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 slidingDiagram showing forces on block

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 topplingDiagram showing forces on block

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.

Taking moments about A:
For toppling, 0.2X > 0.1 × 2g.

So for toppling, X > g.

The answer to the question is that
Equlibrium is broken by sliding,
with a force F of 0.6g Newtons

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