Upthrust and Floating | Physics

📖 In-Depth Theory

Upthrust from Pressure Difference

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

ρ_fluid × V_submerged × g = weight of fluid displaced

Floats — partially submerged until upthrust equals weight

Ballast tanks emptied of water — effective density decreases below seawater

Sinks — even fully submerged, upthrust < weight

⚽ 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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⚡ Upthrust and Floating

Upthrust from Pressure Difference

Applying Archimedes' Principle

Calculating Upthrust

Mr. Badmus AI