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Coefficient of Friction (Optional Extension)

Key idea: Optional extension on static and kinetic friction coefficients, limiting friction and the angle-of-repose model; coefficients are not required in H2 Physics 9478.

  • A-level H2 Physics topic extensions
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Learning objectives

  • Explore friction coefficients, variable-mass systems and the fundamental interactions beyond the H2 syllabus.

1. Definitions (Must Know)

Static vs kinetic friction

  • Static friction fₛ: friction when there is no sliding (can vary in size).
  • Kinetic friction fₖ: friction when the object is sliding (approximately constant in many models).

Coefficient of friction

For a simple model:

fₛ ≤ μₛ N

fₖ = μₖ N

where:

  • N is the normal contact force,
  • μₛ is the coefficient of static friction,
  • μₖ is the coefficient of kinetic friction (often smaller than μₛ).
Not required by syllabus 9478

The current H2 syllabus requires a qualitative understanding of friction and explicitly states that knowledge of coefficients of friction is not required. Use this lesson only after completing the core force and equilibrium route.

2. Key Ideas (What Earns Marks)

  • Static friction adjusts up to a maximum value.
  • At the point of slipping (“limiting equilibrium”), fₛ = μₛ N.
  • Kinetic friction is usually taken as fₖ = μₖ N.

3. Detailed Explanations

A. Incline method (angle of repose)

Increase the angle of an inclined plane until the block is just about to slip. At that point:

  • the friction is at its maximum static value
  • the system is in limiting equilibrium.

In the simplest model, you can show:

μₛ = tan θ_c

where θ_c is the critical angle at which slipping begins.

B. Static-to-kinetic friction model

If you pull a block with a spring balance / force gauge and slowly increase the pull:

  • while the block is still at rest, static friction adjusts to match the applied force (up to a maximum)
  • when the block starts moving, the friction often drops to a lower, roughly constant kinetic friction

Idealised static-to-kinetic friction model

Static friction matches the applied pull until a five-newton limiting value. Once sliding starts, kinetic friction is modelled as a lower constant value of four newtons.

Scroll across the graph to read all labels.

Static friction matches the applied pull until a five-newton limiting value. Once sliding starts, kinetic friction is modelled as a lower constant value of four newtons.Static friction matches the applied pull until a five-newton limiting value. Once sliding starts, kinetic friction is modelled as a lower constant value of four newtons.
This is a simplified extension model. Real friction depends on the materials and conditions and need not remain perfectly constant.
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View figure data
Values and uncertainty for Idealised static-to-kinetic friction model
SeriesApplied pull (N)Applied pull uncertaintyFriction magnitude (N)Friction magnitude uncertainty
Static friction00
Static friction11
Static friction22
Static friction33
Static friction44
Static friction55
Kinetic friction5.014
Kinetic friction64
Kinetic friction74
Kinetic friction84

4. Common Mistakes

  • Using f = μ N even when the friction is not at its maximum.
  • Confusing μₛ and μₖ (static is usually larger).
  • Treating μ as a required 9478 formula instead of optional modelling.

6. Worked Examples

Modelled example 1

Angle of repose

Core

Problem

A block begins to slide when a plane reaches 24.0° to the horizontal. Under the simple limiting-friction model, estimate μₛ.
Study the worked solution

  1. Use limiting equilibrium

    Method

    At impending motion, friction has reached fₛ = μₛN.

    Reason

    The block is at the threshold of sliding rather than at an arbitrary static state.

    Working

    mg sin θ = μₛN

  2. Resolve perpendicular to the plane

    Method

    N = mg cos θ.

    Reason

    There is no acceleration normal to the surface.

    Working

    N-mg cos θ = 0

  3. Eliminate mass and calculate

    Method

    μₛ = 0.445.

    Reason

    Dividing the parallel equation by the perpendicular equation gives the angle-of-repose relation.

    Working

    μₛ = (mg sin θ)/(mg cos θ) = tan 24.0° = 0.445

7. Mind Stretchers

Mind stretcher 1: Static friction below its limiting valueExtension

A horizontal pull of 6.0 N acts on a block that remains at rest. Its maximum possible static friction is 10 N. State the actual friction magnitude and explain why it is not 10 N.

Show answer

Because the block remains at rest, the horizontal resultant is zero. Static friction adjusts to 6.0 N opposite the pull. The 10 N value is only the maximum available static friction, reached at impending motion.

Continue with the next resource in this course.

Course and syllabus information
Course
A-level H2 Physics topic extensions
Syllabus scope
Beyond the syllabus
Edition
A-level H2 Physics topic extensions