UPTHRUST is the upward force on an object submerged in a fluid.
CAUSE:
Pressure increases with depth: P = hฯg.
Pressure on the BOTTOM of a submerged object > pressure on the TOP.
Net upward force = pressure difference ร cross-sectional area = UPTHRUST.
ARCHIMEDES' PRINCIPLE:
Upthrust = weight of fluid displaced by the object.
Upthrust = ฯ_fluid ร V_displaced ร 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 โ if density > fluid, it fully submerges and still sinks (upthrust < weight).
Applying Archimedes' Principle
WORKED EXAMPLE:
A wooden block of volume 0.01 mยณ and density 600 kg/mยณ floats in water (ฯ = 1000 kg/mยณ).
Weight of block = 600 ร 0.01 ร 10 = 60 N.
For floating: upthrust = 60 N.
Volume of water displaced: 60 = 1000 ร V ร 10 โ V = 0.006 mยณ.
So 60% of the block is submerged (6/10 of its volume).
FLOATING vs SINKING:
Density of object < fluid density โ floats (some volume above fluid surface).
Density of object = fluid density โ neutrally buoyant (hovers at any depth).
Density of object > fluid density โ sinks (upthrust < weight at full submersion).
WHY SHIPS FLOAT:
A steel ship is hollow โ effective density of hull + air < water density.
Large volume displaced โ large upthrust = ship's weight.
If flooded: air replaced by water โ density increases โ sinks.
Calculating Upthrust
UPTHRUST EQUATION:
Upthrust = ฯ_fluid ร V_submerged ร 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 โ W_apparent.
4. Volume of object = upthrust รท (ฯ_water ร g).
5. Density of object = mass รท volume.
SUBMARINES:
Control buoyancy by adjusting ballast tanks.
Fill tanks with water โ increase density โ sink.
Blow out water with compressed air โ decrease density โ rise.
At neutral buoyancy: density = seawater density.
โ ๏ธ Common Mistake
Upthrust = weight of DISPLACED FLUID โ 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 โ upthrust < weight.
๐ Variables
UUpthrust (U) is measured in newtons (N)
ฯDensity of fluid (ฯ) is measured in kg/mยณ (kg/mยณ)
VVolume submerged (V) is measured in mยณ (mยณ)
gGravitational field strength (g) is measured in N/kg (N/kg)
๐ Key Equations
Upthrust = ฯ_fluid ร V_submerged ร g
๐ Key Note
Upthrust = ฯ_fluid ร V_submerged ร g = weight of fluid displaced (Archimedes). Float when upthrust = weight โ density_object < density_fluid. Sink when density_object > density_fluid. Ship: hollow hull displaces large volume. Submarine: ballast tanks adjust density.
๐ฏ Matching Activity โ Upthrust and Floating
Match each scenario to the correct upthrust or floating explanation. โ 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
ฯ_fluid ร V_submerged ร g = weight of fluid displaced
Floats โ partially submerged until upthrust equals weight
Ballast tanks emptied of water โ effective density decreases below seawater
Sinks โ even fully submerged, upthrust < weight
โฝ FIFA Worked Examples
Upthrust Calculation
A block of volume 0.005 mยณ is fully submerged in water (ฯ = 1000 kg/mยณ, g = 10 N/kg). Calculate the upthrust.
F
Upthrust = ฯ_fluid ร V_submerged ร g
I
ฯ = 1000 kg/mยณ, V = 0.005 mยณ, g = 10 N/kg
F
Upthrust = 1000 ร 0.005 ร 10 = 50
A
Upthrust = 50 N
โญ Higher Tier Only
HT only โ calculate upthrust using Archimedes' principle. Determine whether objects float or sink by comparing upthrust with weight. Calculate the fraction of a floating object submerged.
๐ฌ Triple Science Only
Upthrust and floating in detail (HT only) โ part of the physics-only pressure in fluids topic.
๐ฏ Test Yourself
Question 1 of 2
1. A 0.002 mยณ object is fully submerged in water (ฯ = 1000 kg/mยณ, 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/mยณ, seawater = 1025 kg/mยณ)
โญ How Well Do You Understand This Topic?
Be honest with yourself โ this helps you know what to revise!
Don't get itGetting thereNailed it!
๐ค Ask Mr Badmus AI
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I'll use FIFA for calculations and flag Higher/Triple content clearly.