---
title: "Friction conditions; sliding or overturning of block"
subject: "Applied Mechanics"
chapter: 5
key: "semester_1/applied_mechanics:friction-conditions-sliding-overturning"
source: https://www.bctengineer.com/q/semester_1/applied_mechanics/friction-conditions-sliding-overturning
site: BCT Engineering
---

# Friction conditions; sliding or overturning of block

Applied Mechanics · Chapter 5: Friction

- Asked in: 2074 Asoj, 3+2 marks; 2072 Chaitra, 3+2 marks (asked 2 times)
- Answer checked by Claude Opus 5.5 (high effort) on 2026-10-14
- Page: https://www.bctengineer.com/q/semester_1/applied_mechanics/friction-conditions-sliding-overturning
- Whole chapter: https://www.bctengineer.com/md/semester_1/applied_mechanics/chapter-5

## Question

Illustrate the conditions of no friction, no motion, impending motion and motion with necessary sketches. How can you assure the condition of sliding or overturning of the block?

## Short answer

No friction: no force, F=0. No motion: P < μsN, F = P. Impending: P = μsN. Motion: sliding with kinetic friction. For sliding vs overturning, block slides if μ < b/(2a); otherwise overturns first.

## Answer

#### Conditions of friction
```text
 No friction      No motion        Impending         Motion
 (P = 0)          (P < F_max)      motion            (P > F_max)
   W                W                W                W
   |                |                |                |
 -----[ ]-----   P->[ ]F<--      P->[ ]F=μsN<-     P->[ ]F=μkN<-
 N = W, F = 0    F = P           F = F_max         F < F_max
 at rest         at rest         about to slide    sliding, accelerates
```
- **No friction:** no applied tangential force (P = 0). Friction force F = 0, only the normal reaction N = W acts.
- **No motion:** P is applied but is small. The body stays at rest and F = P, so F is less than the maximum value, F < μₛN.
- **Impending motion:** P is increased until the body is just about to slide. F reaches its maximum (limiting) value F_max = μₛN.
- **Motion:** if P exceeds F_max the body slides. The friction force falls to the kinetic value F = μₖN, which is slightly less than F_max.

#### Sliding or overturning of a block
A block of weight W, base width b and height h is pulled by a horizontal force P applied at height a above the base. The coefficient of static friction is μ.
```text
          P
      ----->+------+          a = height of P
            |      |          b = width of base
            |  W   |
   ---------+------+---> 
            F      N
```
- **Sliding** starts when P reaches the limiting friction: P_slide = μ W.
- **Overturning (tipping)** about the toe starts when the overturning moment equals the restoring moment, with the normal reaction acting at the toe: P a = W (b/2), so P_tip = W b / (2a).

**Decision:** compare the two values of P.
- If μW < Wb/(2a), that is μ < b/(2a), the block **slides first**.
- If Wb/(2a) < μW, the block **overturns first**.
- At equal values both are about to occur together.

Example: W = 500 N, b = 0.6 m, a = 1.0 m, μ = 0.4. P_slide = 200 N. P_tip = 500 × 0.6/(2 × 1.0) = 150 N. Since 150 N < 200 N, the block overturns before it slides.

## Check yourself

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

1. With P applied but small, the friction force is:
   A. F = μsN
   B. F = 0
   C. F = P, less than the limiting value
   D. F = μkN
   Answer: C. Friction is self-adjusting and equals P while at rest. (Key point: No motion)

2. At impending motion friction is:
   A. F_max = μs N
   B. P/2
   C. μk N
   D. Zero
   Answer: A. The limiting value is reached. (Key point: Impending motion)

3. The force to tip the block about its toe is:
   A. P = Wa/(2b)
   B. P = Wb/(2a)
   C. P = μW
   D. P = W/μ
   Answer: B. P a = W b/2 with N at the toe. (Key point: Tipping force)

4. When does the block slide first?
   A. When a < b
   B. Always
   C. When μ < b/(2a)
   D. When μ > b/(2a)
   Answer: C. Sliding needs the smaller force when μW < Wb/(2a). (Key point: Decision)

## Related in Applied Mechanics

- [Laws of dry friction; overturning and sliding](https://www.bctengineer.com/question.md?key=semester_1%2Fapplied_mechanics%3Alaws-dry-friction-overturning-sliding) — Applied Mechanics, chapter 5
- [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
- [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
- [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
- [Force P to prevent block sliding down incline](https://www.bctengineer.com/question.md?key=semester_1%2Fapplied_mechanics%3Ablock-50kg-force-p-prevent-sliding-down) — Applied Mechanics, chapter 5

## Related in other subjects

- [Sliding and overturning check of gravity dam](https://www.bctengineer.com/question.md?key=semester_6%2Fhydro_power%3Agravity-dam-sliding-overturning-figure) — Hydro Power, chapter 4
- [Trapezoidal masonry wall, sliding and overturning](https://www.bctengineer.com/question.md?key=semester_5%2Ffoundation_engineering%3Atrapezoidal-wall-coulomb-sliding) — Foundation Engineering, chapter 3, asked 2×
- [Overturning and sliding check with shear strength](https://www.bctengineer.com/question.md?key=semester_6%2Fhydro_power%3Agravity-dam-overturning-sliding) — Hydro Power, chapter 4
- [Gravity dam stability: flotation, overturning, sliding](https://www.bctengineer.com/question.md?key=semester_7%2Fhydropower_engineering%3Agravity-dam-stability-flotation-shear-resistance) — Hydropower Engineering, chapter 4