Change the size: the same material always floats or sinks the same way. Then try the egg in tap water and in very salty water.
To find the density of an odd-shaped object, measure its mass on a balance and its volume by dropping it into water in a measuring cylinder: the water rises by the object’s volume (1 mL = 1 cm³). Then density = mass ÷ volume. Can you identify the mystery blocks?
Densities to compare: PVC 1.38 · glass 2.5 · aluminium 2.70 · iron/steel 7.87 · copper 8.96 · lead 11.34 · gold 19.3 g/cm³.
Pour liquids into the jar in any order: they sort themselves into layers, the densest at the bottom. Then drop in objects: each one sinks until it reaches a liquid denser than itself.
In a real jar pour slowly down the side. Water-based liquids (glycerol, washing-up liquid, milk, water) slowly mix if you stir them, and alcohol mixes with water, so the oil layer between them matters. Densities are typical values in g/cm³; honey varies (about 1.36–1.45), so a PVC bead may sink into some honeys.
Hang a 100 cm³ block from a spring scale and lower it into an overflow can filled to the spout. The scale reading drops, and the liquid pushed out runs into a beaker. Archimedes’ principle: the buoyant force equals the weight of the liquid pushed aside.
Steel is 7.85 times as dense as water, yet ships float: the hull is a thin shell of steel around a lot of air. Load cargo and watch the ship sink lower, until it is overloaded.
The buoyancy diagram you draw and label in a test: the forces on a floating object and Archimedes’ experiment with a newton meter and an overflow can. Switch between the labeled diagram, a blank one to test your memory, and a quiz where you place each label yourself. You can also download both versions or print a label worksheet.
Tap a word, then tap the numbered box it belongs to (on the diagram or in the list below). Tap a filled box to take the word back. On a phone, swipe the diagram sideways to see every number.
Tap a card, then tap the box it belongs in. Press Check when all 12 are placed.
A printable worksheet: label the buoyancy diagram, sort float and sink, calculate densities, multiple choice and explain questions, with an answer key.
Density tells you how much mass is packed into each cubic centimetre. 1 cm³ of water has a mass of about 1 g, so water’s density is about 1 g/cm³ (1,000 kg/m³). 1 cm³ of iron has a mass of about 7.9 g; 1 cm³ of cork only about 0.24 g. A big piece and a small piece of the same material have the same density.
Measure the mass with a balance. For a box shape, volume = length × width × height; for an odd shape, lower it into water in a measuring cylinder and see how much the level rises. Then divide mass by volume.
Water pressure grows with depth, so the water pushes harder on the bottom of an object than on its top. The difference is the upward buoyant force (upthrust). Archimedes found that it equals the weight of the liquid the object pushes aside. A floating object sinks just far enough to push aside its own weight of liquid.
A steel ship floats because its hull holds a lot of air, so its average density is less than water’s. About 9/10 of an iceberg is under the sea because ice (0.92 g/cm³) is only a little less dense than sea water (1.025 g/cm³). A submarine sinks or rises by filling its tanks with water or blowing them out with air.
Drop a small and a large piece of pine wood: both float with half under water. Then press Egg test and switch from fresh water to very salty water: the egg rises. Finally lower an iron block in the Archimedes experiment and compare the drop in the scale reading with the weight of the water pushed out.
