# FHSST Physics/Forces/Equilibrium of Forces

Forces The Free High School Science Texts: A Textbook for High School Students Studying Physics. Main Page - << Previous Chapter (Vectors) - Next Chapter (Rectilinear Motion) >> TO DO LIST - Definition - Diagrams - Equilibrium of Forces - Newton's Laws of Motion - Newton's Law of Universal Gravitation - Examples - Important Quantities, Equations, and Concepts

# Equilibrium of Forces

At the beginning of this chapter it was mentioned that resultant forces cause objects to accelerate. If an object is stationary or moving at constant velocity then either:

• no forces are acting on the object, or
• the forces acting on that object are exactly balanced.

A resultant force would cause a stationary object to start moving or an object moving with a given velocity to speed up or slow down or change direction such that the velocity of the object changes.

In other words, for stationary objects or objects moving with constant velocity, the resultant force acting on the object is zero. The object is said to be in equilibrium.

If a resultant force acts on an object then that object can be brought into equilibrium by applying an additional force that exactly balances this resultant. Such a force is called the equilibrant and is equal in magnitude but opposite in direction to the original resultant force acting on the object.

```Definition: The equilibrant of any number of forces is the single force required to produce equilibrium.
```

As an example of an object in equilibrium, consider an object held stationary by two ropes in the arrangement below:

Let us draw a force diagram for the object. In the force diagram the object is drawn as a dot and all forces acting on the object are drawn in the correct directions starting from that dot. In this case, three forces are acting on the object.

Each rope exerts a force on the object in the direction of the rope away from the object.

Since the object has mass, it is attracted towards the centre of the earth. This weight is represented in the force diagram as ${\overrightarrow {W}}$ .

Since the object is stationary, the resultant force acting on the object is zero. In other words the three force vectors drawn tail-to-head form a closed triangle:

[In general, when drawn tail-to-head the forces acting on an object in equilibrium form a closed figure with the head of the last vector joining up with the tail of the first vector. When only three forces act on an object this closed figure is a triangle. This leads to the triangle law for three forces in equilibrium:

Triangle Law for Three Forces in Equilibrium: Three forces in equilibrium can be represented in magnitude and direction by the three sides of a triangle taken in order.