Buoyancy and Archimedes' Principle

Discover why objects float or sink, and how to calculate the buoyant force using Archimedes' principle.

Why Do Things Float?

When an object is submerged in a fluid, the fluid pushes upward on it. This upward force is called the buoyant force (or upthrust).

Archimedes' Principle

Buoyant Force

F_b = \rho_{\text{fluid}} \cdot g \cdot V_{\text{submerged}}

ρ_fluid = fluid density (kg/m³), g ≈ 9.8 m/s², V_submerged = volume of fluid displaced (m³).

In words: the buoyant force equals the weight of the displaced fluid.

Float, Sink, or Hover?

Condition	Result
$F_b > W$	Object floats (rises)
$F_b = W$	Object hovers (neutral buoyancy)
$F_b < W$	Object sinks

This is equivalent to comparing densities: if $\rho_{\text{object}} < \rho_{\text{fluid}}$ , the object floats.

Note Ice floats on water because ice (≈ 917 kg/m³) is less dense than liquid water (1000 kg/m³).

Apparent Weight

An object feels lighter when submerged:

Apparent Weight

W_{\text{apparent}} = W - F_b

W = true weight (N), F_b = buoyant force (N).

1
Find the displaced volume
For a fully submerged object, V_displaced = V_object.
2
Calculate F_b
F_b = ρ_fluid × g × V_displaced.
3
Compare F_b and W
Decide whether the object floats or sinks.

A stone of volume 0.002 m³ is fully submerged in water (ρ = 1000 kg/m³). Find the buoyant force.

$F_b = 1000 \times 9.8 \times 0.002 = 19.6 \text{ N}$

Real world: ships floating

A steel ship hull is hollow, making the average density of the ship much less than that of water. A modern container ship displaces hundreds of thousands of tonnes of water — and by Archimedes' principle, the buoyant force equals the weight of that water, supporting the ship. Engineers calculate hull volume precisely so the buoyant force equals the ship's maximum loaded weight.

Real world: hot-air balloon

A hot-air balloon rises because heated air inside the envelope is less dense than the cooler surrounding air. The buoyant force (weight of displaced cool air) exceeds the weight of the balloon plus passengers, providing net upward lift. Pilots control altitude by adjusting the air temperature with the burner — directly manipulating the density relationship.

Real world: scuba diver neutral buoyancy

A scuba diver uses a buoyancy compensator device (BCD) — an inflatable jacket — to adjust their average density to equal that of water. At neutral buoyancy, the buoyant force exactly equals their weight and they hover effortlessly at depth. Too much air in the BCD and they rise; too little and they sink.

Tip To determine if an object floats, compare densities: if

\rho_{\text{object}} < \rho_{\text{fluid}}

it floats; if greater, it sinks. You don't need to calculate forces unless the question asks for the buoyant force value.

Practice Problems

A block of wood (ρ = 600 kg/m³) is placed in water (ρ = 1000 kg/m³). Does it float or sink?

Show answer

ρ_wood < ρ_water, so it floats.

An object with volume 0.005 m³ is submerged in water. Calculate F_b.

Show answer

F_b = 1000 × 9.8 × 0.005 = 49 N.

A metal block weighs 80 N in air. When submerged in water it weighs 55 N. What is the buoyant force?

Show answer

F_b = 80 − 55 = 25 N.