Floating and buoyancy.

Step 1 of 10

Density

Drop a cork, a pebble and an ice cube into water. The cork bobs high, the ice floats low with most of it under water, and the pebble goes straight to the bottom. The Scene has a tank of water with one cube in it, and you can change the Cube density, the Cube size and the Liquid.

Density is the mass in each unit of volume: $\rho = \dfrac{m}{V}$⁠. Water has 1000 kg/m³, cork about a quarter of that, pine about half, and steel nearly eight times as much.

Step 2 of 10

Archimedes’ principle

Every body in a liquid is pushed upward. The liquid presses harder the deeper you go, so the push on the body’s underside is stronger than the push on its top. The difference is an upward force, the buoyant force. Archimedes found how big it is:

$F_b = \rho_{\text{liquid}} \, g \, V_{\text{under}}$$F_b =$$\rho_{\text{liquid}} \, g \, V_{\text{under}}$⁠

The buoyancy equals the weight of the liquid pushed aside, the liquid that was in the body’s sunken volume. Show the forces is Off, and the cube, the liquid and the size are fixed.

Step 3 of 10

What share is under

Show the forces is On now: the blue arrow is the buoyancy, and the orange one the weight. The blue block marks the volume the cube took from the water, and the blue layer how far the water rose. Both hold the same volume.

A cube less dense than the liquid sinks in only until the liquid pushed aside weighs as much as it does. Then the forces balance and it floats. The share of its height below the surface is:

$\frac{V_{\text{under}}}{V} = \frac{\rho_{\text{obj}}}{\rho_{\text{liquid}}}$$\frac{V_{\text{under}}}{V} =$$\frac{\rho_{\text{obj}}}{\rho_{\text{liquid}}}$⁠

Here it is Ice in Sea water, which is a little denser than fresh water because of its salt.

Step 4 of 10

A bigger cube

Now it is Pine in Fresh water, and the Cube size is free.

Try it: after predicting, choose Cooking oil under Liquid, and watch the cube sink in deeper.

Back to the experiment ↑

Step 5 of 10

A cube that has sunk

A cube denser than the liquid can never push aside enough liquid to balance its weight, even fully under. It sinks, and the floor makes up the rest. Here it is a Steel cube with 8 cm sides, and all three are fixed.

Step 6 of 10

Steel that floats

A steel ship floats because it is not a solid lump of steel but a hollow shell full of air, so the ship as a whole is less dense than water. A submarine dives and surfaces by flooding tanks with water or blowing them full of air. But you can make a solid lump of steel float too.

Step 7 of 10

Weighing with water

A floating body pushes aside exactly its own weight of liquid. So it can be weighed without scales: it is enough to know how much of it is under the surface.

Step 8 of 10

Pine in oil

Oil floats on water because it is less dense: 920 kg/m³. Now the cube floats in Cooking oil.

Step 9 of 10

The level rises

The water the cube pushes aside does not vanish: it raises the level across the whole tank. Under Show the forces the blue layer at the top is the water that rose.

Step 10 of 10

Which liquid?

The same ratio works backwards. Knowing how dense the body is and how much of it is under, you can find how dense the liquid is. That is how a hydrometer works: a weighted glass tube that floats in the liquid.