Physic Labs

Fluid mechanics

Archimedes’ principle

Measure the buoyant force as the liquid density and submerged volume vary. Verify FA=ρl g VF_A=\rho_l\,g\,V and the conditions for floating, sinking, or neutral buoyancy.

Middle school

Equipment

  • 3D model of an object immersed in a liquid tank
  • Sliders for liquid density ρ, submerged volume, and object mass
  • Virtual dynamometer and net-force readout

Procedure

  1. Vary the liquid density

    With submerged volume and mass fixed, drag «Liquid density ρ» from 700 to 1300 kg/m³. Read the buoyant force at several values; check that FAF_A grows linearly with ρ according to FA=ρl g VF_A=\rho_l\,g\,V.

  2. Vary the submerged volume

    Hold ρ = 1000 kg/m³, step «Submerged volume» up, and record the (V, F_A) pairs. The ratio FA/VF_A/V should equal ρlg≈104\rho_l g \approx 10^4 N/m³; while the object is only partly submerged, just the fraction inside the liquid counts.

  3. Find the float–hover–sink conditions

    Adjust «Object mass» until the weight P=mgP=mg balances the maximum buoyancy. The body floats when ρobj<ρl\rho_{obj}<\rho_l, hovers when equal, and sinks when ρobj>ρl\rho_{obj}>\rho_l; record the threshold mass and compare with the effective density m/Vm/V.

  4. Pose a prediction problem

    Pick ρ = 1300 kg/m³ (dense liquid) and any object mass; predict float or sink and the equilibrium depth before dragging «Submerged volume». Check the prediction, then explain why a steel ship floats although steel is denser than water — average density, not material density, decides.

Simulation

Experiment history

Archimedes of Syracuse (3rd century BCE) is bound to the crown anecdote: King Hiero II suspected his goldsmith of mixing in silver, and Archimedes — as Vitruvius retells — realized that displaced water gives a way to compare densities. In On Floating Bodies he stated the principle: a body immersed in a fluid is buoyed up by a force equal to the weight of the displaced fluid. The principle anchored hydrostatics and shipbuilding for two millennia; Stevin and Galileo later grounded it in the geometry of pressure, and today it follows directly from pressure increasing with depth, p=ρghp=\rho g h, in a gravitational field.

Related physicists

Archimedes of Syracuse

Related library topics

Archimedes’ principle