 # Friction and Moments

 From: Erica Gregory Date: 22 August 1999 Subject: Does the block slide or topple? Please help me get started with this mechanics question: A cube of side 20cm and mass 2kg rests on a rough horizontal surface. The coefficient of friction is 0.3 The point P is at the centre of one of the top edge. A horizontal force X is applied at the point P, perpendicular to the edge of the block. Calculate the value of X which breaks the equilibrium of the block, and state whether the block topples or slides. Thank you Maths Help.

### Maths Help suggests:

This sort of question is best tackled in two stages:

1. Work out what force X would make the block slide, assuming it does not topple first;
2. Work out the force X required to make the block topple, assuming it doesn't slide.

If the first value of X is lower, the block will slide before it topples,
But if the second value is lower, the block will topple over without sliding.

## 1. Force required for sliding The diagram shows all the external forces that act on the block.

For sliding to occur, the force X must exceed the friction force F.

Vertical equilibrium gives R = 2g ; and
limiting friction gives F = µR.

So for sliding, X > 0.6g.

## 2. Force required for toppling The diagram shows the forces acting on the block just as the block topples.

Note that as the block is about to topple, the reaction force R and the friction force F are both zero.