How to play Barge Load
- Choose a float and read its size, its mass, and the water's density on the card.
- A floating body pushes aside its own mass of water: ρ·V = M. For a box, V = L × B × d, so d = M ÷ (ρ·L·B).
- Type your prediction and press Load. The crane lowers the float, or the cargo goes on, steadily.
- Watch the orange line on the hull: it shows the waterline your prediction gives, next to the real one.
Why do things float?
Water pushes up on anything in it. This buoyancy equals the weight of the water the object pushes aside: F_b = ρ·g·V, Archimedes' principle. A floating object sinks until that water weighs as much as the object itself, and then the forces balance. So a 24 t barge pushes aside 24 t of water, 24 m³ of fresh water, and floats as deep as that volume needs. Load it and it sinks deeper; once the water reaches the deck it can't push aside any more, and extra cargo floods it. Whether something floats depends on its average density, the whole mass over the whole volume. A steel boat is mostly air inside, so its average density is far below water's, even though steel is almost eight times denser. The water's density matters too: seawater is denser than river water, so a ship floats a little higher in the sea, and ice, 917 kg/m³, floats with about nine tenths below the surface.
A focused learning model
Every float is a box with a flat bottom and straight sides, so the volume under water is A·d, with A = L × B. The water is still and its density fixed, except that it changes steadily from 1025 to 1000 kg/m³ while the barge sails into the river. The load comes onto the water steadily for 2 s, slowly enough that the float always sits at d = M ÷ (ρ·A) without bobbing. If the draft reaches the deck height H, loading stops and the barge is drawn sinking for 1 s; within 0.05% of the deck still counts as afloat. A cargo is right if the barge floats with at most 2% to spare; every other prediction within 2%. g = 9.8 m/s². Plays in real time.