# Conditions of Equilibrium under the Action of Parallel Coplanar Forces

### Topic Content:

- Conditions of Equilibrium under the Action of Parallel Coplanar Forces

**Coplanar forces** are forces that lie in the same plane and parallel forces are forces whose lines of action are parallel to each other.

The conditions for equilibrium of coplanar parallel forces are;**1.** The algebraic sum of the forces acting on a body in any given direction must be zero. In other words, the sum of the upward forces must be equal to the sum of the downward forces.**2.** The algebraic sum of the moments of all the forces about any point on a body must be zero. i.e. the total clockwise moments about a point must be equal to the total anticlockwise moments about the same point.

### Principle of Moments:

The principle of moments states that if a body is in equilibrium, the sum of clockwise moments about any point must be equal to the sum of the anticlockwise moments about the same point.

### Example 4.4.1:

A 100 cm uniform rod has a load of 40 N suspended at 20 cm from one end. If the fulcrum is at the centre of gravity. Calculate the force that must be applied at its other end to keep it in horizontal equilibrium.

**Solution:**

Taking moments about O,

Clockwise moments about O = Anticlockwise moments about the same point.

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