| Material | Density (g/cm³) | In water it… | Material | Density (g/cm³) | In water it… |
|---|---|---|---|---|---|
| Air | 0.0012 | rises (bubbles) | Fresh water | 1.00 | — |
| Balsa wood | about 0.16 | floats | Sea water | 1.025 | — |
| Cork | about 0.24 | floats | Fresh egg | about 1.08 | sinks |
| Pine wood | about 0.5 | floats | Honey | about 1.42 | sinks |
| Alcohol (ethanol) | 0.79 | mixes with water | Glass | about 2.5 | sinks |
| Candle wax | about 0.90 | floats | Aluminium | 2.70 | sinks |
| Ice | 0.917 | floats | Iron | 7.87 | sinks |
| Vegetable oil | about 0.92 | floats | Mercury | 13.5 | sinks |
| Polyethylene (HDPE) | about 0.95 | floats | Gold | 19.3 | sinks |
| Quantity | Formula | Units |
|---|---|---|
| Density | ρ = m ÷ V | g/cm³ or kg/m³ (1 g/cm³ = 1,000 kg/m³) |
| Mass from density | m = ρ × V | g or kg |
| Weight | W = m × g (g ≈ 9.8 N/kg) | newtons (N) |
| Buoyant force (Archimedes) | FB = ρliquid × Vunder × g | newtons (N) |
| Floating: share under the surface | Vunder ÷ V = ρobject ÷ ρliquid | a fraction |
| Apparent weight in a liquid | W − FB | newtons (N) |
Worked example: a 100 cm³ aluminium block has a mass of 2.70 × 100 = 270 g and a weight of 0.270 kg × 9.8 N/kg ≈ 2.65 N. Fully under water it pushes aside 100 cm³ = 100 g of water, which weighs 0.98 N, so a spring scale reads 2.65 − 0.98 ≈ 1.67 N.
The buoyant force comes from pressure: in a liquid p = p0 + ρgh, so on a block of area A and height H the upward push on the bottom exceeds the downward push on the top by ρgAH = ρgV. This works for any shape, which is Archimedes’ principle. Gases give buoyancy too: hot-air balloons and helium balloons rise because they are less dense than the surrounding air. Most materials expand when heated, so their density falls; water is unusual, being densest at about 4 °C, which is why lakes freeze from the top down. A floating ship is stable when its centre of buoyancy can shift sideways to push it upright again (the metacentre lies above the centre of mass).
Density is the mass of each unit of volume of a material: density = mass ÷ volume. Water has a density of about 1 g/cm³ (1,000 kg/m³). A material with a higher density has more mass packed into the same space.
Key takeaway: mass ÷ volume.An object floats if its average density is less than the density of the liquid, and sinks if it is greater. A floating object sinks until it has pushed aside its own weight of liquid; then the buoyant force balances its weight.
Key takeaway: less dense than the liquid floats; denser sinks.It is the upward push of a liquid or gas on an object in it. It happens because pressure increases with depth, so the push on the bottom of the object is bigger than the push on its top.
Key takeaway: the upward push of a fluid, caused by pressure increasing with depth.Any object wholly or partly in a fluid feels an upward buoyant force equal to the weight of the fluid it pushes aside (displaces).
Key takeaway: buoyant force = weight of displaced fluid.Measure its mass with a balance. Put water in a measuring cylinder, read the level, lower the object in and read the new level: the difference is its volume (1 mL = 1 cm³). Divide the mass by the volume.
Key takeaway: balance for mass, water displacement for volume, then divide.A ship’s hull is a thin steel shell enclosing a lot of air, so its average density (steel plus air plus cargo, divided by the volume of the hull) is less than water’s. It settles until it has pushed aside its own weight of water.
Key takeaway: its average density is less than water’s.Sea water (about 1.025 g/cm³) is denser than fresh water, so you push aside less of it to equal your weight. In the very salty Dead Sea (about 1.24 g/cm³) people float with much of their body above the water.
Key takeaway: salt water is denser.When water freezes its molecules lock into an open crystal pattern, so ice (0.917 g/cm³) is less dense than liquid water. That is why ponds freeze from the top and about 9/10 of an iceberg is below the surface.
Key takeaway: ice is less dense than liquid water.No. A bigger piece has more mass but also more volume in the same proportion, so its density is the same. A floating block and a small piece of it float with the same fraction under the surface.
Key takeaway: no: density does not depend on size.It has ballast tanks. Letting sea water into the tanks raises its average density above the water’s and it sinks; blowing the water out with compressed air lowers its average density and it rises. Fish use a gas-filled swim bladder in a similar way.
Key takeaway: by changing its average density with ballast tanks.