TL;DR:
A fluid pushes up on a submerged object with a force equal to the weight of the fluid it displaces (Archimedes' principle).
An object floats when its average density is less than the fluid's. A floating object displaces exactly its own weight of fluid.
A steel ship floats because its hull is mostly air, so the whole ship has a low average density.
A steel nail sinks. A steel ship carrying thousands of tonnes does not. Both are made of the same metal, so material alone cannot decide the answer. What decides it is how much water the object pushes aside.
Where the upward push comes from
Pressure in a fluid grows with depth, as in pressure in fluids and tires. The bottom of a submerged object is deeper than its top, so the fluid pushes up on the bottom harder than it pushes down on the top. The net force upward is the buoyant force.
Archimedes' principle gives its size: the buoyant force equals the weight of the fluid displaced. In symbols, F_b = ρ_fluid × V_sub × g, where V_sub is the volume of the object that is under the surface.
Sink or float: compare densities
Density is mass per volume, ρ = m / V. Fresh water is about 1000 kg/m³. If you push an object completely under, it displaces its full volume, so the buoyant force is 1000 × V × g and its weight is ρ_object × V × g. The V and g cancel, so the contest is simply between the two densities.
Object denser than the fluid: weight wins and it sinks.
Object less dense: buoyancy wins and it rises until it floats.
Equal densities: it hangs in place.
Worked example: a wooden block in water
Say a wooden cube measures 10 cm on each side and has a density of 600 kg/m³. That is a made-up value in the range of light woods. Find how much of it sits below the surface in fresh water.
Volume:
0.10 × 0.10 × 0.10 = 1.0 × 10⁻³ m³.Mass:
600 × 1.0 × 10⁻³ = 0.60 kg.Weight:
0.60 × 9.8 = 5.88 N.Floating means buoyant force equals weight:
1000 × V_sub × 9.8 = 5.88.Solve:
V_sub = 5.88 / 9800 = 6.0 × 10⁻⁴ m³.Fraction submerged:
6.0 × 10⁻⁴ ÷ 1.0 × 10⁻³ = 0.60, which equals the density ratio600 / 1000.Depth below the surface:
0.60 × 10 cm = 6 cm.
Check: the displaced water has mass 1000 × 6.0 × 10⁻⁴ = 0.60 kg, exactly the mass of the block. That is the whole idea of floating: a floating object displaces its own weight in fluid.
Try the same block in salt water, density about 1025 kg/m³. The fraction submerged is 600 / 1025 ≈ 0.585, so it sits slightly higher. Denser fluid needs less displaced volume to hold up the same weight.
Why a steel ship floats
Steel is far denser than water, so a solid steel block sinks. A ship is a thin steel shell enclosing a huge volume of air, so its average density, total mass divided by total enclosed volume, is below that of water.
Take a ship with a mass of 1000 tonnes, which is 1 × 10⁶ kg. To float it must displace that much water: V = 10⁶ / 1000 = 1000 m³ in fresh water. In salt water it needs 10⁶ / 1025 ≈ 976 m³, a bit less, so it floats slightly higher.
If water pours in through a hole, air is replaced by water, the average density rises and the ship sinks once it can no longer displace enough. Designers also care about stability, meaning where the weight and the buoyant force act, which keeps a ship upright.
The same reasoning explains the load line painted on a ship's side. Cargo adds mass, so the ship must displace more water and sit lower. The line marks how low it may safely go.
Water safety: Do experiments with floating objects in a basin, not in open water. Anyone in or near deep water should wear a properly fitted life jacket, and no one should swim alone.
How to check your answer
Density ratio. A floating object's submerged fraction equals its density divided by the fluid's, so it must lie between 0 and 1.
Mass check. Displaced fluid mass must equal the object's mass when it floats.
Units. Convert centimetres to metres before computing volumes.
kg/m³ × m³ = kg.Sense check. Denser fluid means higher floating.
Mistakes that cost marks
Saying heavy things sink and light things float. Density, not weight, decides.
Using the whole object's volume when it is only partly submerged.
Forgetting that a floating object's buoyant force equals its weight, not its volume times the fluid density.
Mixing grams per cubic centimetre with kilograms per cubic metre. Water is 1.0 g/cm³ or 1000 kg/m³.
Where you will use it next
Buoyancy appears with hot-air balloons and submarines, where density is changed on purpose. Density and energy also meet in heat vs temperature, since heated fluids expand and become less dense.
Frequently asked questions
Why is it easier to float in the sea than in a pool?
Salt water is denser, so it supplies the same buoyant force with less displaced volume, and you sit higher.
Does buoyancy work in air?
Yes. Air is a fluid, and a helium balloon rises because the displaced air weighs more than the balloon and its gas.
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