# To study parallel forces in equilibrium

To study parallel forces in equilibrium

A metre rule is weighed and then suspended by vertical threads attached to two spring balances held by clamp and stand (Fig. 6.4). Two weights are attached as shown so that one exerts an upward and the other a downward pull on the rule.
Lastly, the spring balances are raised or lowered as necessary to bring the rule into a horizontal position.

We shall assume, for the time being, that the force of gravity on the rule itself acts downwards through its centre. In this case the centre of the rule is also its centre of gravity, and this will be explained more fully later in the chapter. The results of a typical experiment are indicated in Fig. 6.4. It will be noted that the sum of the upward forces = 1.05 + 0.20 + 1.45 = 2.7 N, and the sum of the downward forces = 2.2 + 0.5 = 2.7 Furthermore, as the rule is in equilibrium, there is no resultant moment acting which would cause it to turn about any point. This may be verified by working out the moments of the forces about any point we choose and showing that the sum of the anticlockwise moments is equal to the sum of the clockwise moments.

It is convenient to do this by entering the various forces and distances in a table. In accordance with convention, anticlockwise moments are given a positive sign and clockwise moments a negative sign. Moments have been taken about the end A.

The experiment shows that, when a number of parallel forces are in equilibrium: (i) the sum of the forces in one direction is equal to the sum of the forces in the opposite direction; (ii) the sum of the anticlockwise moments about any point is equal to the sum of the clockwise moments about the point. When performing this experiment, the reader should use different weights and distances from those used here and draw an appropriate diagram. The results should be entered in a table and a different point chosen about which moments are taken.