Buoyant Force — Cargo Ship (Worked Example)

Given

• V = 50,000 m³

• ρ = 1025 kg/m³

• g = 9.8 m/s²

Find

The buoyant force Fb.

Principle

A floating ship displaces its own weight of water: Fb = ρVg equals the ship's weight.

Formula

Solution

1. Substitute: $F_b = (1025)(50000)(9.8)$

2. Note: at equilibrium this buoyant force exactly equals the total weight of ship plus cargo

3. Multiply: $F_b = 5.0225 \times 10^8\ \mathrm{N}$

Unit check

kg/m³ × m³ × m/s² = N. Displaced-fluid weight is a force — dimensionally correct.

What this means physically

5.02 × 10⁸ N — supporting about 51,000 tonnes of ship plus cargo. Load more containers and the ship sits lower, displacing more water until forces balance again — that is the Plimsoll line's physics.