KinexiaLEARN PHYSICS

Buoyant Force — Iceberg (Worked Example)

Medium
Problem

An iceberg of total volume 1000 m³ floats with 90% submerged in seawater (ρ = 1025 kg/m³). What is the buoyant force on it? (g = 9.8 m/s²)

Given

  • V_displaced = 0.90 × 1000 = 900 m³

  • ρ = 1025 kg/m³

  • g = 9.8 m/s²

Find

The buoyant force Fb.

Principle

Archimedes: Fb equals the weight of displaced fluid — Fb = ρV_displaced·g.

Formula

Solution

  1. Displaced volume: V=900 m3V = 900\ \mathrm{m^3}

  2. Substitute: Fb=(1025)(900)(9.8)F_b = (1025)(900)(9.8)

  3. Multiply: Fb=9,040,500 NF_b = 9{,}040{,}500\ \mathrm{N}

9.04 × 10⁶ N upward

Unit check

kg/m³ × m³ × m/s² = N — correct.

What this means physically

9.04 × 10⁶ N — this exactly balances the iceberg's weight (floating equilibrium). The 10% above water is the famous tip; the berg's fate is decided by the hidden 90%.

Common mistake

Using the full 1000 m³. Only the submerged volume displaces water — use 900 m³.