---
title: "Impending motion; friction force at different stages"
subject: "Applied Mechanics"
chapter: 5
key: "semester_1/applied_mechanics:impending-motion-friction-stages"
source: https://www.bctengineer.com/q/semester_1/applied_mechanics/impending-motion-friction-stages
site: BCT Engineering
---

# Impending motion; friction force at different stages

Applied Mechanics · Chapter 5: Friction

- Asked in: 2069 Chaitra, 4 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/impending-motion-friction-stages
- Whole chapter: https://www.bctengineer.com/md/semester_1/applied_mechanics/chapter-5

## Question

Illustrate impending motion state of friction and demonstrate the change in frictional force for different motion stages using relevant figure.

## Short answer

Impending motion is the state just before sliding where static friction reaches its maximum value F_max = μ_s N. As applied force increases, friction rises linearly with it (self-adjusting) until this peak, then drops slightly to a constant kinetic friction μ_k N once motion begins.

## Answer

#### Impending motion
Impending motion is the state in which a body is just about to slide. The applied force has increased until the friction force has reached its maximum, limiting value F_max = μₛN. Any further increase of the applied force starts the motion.

#### Variation of friction force with the applied force
A block of weight W on a rough horizontal surface is pulled by a force P that is gradually increased from zero.
```text
 F (friction)
  ^
  |               F_max = μs N
  |                +
  |              / |\
  |            /   |  \___________  F = μk N (motion)
  |          /     |
  |        /  F = P (45° line)
  |      /         |
  |    /           |
  +--/-------------+---------------> P (applied)
  O   static zone  impending   motion
      (no motion)  motion
```
| Stage | Applied force | Friction force |
|---|---|---|
| No friction | P = 0 | F = 0 |
| No motion (static) | 0 < P < F_max | F = P (increases with P) |
| Impending motion | P = F_max | F = F_max = μₛN (maximum) |
| Motion | P > F_max | F drops to μₖN and stays nearly constant |

So the friction force first rises linearly with P (it is self-adjusting), reaches its peak at impending motion, then falls slightly to the kinetic value once sliding begins.

## Check yourself

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

1. What is impending motion?
   A. The body is sliding at constant speed
   B. The body is at rest but just about to slide; friction is at F_max
   C. The body has zero friction
   D. The body has just stopped
   Answer: B. At impending motion the friction force has reached its limiting value mu_s N. (Key point: Meaning of impending motion)

2. When 0 < P < F_max, what is the friction force?
   A. F = P
   B. F = mu_k N
   C. F = F_max
   D. F = 0
   Answer: A. In static equilibrium friction equals the applied force and grows with P. (Key point: Friction before limit)

3. What happens to the friction force when P exceeds F_max and sliding begins?
   A. It keeps rising with P
   B. It rises to 2 mu_s N
   C. It drops to mu_k N and stays nearly constant
   D. It becomes zero
   Answer: C. Once sliding, friction falls to the kinetic value mu_k N. (Key point: Friction after motion starts)

4. Which description matches the F vs P graph?
   A. Constant at mu_s N throughout
   B. Rises linearly forever
   C. Falls from F_max to zero
   D. Rises linearly, peaks at F_max, then drops to a lower constant value
   Answer: D. F = P (45° line) up to F_max, then falls slightly to mu_k N. (Key point: Shape of F-P graph)

## Related in Applied Mechanics

- [Force for just motion of block B](https://www.bctengineer.com/question.md?key=semester_1%2Fapplied_mechanics%3Ablock-b-just-motion-force-p-15deg) — Applied Mechanics, chapter 5
- [Force P to start motion of bar and block](https://www.bctengineer.com/question.md?key=semester_1%2Fapplied_mechanics%3Abar-ab-pin-block-force-p-start-motion) — Applied Mechanics, chapter 5
- [Friction force; tipping and sliding of block](https://www.bctengineer.com/question.md?key=semester_1%2Fapplied_mechanics%3Afriction-force-tipping-sliding-block) — 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×
- [Limiting friction; why μs > μk](https://www.bctengineer.com/question.md?key=semester_1%2Fapplied_mechanics%3Alimiting-friction-impending-motion-static-vs-kinetic) — Applied Mechanics, chapter 5
- [Uniformly accelerated motion; angular momentum definition](https://www.bctengineer.com/question.md?key=semester_1%2Fapplied_mechanics%3Auniformly-accelerated-motion-angular-momentum) — Applied Mechanics, chapter 8

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- [Two oscillating masses: motion, centre of mass, energy](https://www.bctengineer.com/question.md?key=semester_3%2Fapplied_mechanics_dynamics%3Atwo-masses-springs-equations-energy) — Applied Mechanics (Dynamics), chapter 3