Explain and calculate upthrust
Explain buoyant force as a result of pressure difference and calculate it from the displaced fluid's density and volume.
Section 4 · Forces, density and pressure
AS Level; Cambridge International Physics 9702, 2025–2027 syllabus, Topic 4. These original explanations and numerical practice support theory study; they do not demonstrate supervised practical competence. Full timed assessment and human subject-teacher review remain outstanding.
Before you begin
- Use SI units, resolve perpendicular components, and distinguish force from pressure.
Work on paper. Try each question before revealing help, and explain why your method works.
Quick readiness check
Which density appears in F = ρgV for upthrust?
What you will learn
- Explain upthrust using the pressure difference between lower and upper surfaces
- Use F = ρgV for displaced fluid
- Relate displaced volume and fluid density to buoyant force
A pressure difference creates an upward resultant force
Hydrostatic pressure increases with depth. For an immersed object, the fluid pressure on its lower surface is greater than on its upper surface. These pressure forces do not cancel, leaving a resultant upward force called upthrust.
Pressure also acts on the sides; for a simple vertical object those side forces balance horizontally. The vertical pressure difference explains why the fluid exerts an upward resultant on the object.
The displaced fluid determines the upthrust magnitude
Archimedes' principle gives upthrust F = ρgV, where ρ is the density of the fluid and V is the volume of fluid displaced. For a fully immersed object, this is the object's immersed volume; for a floating object, it is only the submerged volume.
Upthrust is a force and is measured in newtons. Whether an object rises, sinks or floats also depends on its weight and the other forces acting. At rest in a fluid, the vertical forces must balance.
Pause and explain
For a floating object, what volume is used in the upthrust equation?
Worked example
A block displaces 3.0 × 10⁻³ m³ of water. Take ρ = 1000 kg m⁻³ and g = 10 N kg⁻¹. Find the upthrust.
Show the worked solution
- Use the volume of water displaced, not the object's total volume if it is only partly immersed.
- F = ρgV = 1000 × 10 × 3.0 × 10⁻³.
- Report the upward force in newtons.
Answer 30 N upward.
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Test this topic →From guided practice to a new situation
Write your answer and reasoning first. Use a hint only if you are stuck. The model solution is for self-checking; your written work is not automatically marked.
An object displaces 0.0020 m³ of a liquid with density 900 kg m⁻³. Take g = 10 N kg⁻¹. Calculate the upthrust.
Give me a hint
Use the displaced volume and the surrounding liquid's density.
Compare my reasoning
- F = ρgV.
- F = 900 × 10 × 0.0020.
- Give the upward force in newtons.
18 N upward.
Look for these in your work
- Correct fluid density used
- Displaced volume used
- Force unit and direction stated
A fully immersed object displaces 5.0 × 10⁻⁴ m³ of water. Take ρ = 1000 kg m⁻³ and g = 9.8 N kg⁻¹. Find the upthrust.
Give me a hint
The whole volume is displaced only because the object is fully immersed.
Compare my reasoning
- F = ρgV.
- F = 1000 × 9.8 × 5.0 × 10⁻⁴.
- Report the result in newtons.
4.9 N upward.
Look for these in your work
- Fully immersed volume interpreted
- Substitution correct
- Force unit stated
A floating raft has weight 600 N. It displaces water of density 1000 kg m⁻³. Take g = 10 N kg⁻¹. Find the displaced volume while it is in vertical equilibrium.
Give me a hint
At rest, upthrust balances weight; then rearrange F = ρgV.
Compare my reasoning
- Upthrust = weight = 600 N.
- V = F/(ρg) = 600/(1000 × 10).
- Interpret this as displaced water volume.
V = 0.060 m³ of displaced water.
Look for these in your work
- Equilibrium force balance used
- Equation rearranged correctly
- Volume units and meaning stated
Common mistakes
- Using the object's full volume when only part is submerged
- Using the object's density instead of fluid density
- Confusing upthrust with the object's weight
What can you explain now?
Which density appears in F = ρgV for upthrust?
Compare with the explanation
The fluid's density
The displaced volume is a volume of fluid, so use that fluid's density.
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Make it stick
What physical pressure difference produces upthrust, and which volume enters its calculation?
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