A balanced state of a body under the action of given forces, is known as equilibrium. In this state the net effect of all the forces is nil.
A body in equilibrium has no resultant and no couple acting on it. Such a body has no linear or angular acceleration. It may be either at rest or moving with uniform velocity.
Conditions of equilibrium:
On a body at equilibrium there is no resultant force and also there is no moment i.e. there is no couple acting on it. Resultant is zero only if the algebraic sum of components along two mutually perpendicular axes is zero.
Therefore analytical conditions of equilibrium are:
- ∑Fx = 0 Means algebraic sum of components of all the forces along any direction (say x-axis) is zero.
- ∑Fy = 0 Means algebraic sum of components of all the forces in a direction (say y-axis) at 90 to the first direction is zero.
- ∑M = 0 Means algebraic sum of moments of all the forces about any point in their plane is zero.
The first two conditions are applicable for concurrent forces and all the three conditions must be applicable for non-concurrent forces.
Principles of Equilibrium:
A few common principles equilibrium are:
- Two force principle: States that if two forces are in equilibrium they must be equal, opposite and collinear.
- Three force principle: States that if three forces are in equilibrium then resultant of any two forces must be equal, opposite and collinear with the third force. Also if three forces are in equilibrium they are always concurrent.
- Four force principle: States that if four forces are in equilibrium then resultant of any two forces is equal, opposite and collinear with the resultant of other two forces.
Equilibrant Force (E):
It is defined as a single force which when applied with given forces brings the body in equilibrium.