1.2.9Tools and Inquiry — IB Physics skills
Stoke’s Law — IB Physics SL Revision Notes & Topical Questions
5 min read 5 parts Lesson 27 of 33 Unit 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.
Part 1 of 5Viscous Drag
A body moving through a fluid experiences a resistive force that depends on the speed and on the fluid.
Stokes' law
- Stokes' law For a small sphere moving slowly through a fluid, the drag force is F = 6πηrv.
Variables
- Variables η is the viscosity of the fluid, r is the radius of the sphere and v is its speed relative to the fluid.
Conditions
- Conditions The law holds for smooth spheres at low speed, where the flow is laminar and not turbulent.
Dependence
- Dependence The drag is proportional to the speed, so it grows as the sphere speeds up.
Part 2 of 5Reaching Terminal Velocity
A sphere released in a viscous liquid accelerates until the forces on it balance.
1
At the instant of release the speed is zero, so there is no drag and the sphere accelerates under its weight.
2
As the speed rises, the drag force grows and the upthrust from the fluid also acts upwards.
3
The resultant downward force falls, so the acceleration decreases though the speed is still increasing.
4
When weight equals the sum of drag and upthrust the resultant force is zero and the acceleration is zero.
5
The sphere then moves at constant terminal velocity, found from mg = 6πηrv + upthrust.
Part 3 of 5Using the Idea
Using the Idea
Viscosity
- Viscosity Viscosity measures how strongly a fluid resists flow, and for liquids it generally falls as temperature increases.
Upthrust
- Upthrust Equal to the weight of fluid displaced, it reduces the net downward force on the sphere.
Measuring viscosity
- Measuring viscosity Timing a ball bearing falling through a liquid gives the terminal velocity, and hence η.
Terminal speed formula
- Terminal speed formula Combining the forces gives v = 2r²(ρs − ρf)g / 9η for a sphere of density ρs in fluid of density ρf.
| Change | Effect on terminal velocity |
|---|---|
| Larger radius | Increases, since v ∝ r² |
| More viscous fluid | Decreases |
| Denser sphere | Increases |
Part 4 of 5Worked Example
Question
- A steel ball of radius 1.0 mm (density 7800 kg m⁻³) falls through glycerol of density 1260 kg m⁻³ and viscosity 1.4 Pa s.
- Calculate its terminal velocity using v = 2r²(ρs − ρf)g / 9η.
- Density difference = 7800 − 1260 = 6540 kg m⁻³.
- Numerator = 2 × (1.0 × 10⁻³)² × 6540 × 9.81 = 0.128 (approximately).
- Denominator = 9 × 1.4 = 12.6.
- v = 0.128 / 12.6 = 1.0 × 10⁻² m s⁻¹.
Answer Terminal velocity ≈ 1.0 × 10⁻² m s⁻¹, about 1 cm per second.
Part 5 of 5Exam Checklist & Tips
1.2.9 – Key Points for the Exam
- Viscosity A measure of a fluid's resistance to flow, in Pa s.
- Terminal velocity The constant velocity reached when drag and upthrust balance the weight.
- Drag force The resistive force opposing motion through a fluid.
- Laminar flow Smooth flow in which layers of fluid slide past each other without mixing.
Common Mistakes
- Applying Stokes' law to large, fast objects where the flow is turbulent.
- Forgetting that upthrust acts as well as drag in the terminal velocity balance.
- Using the diameter instead of the radius in the formula.
- Stating that the sphere stops accelerating because the forces have vanished, rather than because they balance.
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