Theme A — Space, Time and Motion
A.2.10 Buoyancy — IB Physics HL Revision Notes & Topical Questions
5 min read 9 parts Lesson 21 of 63 1 quiz
Curriculum Equation Key قوانين الرقم الهيدروجيني والاتزان الأيوني - pH & Acid-Base Equilibrium FormulasFast Exam Solution
pH = -log[H⁺] | pOH = -log[OH⁻] | pH + pOH = 14 | [H⁺][OH⁻] = 10⁻¹⁴
Word Equation & Conditions: الرقم الهيدروجيني = -لوغاريتم تركيز أيون الهيدروجين | pH + pOH = 14
Location & Specifications: الاتزان الأيوني، كيمياء 3 ثانوي، التحصيلي، و AP Chemistry.
Lesson summary
A.2.10 Buoyancy — IB PHYSICS SL notes: Explain upthrust using pressure differences, apply Archimedes' principle and decide whether bodies float or sink.Buoyancy — a force experienced by a body that is partially or totally immersed in a fluid, due to the fluid it displaces.It keep…
- Pressure with depth
- Line of action
- Derivation
- Dependence
- Law of flotation
- Fraction submerged
Part 1 of 7Upthrust from fluid pressure
Buoyancy
- Buoyancy a force experienced by a body that is partially or totally immersed in a fluid, due to the fluid it displaces.
- It keeps boats afloat and lets balloons rise through air.
Pressure with depth
- Pressure with depth p = p0 + ρgh, where ρ is the fluid density and h the depth.
Origin
- Origin the pressure on the bottom surface exceeds that on the top, giving a net upward force called upthrust.
Line of action
- Line of action it acts vertically upwards through the centre of the displaced fluid, the centre of buoyancy.
Part 2 of 7Archimedes' principle
Principle
- Principle the upthrust on a body wholly or partly immersed in a fluid equals the weight of the fluid displaced.
Equation
- Fb = ρVg.
- ρ is the density of the fluid, not of the object.
- V is the volume of fluid displaced, in m3.
- g is the acceleration of free fall.
Derivation
- Derivation for a cuboid of base area A and height h, the pressure difference gives ρghA = ρgV.
Any fluid
- Any fluid it also holds in air, which explains why helium balloons rise.
Dependence
- Dependence upthrust depends on the immersed volume and fluid density, not on the material or mass of the object.
Part 3 of 7Floating and sinking
| Condition | Result |
|---|---|
| Object density greater than fluid density | The object sinks |
| Object density less than fluid density | It rises and floats with part above the surface |
| Equal densities | Neutral buoyancy at any depth |
Floating
- Floating the weight of the body equals the upthrust, mg = Fb.
Law of flotation
- Law of flotation a floating body displaces fluid equal to its own weight.
Fraction submerged
- ρobject/ρfluid; ice (917 kg m−3) in water (1000 kg m−3) is about 92% below the surface.
Ships
- Ships a hollow shape displaces a large volume, so the mean density is less than that of water.
Salt water
- Salt water it has a higher density than fresh water, so it gives more upthrust and a ship rides higher.
Part 4 of 7Apparent weight and measurement
Apparent weight
- Apparent weight for a submerged body hanging from a newton meter, Wapp = W − Fb.
Volume and density
- Volume and density the upthrust gives V = Fb/(ρfg), and then the density of the object.
Hydrometer
- Hydrometer it floats higher in denser liquids, so its scale reads the liquid density.
Submarine
- Submarine it changes its mean density by flooding or emptying ballast tanks.
Fish
- Fish it adjusts its swim bladder.
Part 5 of 7Buoyancy in motion
Free-body diagrams
- Free-body diagrams include upthrust for any submerged object.
Initial acceleration
- Initial acceleration on release in a liquid it is a = (mg − Fb)/m, positive downwards for dense objects.
Drag and terminal speed
- Drag and terminal speed drag appears as the object moves, and a terminal speed follows.
