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Mechanics

Conditions for the Equilibrium of Three Non-Parallel Forces

If we say that an object is under the influence of forces which are in equilibrium, we mean that the object is not accelerating.

The following rules help to solve problems in which a body is acted on by three forces.

i) The lines of action of the three forces must all pass through the same point.
ii) The principle of moments: the sum of all the clock-wise moments about any point must have the same magnitude as the sum of all the anti-clockwise moments about the same point.
iii) a) The sum of all the forces acting vertically upwards must have the same magnitude as the sum of all the forces acting vertically downwards
b) The sum of all the forces acting horizontally to the right must have the same magnitude as the sum of all the forces acting horizontally to the left.

In practice, when using condition iii), we will usually be considering the vertical and horizontal components of forces.

Example to illustrate the use of rule i)

The diagram below represents a uniform ladder leaning against a smooth vertical wall. Find the direction of the force exerted by the ground on the ladder.

An example to illustrate the use of rule ii) and iii)

 

© David Hoult 2008