Floating equilibrium 2026-10-14
A freely floating body at rest has no supporting contact or applied holding force. Neglecting surface tension and the buoyancy of air, its upward buoyancy balances its downward force from gravity:For a body of uniform mass density and total volume , its mass is . Substitution into Archimedes' principle givesPartial immersion is possible when . A nonuniform body uses its mean mass density instead; for a hollow body this volume must count the enclosed space that excludes water. This explains how the amount of displaced water can support a vessel whose walls alone are denser than water. [ref]
For the cube in water of mass density , the displaced fraction is : sixty percent of its volume lies below the surface. With a horizontal top and bottom, the immersed depth satisfies , soIts remaining height is , and the buoyancy is , exactly balancing its downward force from gravity.
Neutral buoyancy 2026-10-14
Neutral buoyancy means a fully immersed body's upward buoyancy equals its downward force from gravity. For a body of fixed volume in a constant-mass density fluid under a uniform gravitational field, this occurs when its mean mass density equals the surrounding mass density. A cube of mass density in the stipulated water has mass , so both forces are .
Ideally it can remain at rest at any depth for which it stays fully immersed and clear of boundaries. Raising or lowering it changes the absolute pressure, but neither its displaced volume nor the difference between the vertical pressure forces. There is therefore no vertical restoring force toward a preferred depth in this model. Neutral buoyancy is a vertical force balance, not a claim about resistance to tilting or about a compressible body whose volume changes with pressure.
