Resolve a force system in to single force:

Resolve a force system in to single force and a couple systems. Also explain the Equivalent force couple system.

Or

'Any system of co planer forces can be reduced to a force couple system at an arbitrary point'. Explain above statement by assuming suitable system

The given force 'F' applied to a body at any point A is always is replaced by an equal force applied at another point B together with couple which will be equivalent to original force.

Let given force F is acting at 'A' as shown in the figure a.

This force is to be replaced at 'B'. Introduce two equal and opposite forces at point B, each of magnitude F and acting parallel to force at A as shown in the figure b. The force system of the figure b is equivalent to the single force acting at point A of figure a. In figure b three equal forces are acting. The two forces that is force F at point A and the oppositely directed force F at B (that is vertically downwards force at B) from a couple. The moment of this couple is F × x clockwise where x is perpendicular distance between the lines of action of forces at points A and B. The third force is acting at B in same direction in which the force at point A is acting.

In figure c the couple is shown by curved arrow with the symbol M. The force system of figure c is equivalent to figure b. Or in other words the Figure c is equivalent to Figure a. Hence the given force F acting at point A has been replaced by an equal and parallel force applied at B in same direction together with couple of moment F × x.

Therefore force acting at a point in rigid body can be replaced by an equal and parallel force at any other point in body, and couple.