Statement of Archimedes' principle

Summary

Archimedes' principle states that the upward buoyant force on a body immersed in a fluid (partly or fully) equals the weight of the fluid displaced by the body. The body’s downward force is its own weight, so the net force is the difference between buoyant force and weight: if buoyant force is greater, the object rises; if smaller, it sinks; and if equal, it is neutrally buoyant. In terms of forces and equilibrium, buoyancy arises because pressure in a fluid increases with depth, creating a higher pressure on the bottom of an immersed object than on the top. This pressure difference produces an upward resultant force that can be computed by integrating the fluid stress over the object’s surface, which reduces to the displaced-fluid form. For a fully submerged object in equilibrium, the condition mg = ρfVdisp g implies that the equilibrium sinking depth (and displaced volume) depends on the object’s mass relative to the fluid density, not on the location’s gravity. Archimedes’ principle also leads to the related idea of flotation: a floating object displaces a weight of fluid equal to its own weight, which is why ships, submarines, and dirigibles must be designed to displace enough fluid (or air) to balance their weight. The principle is distinct from the “displaced volume” intuition used in some demonstrations, which may fail for submerged objects because water-level rise depends on volume rather than mass.

Key Points

• 1

  Buoyant force equals the weight of the fluid displaced by the immersed body; compare it to the object’s weight to predict rise, sink, or neutral buoyancy.

• 2

  Buoyancy results from hydrostatic pressure increasing with depth, producing a net upward force on the object.

• 3

  For equilibrium of a fully submerged object, mg = ρfVdisp g, linking displaced volume to object mass and fluid density.

• 4

  A floating object satisfies flotation: it displaces fluid whose weight equals the object’s weight, guiding the design of ships and other vessels.