---
title: "Limiting friction; why μs > μk"
subject: "Applied Mechanics"
chapter: 5
key: "semester_1/applied_mechanics:limiting-friction-impending-motion-static-vs-kinetic"
source: https://www.bctengineer.com/q/semester_1/applied_mechanics/limiting-friction-impending-motion-static-vs-kinetic
site: BCT Engineering
---

# Limiting friction; why μs > μk

Applied Mechanics · Chapter 5: Friction

- Asked in: 2067 Asar, 5 marks
- Video: [Frictional Forces: Static and Kinetic](https://www.youtube.com/watch?v=3EbUa5ZDybg) — Professor Dave Explains
- Answer checked by Claude Opus 5.5 (high effort) on 2026-10-14
- Page: https://www.bctengineer.com/q/semester_1/applied_mechanics/limiting-friction-impending-motion-static-vs-kinetic
- Whole chapter: https://www.bctengineer.com/md/semester_1/applied_mechanics/chapter-5

## Question

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

## 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.

## Answer

#### 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.

## Check yourself

The answer's key points as multiple-choice questions, with the correct option and why.

1. What is limiting friction?
   A. The maximum static friction, F_max = mu_s N, reached when the body is about to slide
   B. The friction during sliding
   C. Friction at zero applied force
   D. The friction on a smooth surface
   Answer: A. It is the maximum value of static friction beyond which equilibrium is impossible. (Key point: Limiting friction)

2. Why is more force needed to start motion than to maintain it?
   A. Weight of the body increases at rest
   B. At rest, cold-welded junctions and interlocking of surface peaks are strong
   C. Contact area is larger at rest
   D. The normal reaction is larger at rest
   Answer: B. At rest, microscopic peaks form strong adhesion/interlocking that must be broken. (Key point: Why mu_s > mu_k at rest)

3. Why is kinetic friction less?
   A. The surfaces become perfectly smooth
   B. The normal reaction decreases
   C. The surfaces ride over each other and junctions do not have time to form fully
   D. The body loses weight
   Answer: C. Junctions form only partly while sliding, so less force is needed. (Key point: Reason during sliding)

4. Which statement about a body in impending motion is correct?
   A. It is moving at constant speed
   B. Its friction is zero
   C. Its friction is mu_k N
   D. It is still at rest, but any increase in force makes it move
   Answer: D. Friction equals its limiting value and equilibrium is just maintained. (Key point: Impending motion state)

## Related in Applied Mechanics

- [Impending motion; friction force at different stages](https://www.bctengineer.com/question.md?key=semester_1%2Fapplied_mechanics%3Aimpending-motion-friction-stages) — Applied Mechanics, chapter 5
- [Define limiting friction, angle of friction, coefficients](https://www.bctengineer.com/question.md?key=semester_1%2Fapplied_mechanics%3Alimiting-friction-angle-coefficient-definitions) — Applied Mechanics, chapter 5
- [Angle of friction; laws of static friction](https://www.bctengineer.com/question.md?key=semester_1%2Fapplied_mechanics%3Aangle-of-friction-laws-static-friction) — Applied Mechanics, chapter 5
- [Friction conditions; sliding or overturning of block](https://www.bctengineer.com/question.md?key=semester_1%2Fapplied_mechanics%3Afriction-conditions-sliding-overturning) — Applied Mechanics, chapter 5, asked 2×

## Related in other subjects

- [Kinetic energy and work of rigid body](https://www.bctengineer.com/question.md?key=semester_3%2Fengineering_mechanics%3Akinetic-energy-rigid-body-work-energy) — Engineering Mechanics, chapter 7