How to play Weighed Under Water
- Choose a test and read the mass, the volume, or the readings in air and in water on the card.
- Under the liquid, the object pushes aside its own volume, and the liquid pushes up with the weight of that much liquid: F_b = ρ·g·V.
- The scale reads the weight minus that push: R = W − F_b. Type your prediction and press Start.
- Watch the cup: the liquid that spills out weighs exactly what the scale loses.
Why does a stone weigh less under water?
Water presses harder the deeper you go, so on anything under water the push from below is bigger than the push from above. The difference is an upward force, and Archimedes found how big it is: the weight of the liquid the object pushes aside, F_b = ρ·g·V. Hang a stone from a spring scale and lower it into a can full to the spout: the water it pushes out runs into a cup, and the scale loses exactly what that water weighs. That turns a spring scale into a measuring tool. What the scale loses gives the volume of any odd shape, V = F_b ÷ (ρ·g). The weight in air divided by what it loses tells you how many times denser than water the object is, which is how a goldsmith's crown can be tested without melting it. In a less dense liquid such as oil the same volume pushes up less, so the scale reads more. And only the part under the liquid counts, so a half-sunk object feels half the push.
A focused learning model
The object hangs from a spring scale and is lowered steadily for 2 s, from 3 cm above the surface to 2 cm past full submersion, or to the depth you type (never deeper than that). The can is full to its spout, so every cm³ that goes under pushes one cm³ out into the cup, and the surface stays at the spout. The push is F_b = ρ·g·V, where V is the part under the liquid, and the scale reads R = W − F_b. The object never touches the can. The object and the can are to scale; the cup is not. Answers within 2% are right. Water is 1000 kg/m³, oil 800 kg/m³; g = 9.8 m/s². Plays in real time.