Bobbing
- Bobbing a floating object displaced slightly feels a restoring change in upthrust and oscillates.
Part 6 of 7Stability
Pressure rule
- Pressure rule the same p = p0 + ρgh explains why dams are thicker at the base and why the force on a submarine hatch grows with depth.
Stable floating body
- Stable floating body the weight and upthrust form a couple that rights it after a tilt.
Ballast
- Ballast ships carry heavy ballast low in the hull for stability.
Shifting cargo
- Shifting cargo it reduces the restoring effect and can cause capsizing.
Part 7 of 7More from the specification
More from the specification
Opposing hydrodynamic resistive forces
- Opposing hydrodynamic resistive forces a submerged body moving through viscous fluid experiences frictional drag acting in the opposite direction to motion.
Centripetal buoyancy forces in fluids
- Centripetal buoyancy forces in fluids fluids rotating in a horizontal circle experience pressure gradients that exert centripetal forces towards the central axis.
Balanced vertical forces in floating bodies
- Balanced vertical forces in floating bodies floating objects remain in static equilibrium because upward buoyant upthrust equals downward gravitational weight in magnitude.
Archimedes' buoyancy principle
- The buoyant force exerted upward on a submerged or floating body equals the weight of the fluid displaced by the body: Fb = rho * V * g.
Equilibrium of floating bodies
- A floating vessel reaches hydrostatic equilibrium when upward buoyant force exactly balances total downward gravitational weight.
Apparent weight in fluids
- An object weighed while submerged displays an apparent weight equal to its true weight in vacuum minus the upward buoyant force.
Archimedes' buoyancy principle
- The buoyant force exerted upward on a submerged or floating body equals the weight of the fluid displaced by the body: Fb = rho * V * g.
Equilibrium of floating bodies
- A floating vessel reaches hydrostatic equilibrium when upward buoyant force exactly balances total downward gravitational weight.
Apparent weight in fluids
- An object weighed while submerged displays an apparent weight equal to its true weight in vacuum minus the upward buoyant force.
Normal reaction
- The contact force perpendicular to a surface.
Reaction force
- Force from a support pushing up on an object.
Contact force
- Force requiring touching objects.
Radius
- Distance from the centre to the circular path.
Normal
- Line at 90° to a surface.
Tension
- Force transmitted along a string or rope.
Centripetal force
- Net force toward the centre, mv2/r.
Static friction
- Friction between surfaces at rest relative to each other; fs ≤ μsFN.
Circular motion
- Motion along a circular path with a force towards the centre.
Kinetic energy
- K = ½mv2, energy of motion.
Angular speed
- Magnitude of the angular velocity.
Momentum
- P = mv, a vector.
Velocity
- Rate of change of displacement.
Friction
- Force parallel to the surface opposing relative motion or its tendency.
Constant
- Not changing.
Collision
- Short interaction with large internal forces.
Linear
- A graph that is a straight line through the origin, so resistance is constant.
Impulse
- J = FΔt = Δp.What the symbols mean: F = force (N) · Δt = time the force acts (s) · Δp = change in momentum (kg m s−1); FΔt is the impulse (N s)
Key terms
| Term | Meaning |
|---|---|
| Buoyancy (upthrust) | Upward force on a body in a fluid caused by the pressure difference between bottom and top |
| Archimedes' principle | Upthrust equals the weight of the fluid displaced |
| Displaced fluid | Fluid pushed aside by the immersed part of a body |
| Neutral buoyancy | State in which an object's density equals the fluid density |
| Apparent weight | True weight minus the upthrust |
| Law of flotation | A floating body displaces fluid equal to its own weight |
Avoid these mistakes
1
Using the density of the object in Fb = ρVg — use the density of the fluid.
2
Using the volume of the whole object for a floating body — use only the volume submerged.
3
Thinking upthrust depends on the mass of the object — it depends on displaced fluid.
4
Believing heavy objects always sink — it is the average density that matters.
5
Leaving upthrust out of the free-body diagram of a submerged object — include it.
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