Grade by Grade
C. Matter and Energy · Fluids

Buoyancy: Will It Float?

C2.5 C2.2 A1.2 A1.3About 50 minutes
Learning goals
  • I can explain buoyant force and Archimedes' principle.
  • I can use density to predict whether an object will float, sink or hover in different fluids.
  • I can calculate what fraction of a floating object is under the surface.
  • I can explain how ships, submarines and balloons control their buoyancy.

Words to know

buoyancy
The ability of an object to float in a fluid.
buoyant force
The upward push a fluid gives to an object in it.
Archimedes' principle
The buoyant force on an object equals the weight of the fluid the object pushes aside (displaces).
positive buoyancy
When an object is less dense than the fluid, so it floats up.
neutral buoyancy
When an object has the same average density as the fluid, so it hovers without rising or sinking.
negative buoyancy
When an object is denser than the fluid, so it sinks.
average density
The total mass of an object divided by its total volume, including any air spaces inside it.

Remember from Grade 2

In Grade 2 you sorted objects into floaters and sinkers, and found that shape matters, not just size. In Grade 6 you learned that a hot-air balloon rises because the cooler air around it gives it an upward push. Now you have the tool that ties it all together: density.

A steel ship floats. A steel nail sinks. How?

A giant lake freighter on the Great Lakes is made of steel and can carry thousands of tonnes of iron ore. A steel nail dropped off the dock sinks straight to the bottom. Same material, opposite results. Let's find out why.

A very long freighter ship with a dark red steel hull sailing on a blue lake.
A Great Lakes freighter is made of steel, yet it floats. Its hull holds a huge volume of air, so the ship as a whole is less dense than water. AI-generated image

Buoyant force

Whenever an object is in a fluid, the fluid pushes up on it. This upward push is the buoyant force. At the same time, gravity pulls the object down (its weight).

  • If the buoyant force can match the weight, the object floats.
  • If the weight is bigger than the biggest buoyant force the fluid can give, the object sinks.

Archimedes' principle: the buoyant force on an object equals the weight of the fluid it displaces (pushes aside). An object that is completely under water pushes aside its whole volume of water. A floating object sinks just far enough to push aside its own mass of water.

blockbuoyant force (up)weight (down)
A floating block. The fluid's buoyant force pushes up, and the block's weight pulls down. When the block floats, the two forces are balanced. The arrows show the two forces acting on the block.

Use density to predict buoyancy

Compare the average density of the object with the density of the fluid:

  • Object less dense than the fluid → floats (positive buoyancy).
  • Object the same density as the fluid → hovers (neutral buoyancy).
  • Object denser than the fluid → sinks (negative buoyancy).

The fluid matters too. The same object can sink in one fluid and float in another.

How much of a floating object is under the surface? Divide: object's density ÷ fluid's density. A block of density 0.75 g/cm³ in water (1.00) floats with 0.75 ÷ 1.00 = 0.75, or 75%, of its volume under the surface.

FluidApproximate density (g/mL)
helium0.00018
air0.0012
cooking oil0.92
fresh water1.00
sea water1.03
maple syrup1.33
Densities of some fluids at room temperature.
Worked example

Let's predict buoyancy in different fluids

A plastic toy has a density of 0.95 g/cm³. Will it float, sink or hover in (a) fresh water, (b) cooking oil, (c) maple syrup? In fresh water, what percent of it is under the surface?

  1. Step 1. Compare with fresh water (1.00). 0.95 < 1.00, so it floats.
  2. Step 2. Compare with cooking oil (0.92). 0.95 > 0.92, so it sinks.
  3. Step 3. Compare with maple syrup (1.33). 0.95 < 1.33, so it floats.
  4. Step 4. Fraction under water. 0.95 ÷ 1.00 = 0.95, so 95% of the toy is under the surface. It floats very low.

(a) Floats in fresh water, with about 95% under the surface. (b) Sinks in cooking oil. (c) Floats in maple syrup (it would float high, with only about 0.95 ÷ 1.33 ≈ 71% under).

The same toy (density 0.95 g/cm³) in three fluidstoycooking oil (0.92 g/mL)sinkstoyfresh water (1.00 g/mL)floats, 95% undertoymaple syrup (1.33 g/mL)floats, about 71% under
Compare densities: the toy is denser than oil, so it sinks; it is a little less dense than water, so it floats low; it is much less dense than syrup, so it floats high.

Steel ships, submarines and balloons

  • Ships: a ship's steel hull is shaped like a huge bowl full of air. The ship's average density (steel + air + cargo, divided by the total volume) is less than water's, so it floats. A solid lump of the same steel would sink. Load more cargo, and the ship sinks lower, until it displaces enough extra water to hold up the extra weight. That's why ships have load lines painted on the hull showing the safe depth.
  • Fresh water vs sea water: sea water is denser, so a ship floats a little higher in the ocean than in the fresh water of the Great Lakes.
  • Submarines: they have ballast tanks. Letting water in raises their average density, so they sink. Pushing water out with compressed air lowers it, so they rise. Balancing the two gives neutral buoyancy.
  • Fish: many fish have a swim bladder, a gas-filled sac they can adjust to hover at a chosen depth.
  • Balloons: air is a fluid too. A helium balloon floats because helium is far less dense than air.
Float like a cork

The water of the Dead Sea is so salty that its density is about 1.24 g/mL. That's denser than a person's average density, so swimmers float high without even trying. People famously lie back and read a newspaper on the surface!

