Calculating Equilibrium in a System of Force

What is Equilibrium?
When a system is said to be in equilibrium this means it is in balance and is either moving at constant velocity motion or is at rest.

Situations that must exist for a system to be at equilibrium:

1. The resultant force in any direction must be zero.
2. The total moments of the system must be zero. Meaning:

Clockwise Moments = Anti- Clockwise Moments

How to calculate equilibrium?


Example 1
If the system below is in equilibrium find the unknown force “F”.

System in equilibrium

Step 1
In the question they stated that the system is in equilibrium, therefore you can go ahead and use the equation:

Clockwise Moments = Anti-Clockwise Moments

But remember that formula for moments is:
Force × Perpendicular distance from pivot

Therefore:

Clockwise Force × Perpendicular distance = Anti-clockwise Force × Perpendicular Distance

Step 2
Identify the forces in the system that are moving clockwise and anti-clockwise with their respective perpendicular distances, and then substitute those values in the above equation:

After substituting the values above into the formula you should get:

Clockwise Moments = Anti-Clockwise Moments

Clockwise Force × Perpendicular distance = Anti-clockwise Force × Perpendicular Distance

F × 8m = 120N × 6m

Step 3
After placing the values into the formula all that is left to do is transpose the formula to make “F” the subject then solve for “F”. The overall calculation would then be:

Calculating Equilibrium