a ship's hull displaces a huge volume of water for its weight, while a solid coin displaces very little.
Floating vs sinking
Average density determines fate: objects less dense than the fluid float with part of their volume submerged until displaced fluid matches their weight.
Archimedes' Principle
When an object sits in a fluid, it pushes some fluid out of the way — this is called displacement. The fluid pushes back with an upward force equal to the weight of the fluid that got displaced. If that upward push can equal the object's own weight, it floats; if the object is too heavy for the fluid it displaces, it sinks.
The formula
F_b = ρ · V · g
- ρ — fluid density (kg/m³): the fluid's mass per unit volume
- V — displaced volume (m³): the volume of fluid the object pushes out of the way
- g — gravitational acceleration (m/s²): the gravitational acceleration pulling everything down
Worked example
A block pushes 0.002 cubic meters of water out of the way. Water has a density of 1000 kilograms per cubic meter. What buoyant force does the water push back with?
- ρ = 1000 kg/m³
- V = 0.002 m³
- g = 9.8 m/s²
- F_b = ρ · V · g
- F_b = 1000 kg/m³ · 0.002 m³ · 9.8 m/s²
F_b = 19.6 N
Test yourself
The same block now displaces 0.004 cubic meters of water instead of 0.002. What is the new buoyant force?
- 19.6 N
- Correct answer: 39.2 N
- 9.8 N
Right! Doubling the volume doubles the buoyant force: 1000 kg/m³ × 0.004 m³ × 9.8 m/s² = 39.2 N.
A block weighing 15 N is placed in water where it could displace up to 20 N worth of water at full submersion. What happens?
- Correct answer: It floats, since the buoyant force can equal its weight
- It sinks, since buoyant force only depends on volume
- It floats, since all objects in water float
Correct — a 15 N block in water that can push back with up to 20 N of buoyant force will float, sitting low enough that displaced water weighs exactly 15 N.
Where you see this
A steel ship floats even though steel is much denser than water, because the hull encloses enough air to displace an enormous volume of water — and the weight of that displaced water is exactly what holds the ship up. An iceberg makes the same point in reverse: ice is only slightly less dense than seawater, so about 90 percent of the berg rides below the surface.
Common mistakes
The most common error is judging sink-or-float from the object alone — heavy does not mean sinking. A 15 N block floats in water if it can displace up to 20 N of water, because floating is decided by comparing the object's weight with the weight of the fluid it can push aside. A second slip: pushing a fully submerged object deeper does not increase the buoyant force — the displaced volume has already stopped changing, so F_b = ρ · V · g has too.
How it connects
The upward push is hydrostatic pressure in disguise: the bottom of a submerged object sits deeper than its top, and since pressure grows with depth, the fluid pushes up on the bottom harder than it presses down on the top — that imbalance is the buoyant force. Bernoulli's principle, next, picks up the same fluid once it moves, and trades that pressure away for speed.