UPTHRUST is the upward force on an object submerged in a fluid.
CAUSE:
Pressure increases with depth: P = hρg.
Pressure on the BOTTOM of a submerged object > pressure on the TOP.
Net upward force = pressure difference × cross-sectional area = UPTHRUST.
ARCHIMEDES' PRINCIPLE:
Upthrust = weight of fluid displaced by the object.
Upthrust = ρ_fluid × V_displaced × g
where V_displaced = volume of the object submerged in the fluid.
FLOATING CONDITION:
Object floats when upthrust = weight.
The object sinks until it has displaced enough fluid for the upthrust to equal its weight.
A denser object displaces less volume before sinking — if density > fluid, it fully submerges and still sinks (upthrust < weight).
Applying Archimedes' Principle
WORKED EXAMPLE:
A wooden block of volume 0.01 m³ and density 600 kg/m³ floats in water (ρ = 1000 kg/m³).
Weight of block = 600 × 0.01 × 10 = 60 N.
For floating: upthrust = 60 N.
Volume of water displaced: 60 = 1000 × V × 10 → V = 0.006 m³.
So 60% of the block is submerged (6/10 of its volume).
FLOATING vs SINKING:
Density of object < fluid density → floats (some volume above fluid surface).
Density of object = fluid density → neutrally buoyant (hovers at any depth).
Density of object > fluid density → sinks (upthrust < weight at full submersion).
WHY SHIPS FLOAT:
A steel ship is hollow — effective density of hull + air < water density.
Large volume displaced → large upthrust = ship's weight.
If flooded: air replaced by water → density increases → sinks.
Calculating Upthrust
UPTHRUST EQUATION:
Upthrust = ρ_fluid × V_submerged × g
For a fully submerged object: V_submerged = V_object.
For a floating object: V_submerged < V_object (only partially submerged).
FINDING DENSITY OF AN OBJECT:
1. Weigh in air: W = mg.
2. Weigh fully submerged in water: W_apparent < W (upthrust reduces apparent weight).
3. Upthrust = W − W_apparent.
4. Volume of object = upthrust ÷ (ρ_water × g).
5. Density of object = mass ÷ volume.
SUBMARINES:
Control buoyancy by adjusting ballast tanks.
Fill tanks with water → increase density → sink.
Blow out water with compressed air → decrease density → rise.
At neutral buoyancy: density = seawater density.
⚠️ Common Mistake
Upthrust = weight of DISPLACED FLUID — not the weight of the object. A 100 N steel block submerged in water experiences upthrust equal to the weight of water it displaces, which is much less than 100 N (since steel is denser than water). This is why it sinks — upthrust < weight.
📐 Variables
UUpthrust (U) is measured in newtons (N)
ρDensity of fluid (ρ) is measured in kg/m³ (kg/m³)
VVolume submerged (V) is measured in m³ (m³)
gGravitational field strength (g) is measured in N/kg (N/kg)
📐 Key Equations
Upthrust = ρ_fluid × V_submerged × g
📌 Key Note
Upthrust = ρ_fluid × V_submerged × g = weight of fluid displaced (Archimedes). Float when upthrust = weight → density_object < density_fluid. Sink when density_object > density_fluid. Ship: hollow hull displaces large volume. Submarine: ballast tanks adjust density.
🎯 Matching Activity — Upthrust and Floating
Match each scenario to the correct upthrust or floating explanation. — drag the symbols on the right to match the component names on the left.
Object with density < water
Drop here
Object with density > water
Drop here
Upthrust calculation
Drop here
Submarine rising
Drop here
Ballast tanks emptied of water — effective density decreases below seawater
Sinks — even fully submerged, upthrust < weight
Floats — partially submerged until upthrust equals weight
ρ_fluid × V_submerged × g = weight of fluid displaced
⚽ FIFA Worked Examples
Upthrust Calculation
A block of volume 0.005 m³ is fully submerged in water (ρ = 1000 kg/m³, g = 10 N/kg). Calculate the upthrust.
F
Upthrust = ρ_fluid × V_submerged × g
I
ρ = 1000 kg/m³, V = 0.005 m³, g = 10 N/kg
F
Upthrust = 1000 × 0.005 × 10 = 50
A
Upthrust = 50 N
⭐ Higher Tier Only
HT only — calculate upthrust using Archimedes' principle. Determine whether objects float or sink by comparing upthrust with weight. Calculate the fraction of a floating object submerged.
🔬 Triple Science Only
Upthrust and floating in detail (HT only) — part of the physics-only pressure in fluids topic.
🎯 Test Yourself
Question 1 of 2
1. A 0.002 m³ object is fully submerged in water (ρ = 1000 kg/m³, g = 10 N/kg). Its weight is 30 N. What happens to it?
2. What fraction of a floating iceberg is below water? (Density of ice = 917 kg/m³, seawater = 1025 kg/m³)
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