Pressure in a fluid grows with depth, pushing harder on the deeper face of any submerged object. The result is a net upward push, the upthrust, equal to the weight of fluid displaced. Compare that upthrust with the object's weight and you know at once whether it floats or sinks.
Density is mass per unit volume, ρ = m / V. Pressure is force per unit area, p = F / A, in pascals. In a fluid, pressure increases with depth: Δp = ρgΔh. Because the deeper face of a submerged body is pushed harder than the upper face, there is a net upward force, the upthrust, equal to the weight of the displaced fluid: F = ρgV (Archimedes' principle).
Lower a 1 litre block into the liquid and change the two densities. The weight and the upthrust are drawn to the same scale: when the block floats they are equal, and the block sinks only far enough for that to happen. Find the rule for floating before you read it.
| Quantity | Relation | Note |
|---|---|---|
| density | ρ = m / V | unit kg m⁻³ |
| pressure | p = F / A | unit pascal, Pa = N m⁻² |
| hydrostatic pressure | Δp = ρgΔh | extra pressure due to depth h |
| upthrust | F = ρgV | weight of fluid displaced |
A body floats when its average density is less than the fluid's. It then floats with a fraction ρ_body / ρ_fluid of its volume submerged, just enough for the upthrust to equal its weight. If its density is greater, the maximum upthrust (fully submerged) is still less than its weight, so it sinks.
Four quick checks on density, pressure and upthrust. Each correct answer earns XP and lights this skill on your star map.
A block floats in a liquid. From the simulator, this happens when the block's density is:
The pressure at a point in a still liquid depends on:
The upthrust on a submerged object is equal to the:
Water has a density of 1000 kg m⁻³. The extra pressure at a depth of 2.0 m below the surface (g = 9.8 m s⁻²) is about:
Liquid pressure depends on depth and density only, never on the shape of the container or the area of its base; a narrow tube and a wide tank filled to the same depth have the same pressure at the bottom. When asked for the total pressure at a depth, add the atmospheric pressure: p = p_atmosphere + ρgΔh. And the upthrust uses the submerged volume and the fluid's density, not the object's.
Unlocks once the four checks above are done. Worth more XP, written to AS Paper 1 and 2 standard.
A block has a mass of 2.4 kg and a volume of 8.0 × 10⁻⁴ m³. Its density is:
A diver is 15 m below the surface of seawater of density 1030 kg m⁻³. Taking g = 9.8 m s⁻² and atmospheric pressure as 1.0 × 10⁵ Pa, the total pressure on the diver is closest to:
An object of volume 5.0 × 10⁻⁴ m³ is fully submerged in water of density 1000 kg m⁻³ (g = 9.8 m s⁻²). The upthrust on it is:
A wooden block of density 600 kg m⁻³ floats in water of density 1000 kg m⁻³. The fraction of its volume that is below the surface is:
This skill is now lit gold on your star map. You have finished the lessons of Topic 4; the Paper 1 set awaits.