---
title: "Laws of friction; usage in engineering"
subject: "Applied Mechanics"
chapter: 5
key: "semester_1/applied_mechanics:laws-of-friction-engineering-usage"
source: https://www.bctengineer.com/q/semester_1/applied_mechanics/laws-of-friction-engineering-usage
site: BCT Engineering
---

# Laws of friction; usage in engineering

Applied Mechanics · Chapter 5: Friction

- Asked in: 2069 Asar, 4 marks
- Video: [Engineering Mechanics | Lecture 22 | Friction Concepts & Principles](https://www.youtube.com/watch?v=oIo6wehxO9o) — PK StrucEd
- Answer checked by Claude Opus 5.5 (high effort) on 2026-10-14
- Page: https://www.bctengineer.com/q/semester_1/applied_mechanics/laws-of-friction-engineering-usage
- Whole chapter: https://www.bctengineer.com/md/semester_1/applied_mechanics/chapter-5

## Question

Explain the laws of friction. Also give two examples of engineering usage of friction.

## Short answer

Laws: friction opposes motion, self-adjusting up to limit, F_max = μN, independent of area, depends on surfaces, kinetic μ_k < μ_s. Engineering uses: brakes and clutches use friction to stop or transmit torque; belt drives transmit power via friction (T1/T2 = e^(μθ)), and friction grip bolts carry load through friction between clamped plates.

## Answer

#### Laws of friction
1. The friction force acts along the surfaces in contact and opposes the motion or the tendency to motion.
2. For bodies at rest the friction force equals the applied tangential force, up to a maximum: F ≤ μₛN.
3. The limiting friction is proportional to the normal reaction, F_max = μₛN.
4. It does not depend on the area of contact.
5. It depends on the nature of the surfaces (μₛ).
6. Sliding (kinetic) friction is F = μₖN with μₖ < μₛ, and is almost independent of the speed of sliding.

#### Two examples of engineering usage
1. **Brakes and clutches:** the braking force in vehicles (disc and drum brakes) and the torque transmitted by a clutch plate come from friction. Brake torque = μ N r.
2. **Belt drives and friction grip bolts:** a belt transmits power to a pulley by friction (T₁/T₂ = e^(μθ)); friction-grip bolts in steel joints carry the load by friction between the clamped plates. Other uses: screw threads and nails holding by friction, walking and tyre grip on roads.

## Check yourself

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

1. According to the laws of friction, how does limiting friction depend on contact area?
   A. It increases in proportion to area
   B. It does not depend on it
   C. It decreases as area increases
   D. It depends on area squared
   Answer: B. Limiting friction depends on N and the surface nature, not on contact area. (Key point: Effect of contact area)

2. Which expression gives limiting friction?
   A. F_max = mu_s N
   B. F_max = mu_s W / N
   C. F_max = N / mu_s
   D. F_max = mu_k N^2
   Answer: A. Limiting friction is proportional to the normal reaction: F_max = mu_s N. (Key point: Limiting friction law)

3. How does kinetic friction compare with limiting static friction?
   A. mu_k > mu_s
   B. mu_k = mu_s always
   C. mu_k < mu_s
   D. mu_k increases with speed
   Answer: C. Sliding friction is slightly less than limiting static friction and almost independent of speed. (Key point: Static vs kinetic)

4. In a belt drive, power is transmitted by friction. Which relation governs the tension ratio?
   A. T1/T2 = mu theta
   B. T1 - T2 = mu N
   C. T1/T2 = sin theta / mu
   D. T1/T2 = e^(mu theta)
   Answer: D. The belt friction formula is T1/T2 = e^(mu theta). (Key point: Belt drive)

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- [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

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