Buoyant force and displaced fluid
Archimedes' principle states that when an object is fully or partly immersed in a fluid, the upward buoyant force equals the weight of the fluid displaced. This explains why objects feel lighter in water and why ships float.
Key formula / 关键公式
Buoyant force: FB = ρVg
where ρ = density of the fluid (kg m⁻³), V = volume of fluid displaced (m³), g = 10 m s⁻².
This equals the weight of displaced fluid: FB = weight of displaced fluid.
Floating and sinking
- If buoyant force ≥ weight, the object floats.
- If buoyant force < weight, the object sinks.
- A floating object displaces its own weight of fluid.
Worked example / 例题
A metal block of volume 0.002 m³ is fully submerged in water (ρ = 1000 kg m⁻³, g = 10 m s⁻²). Find the buoyant force.
FB = ρVg = 1000 × 0.002 × 10 = 20 N.
Worked example / 例题
An object weighs 50 N in air and 30 N when submerged in water. Find the buoyant force and the volume of water displaced (ρ = 1000 kg m⁻³, g = 10 m s⁻²).
Buoyant force = 50 − 30 = 20 N.
V = FB / (ρg) = 20 / (1000 × 10) = 0.002 m³.
Remember / 记住
- Buoyant force = weight of fluid displaced = ρVg.
- Apparent loss in weight = buoyant force.
- A floating object displaces a weight of fluid equal to its own weight.