ABSTRACT
When a force acts upon a particle of matter, and that particle moves in space, work is done on the particle. The formal mathematical expression of this statement is
W= f: F.ds (4.1) in which s represents the particle path co-ordinate, and A and B represent the beginning and end points of the path. The instantaneous rate at which the force does work at any point on the path is
dW/dt = F.(ds/dt) = F.u (4.2) where u is the particle velocity vector. The scalar products of the vector quantities in eqns (4.1) and (4.2) indicate that work is done only by that component of the force in the direction of the particle displacement, or of the particle velocity, which is the same.
