Condition for Equilibrium

An object is in equilibrium if it satisfies Newtons' first law:

"An object at rest or moving in a straight line with constant velocity will remain in this state unless it is subjected to an unbalanced force"

Quite simply put, an object is in equilibrium if the sum of forces acting on it equals zero:

This equation is called the equation of equilibrium.

Engineering Mechanics (Statics) - Equilibrium of a Particle

Before we discuss "equilibrium" lets go back a little and see what we understand about the whole subject of Mechanics.

Mechanics is a subject that is concerned with what happens to the motion of an object when forces are acting on it.  Mechanics can be divided into three branches¹:

1. Rigid-body mechanics (under the assumption that forces acting on the object cause no deformation upon the object)
2. Deformable-body mechanics
3. Fluid mechanics

At this point in time we are concerned with rigid-body mechanics which can be further divided into two areas:

1. Statics
2. Dynamics

When we talk of equilibrium we are in the Statics area of rigid-body mechanics.

An object is said to be in equilibrium when it is static or moving at constant velocity (not accelerating)

Dynamics on the other hand deals with object that are accelerating.

Addition of Coplanar Forces - Using Cartesian Vector Notation

Useful book to have

Schaum's Outline of Engineering Mechanics: Statics

For problems and solutions on addition of coplanar forces click HERE.

Given the coplanar forces F₁, F₂ and F₃ below, find the resultant force F_R = F₁ + F₂ + F₃

Step 1:

Represent each force as a Cartesian vector:

Step 2:

Finally, determine the resultant force: