Statement of Archimedes' principle

Summary

Archimedes' principle states that an object immersed in a fluid experiences an upward buoyant force equal to the weight of the fluid it displaces (whether the object is fully or partially submerged). The object’s net vertical force is the difference between its own weight (downward) and the buoyant force (upward): if the net force is positive the object rises, if negative it sinks, and if zero it is neutrally buoyant. In equilibrium (such as for a floating or stably submerged object), the buoyant force can be written as Fb = ρgV, where ρ is the fluid density, V is the displaced (submerged) volume, and g is gravitational acceleration. This leads directly to the flotation condition: a floating object displaces a weight of fluid equal to its own weight. The principle is also used to explain pressure differences within fluids—higher pressure at greater depth produces a net upward force—and it underpins related ideas like flotation and buoyancy-based measurements (e.g., determining an object’s density or detecting impurities in a crown).

Key Points

• 1

  Buoyant force on an immersed body equals the weight of the displaced fluid.

• 2

  Net force determines motion: rise if buoyant force exceeds weight, sink if less, neutral buoyancy if equal.

• 3

  For equilibrium, buoyancy can be expressed as Fb = ρgV, linking displaced volume to fluid density and gravity.