Equilibrium is a state of an object with respect to a given observable quantity. For example a body acted on by several forces is said to be in equilibrium if it does not move or rotate during the time the forces acting on it do not change. A body is said to be in equilibrium when:
(i) the body as a whole either remains at rest or moves in a straight line with constant speed and;
(ii) the body is either not rotating at all or is rotating at a constant angular velocity.
Resultant and Equilibriant Forces
A body acted upon by two or more forces is said to be in equilibrium if it does not move or rotate. Under this condition the sum of the forces moving the body in one direction is equal to the sum of the forces pushing the body in the opposite direction. Thus we can distinguish between resultant force and equilibriant force as follows:
THE RESULTANT FORCE IS THAT SINGLE FORCE WHICH ACTING ALONE WILL HAVE THE SAME EFFECT IN MAGNITUDE AND DIRECTION AS TWO OR MORE FORCES ACTING TOGETHER.
The resultant force is found by the parallelogram law of vectors.
THE EQUILIBRIANT OF TWO OR MORE FORCES IS THAT SINGLE FORCE WHICH WILL BALANCE ALL THE OTHER FORCES TAKEN TOGETHER. IT IS EQUAL IN MAGNITUDE BUT OPPOSITE IN DIRECTION TO THE RESULTANT FORCE.
If three forces F1, F2 and F3 acting at a point are in equilibrium, the resultant of any two of the forces is equal but opposite in direction to the third forces. Any one of these forces is said to be the equilibrium of the other two. The equilibriant of F1 and F2 is F3, the equilibriant of F1 and F3 is F2 and vice versa.
Two forces 10N each are inclined at 120degree to each other. Find the single force that will:
a. replace the given force system.
b. balance the given force system.
a. The resultant force is given by:
Using the sine rule we have:
b. The equilibriant force is the force that will balance the given system of forces.
Equilibriant is equal and opposite to the resultant. Hence Equilibrian = 10N directed opposite to the resultant R.
SOURCE: New school physics by M.W ANYAKOHA, Ph D