Archimedes' Principle
Simple Explanation
Archimedes' principle states that any object submerged (fully or partly) in a fluid experiences an upward buoyant force equal to the weight of the fluid the object displaces.
Why Do We Need It?
This principle explains why objects float or sink, and is essential for designing ships, submarines, hot air balloons, and anything else meant to float or control its buoyancy.
Formula
Buoyant Force (Archimedes' Principle)
Fᵦ = ρVg
The upward buoyant force on an object submerged (fully or partly) in a fluid equals the weight of the fluid that the object displaces.
- Fᵦ
- — Buoyant force, in newtons
- ρ
- — Density of the fluid the object is submerged in, in kg/m³
- V
- — Volume of fluid displaced by the object, in m³
- g
- — Acceleration due to gravity, 9.8 m/s²
When to use it: Use to find the upward force a fluid exerts on a submerged or floating object, and to determine whether an object will float or sink.
Worked Example
Finding buoyant force
An object displaces 0.02 m³ of water when submerged. Find the buoyant force acting on it (ρ_water = 1000 kg/m³, g = 9.8 m/s²).
Why Does This Work?
Fluid pressure increases with depth, so the fluid pushes upward on the bottom of a submerged object with more pressure than it pushes downward on the top — this net upward pressure difference, summed over the object's surface, is exactly equal to the weight of the fluid displaced.
Real-Life Example
Why massive steel ships float
A steel ship, despite being made of a material far denser than water, floats easily.
The ship's hollow hull shape displaces a huge volume of water — since the buoyant force depends on the volume of water displaced (not the material the ship is made of), the ship's overall shape displaces enough water that the buoyant force equals the ship's total weight, allowing it to float.
Practice
An object displaces 0.005 m³ of water. Find the buoyant force (ρ = 1000 kg/m³, g = 9.8 m/s²).
MediumCommon mistake
Thinking buoyant force depends on the object's own weight or density — it depends only on the VOLUME OF FLUID DISPLACED and the fluid's density; a heavy, dense object displacing little fluid gets little buoyant force (and sinks), while a light object shaped to displace a lot of fluid (like a ship's hull) gets a large buoyant force (and floats).
Quick Review
- Buoyant force Fᵦ = ρVg equals the weight of fluid displaced.
- Depends on the volume of fluid displaced, not the object's own material or weight.
- Ships float because their hull shape displaces enough water to equal the ship's weight.