Buoyancy and Archimedes' Principle: Floating, Sinking and Apparent Weight

A fluid pushes up on any object in it with a force equal to the weight of the fluid the object displaces. That is Archimedes' principle. The MCAT uses it to ask whether something floats, how much of it is submerged, and what a scale reads when it hangs underwater.

Core formulas

The volume that counts is the volume of fluid displaced, which is the submerged volume, not the whole object.

Float or sink

A floating object is in equilibrium, so F_B = W. That is why the submerged fraction equals the density ratio.

Worked example

A block of density 600 kg/m³ floats in water (1000 kg/m³).

• Submerged fraction = 600/1000 = 0.6, so 60% is below the surface.
• In a fluid of density 1200 kg/m³ the fraction is 600/1200 = 0.5.
• A 2 kg mass of density 4000 kg/m³ hung fully in water has V = 0.0005 m³, so F_B = 1000 x 0.0005 x 10 = 5 N. Its weight is 20 N, so the scale reads 15 N.

Common traps

• Using the object's density in F_B. Buoyant force uses the fluid density.
• Using the full volume for a floating object. Use the submerged part.
• Thinking heavier objects always sink. Only density matters, so a steel ship floats.
• Forgetting the object's own weight when finding apparent weight.

One-minute recap

F_B = ρ_fluidV_subg. Floats if the object is less dense than the fluid. Floating means F_B = W, so submerged fraction = density ratio. Apparent weight = W - F_B.