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Limiting friction; why μs > μk

Short answer

Limiting friction is the maximum static friction F_max = μ_s N; impending motion is the state just before sliding when applied force equals this limit. μ_s exceeds μ_k because at rest surface asperities interlock and form cold-welds requiring higher force to break; during sliding, less interlocking occurs, reducing friction.

Define limiting friction and impending motion. Justify why coefficient of static friction is greater than coefficient of kinetic friction.

Limiting friction

The maximum value of the static friction force, reached when a body is just about to slide on a surface: F_max = μₛN. Beyond this value, equilibrium is not possible and the body slides.

Impending motion

The state of a body in which it is just on the point of starting to move, because the applied force has made the friction force equal to its limiting value. The body is still at rest but any increase in force makes it move.

Why μₛ is greater than μₖ

  • Surfaces are never perfectly smooth. At rest the microscopic peaks of the two surfaces press into each other and form strong cold-welded junctions (adhesion) and interlocking. A larger force is needed to break these junctions and start motion.
  • Once sliding starts, the surfaces ride over one another and there is not enough time for the junctions to form fully, so the interlocking and adhesion are less. Less force is needed to keep the body moving.
  • Experiments show that the friction force falls a little when the sliding begins, so μₖ < μₛ.

This is why it is harder to start pushing a heavy box than to keep it moving, and why a body that has just started sliding accelerates.

✓ Answer checked by Claude Opus 5.5 (high effort)

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