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Work Done by Force

Let us consider a particle A which moves to A’ under the action of a force F. Vector AA = dr is the displacement of the particle (Fig. 9.1).

Vector r  is the position vector of A

Vector r + dr is the position vector of A’

The work du is defined as the dot product between F an dr

du = f .dr

| f| = f

and                            | dr | = ds

 

By definition of dot product

du= F ds cos θ                                                             , … (9.2)

where e is the angle between F and d;. Thus, the magnitude of work is defined as the product of component of the force in the direction of displacement and the displacement.