Floating, Sinking, and Fraction Submerged

A steel bolt sinks because solid steel, shape and all, can never displace enough water to weigh as much as the bolt itself — steel is denser than water, so even fully submerged the buoyant force can't catch up to gravity. A steel ship floats because its shape traps a huge volume of air inside the hull. The ship's total weight, spread over that much greater volume, gives it a much lower average density than solid steel. Floating is about the average density of the whole object compared to the fluid, not the material alone.

For anything floating at rest, buoyant force equals weight, no exceptions. Buoyant force is the weight of fluid displaced: rho_fluid times g times the submerged volume. Setting that equal to the object's weight, rho_object times g times its total volume, the g's and volumes cancel down to one clean rule: fraction submerged = rho_object / rho_fluid. Low density relative to the fluid means only a sliver goes under; density close to the fluid's means it rides almost fully submerged, just barely afloat.

This sits right next to Archimedes' principle and connects forward to fluids in motion: both rest on the same idea that a fluid pushes back on anything that displaces it. Moving a floating block from fresh water (1000 kg/m³) to salt water (1025 kg/m³) doesn't change the block's weight or density, but it changes the fluid density in that ratio. Denser fluid means less volume needs to be submerged to displace the same weight, so the block rises slightly and floats higher in salt water.