what is the relation between resultant and equilibrant?
they are equal and in opposite directions.
The relation between the resultant and equilibrant lies in their effects on an object subject to multiple forces.
When several forces act on an object, their combined effect is represented by the resultant. The resultant force is a single force that has the same effect as all the individual forces acting together. It represents the net force acting on the object, taking into account both the magnitudes and directions of the individual forces.
On the other hand, the equilibrant is a force that, when applied to an object along with the other forces, balances out the net force and brings the object into a state of equilibrium. It is equal in magnitude but opposite in direction to the resultant force, effectively canceling out its effect.
Mathematically, if F1, F2, F3, etc. are the individual forces acting on an object, then the resultant R is given by:
R = F1 + F2 + F3 + ...
And the equilibrant E is given by:
E = -R
Therefore, the resultant and equilibrant forces have a special relationship: they are equal in magnitude but opposite in direction. This balancing effect ensures that an object remains in a state of equilibrium when the equilibrant force is present.
To find the relation between the resultant and equilibrant forces in practical situations, you can use vector addition and subtraction techniques. By adding all the forces acting on an object, you can find the resultant force. Then, by multiplying the resultant force by -1 or reversing its direction, you can obtain the equilibrant force.