Archimedes' Principle — Buoyant Force on a Boat (Worked Example)

Given

• V_displaced = 2.5 m³

• ρ = 1025 kg/m³

• g = 9.81 m/s²

Find

Buoyant force F_b and supportable mass m.

Principle

Archimedes' principle: the buoyant force equals the weight of the fluid displaced by the hull.

Formula

Solution

1. Write the principle: $F_b = \rho V g$

2. Substitute: $F_b = 1025 \times 2.5 \times 9.81$

3. Calculate: $F_b = 25{,}138\ \mathrm{N} \approx 2.51 \times 10^4\ \mathrm{N}$

4. Mass supported: $m = F_b/g = \rho V = 1025 \times 2.5 = 2562.5\ \mathrm{kg}$

Unit check

(kg/m³)(m³)(m/s²) = kg·m/s² = N. Correct.

What this means physically

About 25 kN of lift — enough for the boat plus roughly 2.5 tonnes of crew and cargo. Load beyond that and the hull must displace more water, sitting lower, until it swamps.