Buoyancy Force (Archimedes' Principle)
Calculate the upward force on an object submerged in fluid.
Explains why objects float or sink.
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