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Understanding Coefficient of Friction

Apr 22, 2025

The Coefficient of Friction: A-Level Maths Revision

Introduction to Friction

  • Definition: Friction is "the resistance an object encounters in moving over another".
  • Comparative Example: Easier to drag an object over glass than sandpaper due to different levels of frictional resistance.
  • Assumptions in Problems:
    • "Smooth" surface: assumed to exert no frictional force.
    • "Rough" surface: offers some frictional resistance.

Limiting Equilibrium

  • Concept: When pushing an object (e.g., a book), initially, the frictional force equals the applied force.
  • Behavior of Frictional Force:
    • Increases with the applied force until a maximum value is reached.
    • At maximum value, friction is "limiting".
    • A stationary object under maximum friction is in "limiting equilibrium".
    • If pushed slightly harder, the object begins to move.
  • Summary:
    • Frictional force increases to a maximum, beyond which the object either moves or is on the verge of moving.

Coefficient of Friction

  • Definition: Number representing friction between two surfaces.
  • Symbol: Typically denoted as ( \mu ).
  • Maximum Frictional Force Formula:
    • ( F = \mu R )
    • ( \mu ): Coefficient of friction.
    • ( R ): Normal reaction force.
  • Direction: Acts parallel to surfaces in contact, opposing motion.

Example Problem

  • Given: Particle of mass 5 kg on a rough incline (angle: 30 degrees).
  • Objective: Find the coefficient of friction between the particle and the plane.
  • Equations:
    • Resolving up the plane: ( F - 5g \sin 30 = 0 )
    • Resolving perpendicular to the plane: ( R = 5g \cos 30 )
  • Result in Limiting Equilibrium:
    • ( F = \mu R )
    • ( 5g \sin 30 = \mu 5g \cos 30 )
    • ( \mu = \frac{\sin 30}{\cos 30} = 0.577 ) (3 significant figures)