Buoyancy Force (Archimedes' Principle)
Reference for the Archimedes buoyancy principle: F = rho x g x V.
Explains why objects float or sink with examples for water, seawater, and oil.
The Formula
Archimedes' principle states that the buoyant force equals the weight of fluid displaced by the object. An object floats when the buoyant force equals or exceeds its weight.
Variables
| Symbol | Meaning |
|---|---|
| F_b | Buoyant force (Newtons) |
| ρ_f | Density of the fluid (kg/m³) |
| V | Volume of fluid displaced by the object (m³) |
| g | Acceleration due to gravity (9.81 m/s²) |
Example 1
A 0.5 m³ block is fully submerged in water. Find the buoyant force.
ρ_f = 1000 kg/m³ (water), V = 0.5 m³
F_b = 1000 × 0.5 × 9.81
F_b = 4,905 N (about 500 kg of upward force)
Example 2
A helium balloon has a volume of 0.01 m³. Will it float in air?
Buoyant force: F_b = 1.225 × 0.01 × 9.81 = 0.120 N
Weight of helium: 0.164 kg/m³ × 0.01 × 9.81 = 0.016 N
Net upward force = 0.120 - 0.016 = 0.104 N
Yes — the buoyant force exceeds the helium's weight (before accounting for balloon material)
When to Use It
Use the buoyancy formula when:
- Determining whether an object will float or sink
- Designing boats, submarines, and flotation devices
- Calculating the lifting capacity of balloons or blimps
- Measuring density using fluid displacement methods
Key Notes
- Archimedes' principle: F_b = ρ_fluid × V_displaced × g: The buoyant force equals the weight of the fluid displaced by the object. It acts upward regardless of the object's weight or material.
- Float vs sink condition: An object floats when ρ_object ≤ ρ_fluid. It sinks when ρ_object > ρ_fluid. At exactly equal densities, the object is neutrally buoyant and remains at any depth.
- Partial vs full submersion: A floating object displaces only enough fluid to equal its own weight. A fully submerged object displaces a volume of fluid equal to its entire volume.
- Submarines use variable buoyancy: Submarines control depth by pumping water into or out of ballast tanks. Adding water increases overall density above seawater, causing descent. Pumping it out lowers density, causing ascent.
- Buoyancy in gases: Archimedes' principle applies to gases too. Hot air balloons, helium blimps, and weather balloons all rely on the buoyant force of surrounding air (ρ_air ≈ 1.225 kg/m³ at sea level).