The big idea: Push a beach ball underwater and it fights back, shoving upward — the deeper you push, the harder it shoves.
That upward push is buoyancy (or upthrust). To fit in, the ball has to shove water out of the way. Archimedes' principle: weigh the water it shoved aside, and that is exactly how big the upthrust is.
Floats
- Buoyancy ≥ weight
- Object is less dense than the fluid
- e.g. a cork on water
Sinks
- Buoyancy < weight
- Object is more dense than the fluid
- e.g. a steel ball in water
Spot it: Buoyancy depends on the fluid's density and the volume pushed aside — not on the object's own density or what it is made of.
More of the object underwater → more fluid pushed aside → bigger upthrust.
Same ball, same tank — only how far in it goes changes.
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Archimedes' principle in symbols: the upthrust equals the weight of fluid displaced, which is the fluid's density × the volume pushed aside × g.
- buoyancy (upthrust) force (N)
- density of the fluid (kg m⁻³)
- volume of fluid pushed aside (m³)
- gravitational field strength (9.8 N kg⁻¹)
Two things to get right: 1. Use the fluid's density for ρ — not the object's.
2. V is only the submerged volume (the part actually under the surface), not always the whole object.
You also need density = mass ÷ volume to swap between an object's mass and its size. It's a simple quotient, so use a formula triangle:
- density (kg m⁻³)
- mass (kg)
- volume (m³)
m = mass, ρ = density, V = volume. Cover the one you want: two side by side → multiply; one above the other → divide.
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Two forces on an object in a fluid: weight (mg) pulls down, buoyancy (Fb) pushes up. Floating ⇒ they balance.
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A metal sphere of volume 2.0 × 10⁻³ m³ is held fully underwater. Water has density 1.0 × 10³ kg m⁻³ and g = 9.8 N kg⁻¹. Find the buoyancy force on it.
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How this is tested — buoyancy almost always comes paired with a force balance. Two flavours:
Paper 1A
- Compare the upthrust on two objects in the same fluid (Fb ∝ V).
- Does it float or sink?
Paper 2
- 'Show that' on floating objects — set buoyancy = weight.
- Find a submerged fraction, a mass, or a density.
The classic trap: Using the object's density for ρ instead of the fluid's — or using the whole volume when only part is submerged.
The floating rule: A floating object is in equilibrium: the upward buoyancy exactly balances its weight.
Fb = weight, so ρfluid × Vsubmerged × g = ρobject × Vtotal × g.
Cancel g from both sides → the fraction submerged equals the density ratio ρobject ÷ ρfluid.
A wooden block floats in water. The wood has density 6.0 × 10² kg m⁻³; water 1.0 × 10³ kg m⁻³. Show that the fraction of the block below the surface is 0.60.
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