FLOAT
Archimedes’ crown test: two weighings and the density has nowhere to hide.
Use the simulation above to change the variables and play through the guided stages. The explanation below describes the default starting values; the simulation updates its explanation as you experiment.
Setup
A block hangs from a scale above a tank of fluid. One question, older than physics itself: when it goes in, will the fluid carry it? The answer is already written in two densities.
Forces
In air the ledger is short: weight down, tension up, equal and opposite, and the scale reads the truth. The fluid hasn’t spoken yet — but every centimetre of descent is about to give it a vote.
Archimedes
The principle in one line: the fluid pushes up with the weight of the fluid the block displaced — F_b = ρ_f g V_sub. Divide the densities and the verdict falls out before the block is even wet: the submerged fraction is ρₒ/ρ_f.
Lower
Lower it in and watch the scale: the reading falls in a perfectly straight line as displaced volume grows. Either it reaches zero — the line goes slack, the block floats, experiment confirms prediction — or the bottom of the scale is never reached, and release means sinking.
Audit
Close the books with the oldest audit in science: weigh in air, weigh in water, and the two numbers surrender the density — ρₒ = ρ_f W/(W−T). Archimedes ran this exact check on a crown in 250 BC. The goldsmith did not pass.