What if water were denser?

Drop a stone in water. Plop! It sinks.

A leaf stays on top. What if the water were much heavier? Would the stone float too?

Some things float and some things sink. A rubber duck bobs on top of the bath, but a marble drops to the bottom. Whether something floats depends on the thing and on the liquid it is in.

So what if water itself were heavier for its size, or denser? Would things that sink today start to float? In this lab you can make a pretend liquid twice as dense as water and drop a block in.

Archimedes' principle says that any object in a fluid feels an upward buoyant force equal to the weight of the fluid it displaces. Whether it floats depends on comparing its average density with the fluid's.

This lab holds the object fixed and changes the fluid. A block slightly denser than water sinks in it. What happens if the fluid's density doubles to 2,000 kg/m³, a pretend value the model labels imaginary?

Water pushes up on things in it. You can feel it in the bath.

If a thing is too heavy for its size, the push is not enough. It sinks.

Water has a density of about 1 gram for every milliliter. Our lab block is a little denser than that: 1.2 grams per milliliter. It measures 1 meter by half a meter by 40 centimeters and has a mass of 240 kilograms.

In fresh water the block sinks. Water still pushes up on it, but the push is only as big as the weight of the water the block moves aside, which is less than the block's own weight. So down it goes.

The block's volume is 0.2 m³, so at 1,200 kg/m³ its mass is 240 kg and its weight 2,354 N. Fully submerged in fresh water at 1,000 kg/m³, it displaces 200 kg of water, giving a buoyant force of 1,962 N.

The buoyant force supports about 83 percent of its weight, so a net 392 N pulls it down. An object floats only if its average density is less than the fluid's, so this block cannot float in water.

In our pretend lab, Olly makes the water twice as heavy.

Now the block floats! Part of it sticks up above the top.

Choose 'Twice as dense (imaginary)'. Now every bucketful of liquid weighs twice as much, so the same block pushes aside heavier liquid and gets a bigger push up.

In the model the block floats, with 60 percent of it below the surface and 16 centimeters sticking out. It could even carry another 160 kilograms before going under. This liquid is pretend: the lab invents it so we can see what the rule of floating says.

With ρ_liquid = 2,000 kg/m³ the block's full volume could displace 400 kg, more than its 240 kg mass, so it floats. It settles at the draft d = m/(ρ_liquid·L·W) = 240/(2,000 × 0.5) = 0.24 m, 60 percent submerged, with 0.16 m of freeboard and room for 160 kg of cargo.

The model's 2,000 kg/m³ setting is labeled imaginary. The model treats the block as a level box that never tips, so it shows the balance of forces, not how a real object would settle.

The water pushes up as hard as the water moved out of the way weighs.

Heavier water gives a bigger push. A big push holds things up.

When something goes into a liquid, it pushes some of the liquid out of the way. The liquid pushes back up with a force equal to the weight of the liquid that was moved. This is called Archimedes' principle.

In a denser liquid, the same amount pushed aside weighs more, so the push up is stronger. The block only needs to go part of the way under before the push matches its weight. That is why it floats.

Pressure in a fluid increases with depth, so the upward pressure on an object's base exceeds the downward pressure on its top; the net force is ρ_fluid·g·V_displaced. A floating body sinks until that force equals its weight, so the fraction submerged equals ρ_object/ρ_fluid. For the block that is 1,200/2,000 = 0.60.

The model's limits: a straight-sided box that stays level, cargo that adds mass but no volume, and a damped settling motion chosen to look reasonable rather than measured.

Ice floats on water because ice is lighter for its size.

People can float in a pool too, most of all with full lungs. Most of the body stays under the water.

Real water's density changes a little with temperature and with what is dissolved in it. Ice is less dense than liquid water, which is why ice cubes float in a glass, and almost all of an iceberg sits below the waterline.

People float too. In a physics textbook example, a person with full lungs floats with 97 percent of her body under fresh water. In a liquid twice as dense, the same rule says only about half would be under.

USGS gives water's density as very close to 1 g/cm³ (0.99987 at 0 °C, 1.00000 at 4 °C), changing with temperature and dissolved substances; ice is less dense, so it floats with most of its volume submerged.

OpenStax's worked example has a 60 kg person floating 97 percent submerged in fresh water, giving an average density of about 970 kg/m³. Applying the fraction-submerged relation to a 2,000 kg/m³ fluid gives 970/2,000 ≈ 49 percent submerged. That is our own calculation for a pretend fluid, not a measurement.