Hands-on activity

Foil-boat challenge and the floating egg

Part 1: foil boats (engineering design). You need: aluminium foil (a 20 cm × 20 cm square for each boat), a sink or large bowl of water, and many identical small masses such as nickels or metal washers.

  1. Design: sketch two different boat shapes (for example a flat raft with low sides, and a deeper box).
  2. Build each boat from one square of foil.
  3. Test: float the boat and add nickels one at a time, spreading them out, until it sinks. Record the number.
  4. Improve: change one thing and test again.
  5. Explain using average density and displaced water: why did the winning shape hold more?

What to look for: boats with bigger volume (wide base, taller sides) can push aside more water before it pours in, so they hold more coins. A crumpled foil ball sinks or floats low because it holds little air.

Part 2: the floating egg. You need: a raw egg, a tall glass of water, salt, a spoon.

  1. Gently put the egg in plain tap water. It usually sinks: it is denser than fresh water.
  2. Take the egg out. Stir in salt one spoonful at a time until no more dissolves easily.
  3. Put the egg back in. Keep adding salt and stirring if needed until it floats.
  4. Explain: dissolving salt increased the water's density until it was greater than the egg's.

Safety: wash your hands after touching a raw egg. Handle the egg gently; a cracked egg goes in the garbage, not back in the fridge. Keep coins and washers away from small children. Mop up spills.

Your turn

1

What is buoyant force?

2

An object with a density of 0.6 g/cm³ is put in fresh water. Will it float, sink or hover?

3

An object has a density of 1.2 g/cm³. Predict what it does in fresh water, cooking oil and maple syrup.

4

What does neutral buoyancy mean?

5

A 250 g toy boat floats in a bathtub. How much water does it displace (in g and in mL)?

6

Why does a steel ship float even though steel is about 8 times as dense as water?

7

State Archimedes' principle in your own words.

More practice: warm-up

1

An object is denser than the fluid it's in. Does it float or sink?

2

A block with density 0.5 g/cm³ is placed in water. Float or sink?

3

Which force pushes up on a floating object?

4

Which is denser: sea water or fresh water?

5

Why does a helium balloon rise?

More practice: on your own

1

A block of wood has a density of 0.75 g/cm³. What percent of it is under the surface in fresh water?

2

The same wood block floats in sea water (1.03 g/mL). Is more or less of it under the surface than in fresh water? Calculate.

3

An egg has a density of about 1.03 g/cm³. Explain why it sinks in tap water but floats in very salty water with a density of 1.10 g/mL.

4

A ship sails from the Atlantic Ocean up the St. Lawrence River into fresh water. Does it sit higher or lower in the water? Why?

5

How does a submarine sink and then rise again?

Challenge

1

A bead with a density of 0.95 g/cm³ is dropped into a jar with cooking oil (0.92) floating on top of water (1.00). Where does the bead end up? Explain.

2

A foil boat has a mass of 5 g. It can push aside at most 150 mL of water before water spills in. Canadian nickels have a mass of 3.95 g each. What is the most nickels it can hold? Show your work.

3

People say "that's just the tip of the iceberg." Ice is about 0.92 g/cm³ and sea water about 1.03 g/mL. What percent of an iceberg is under the surface? Why does this matter for ships?

Check your understanding

Quiz

1.

Archimedes' principle says the buoyant force equals...

2.

An object with a density of 1.10 g/cm³ is placed in fresh water (1.00 g/mL). It will...

3.

The same object (1.10 g/cm³) is placed in maple syrup (1.33 g/mL). It will...

4.

An object hovers in water without rising or sinking. Its density is...

5.

A steel ship floats because...

6.

A floating object has a density of 0.80 g/cm³. What fraction of it is under the surface of fresh water?

For parents and teachers

Big idea (C2.5): an object's buoyancy in a fluid depends on comparing its (average) density with the fluid's density: less dense floats, equal hovers, denser sinks. The same object can float in one fluid and sink in another. Archimedes' principle explains the upward buoyant force. The foil-boat challenge uses the engineering design process (A1.3) and the egg test is an experiment (A1.2).

How to help: at bath time or in the kitchen sink, ask your child to predict before testing: a carrot, an apple, a lemon, an ice cube. Talk about lifejackets: they add lots of volume with little mass, lowering a swimmer's average density.

Common difficulties:

  • Thinking heavy things always sink. Huge ships float; tiny pebbles sink. It's density, not mass.
  • Forgetting the fluid matters. Always compare with the density of the fluid, not always water.
  • Dividing the wrong way when finding the fraction under the surface: it's object ÷ fluid.

Safety: you supervise water play near the sink. Wash hands after touching raw egg. Keep coins and washers away from young children.