Page:Elementary Text-book of Physics (Anthony, 1897).djvu/45

§ 29] thereby do work. The particle possessing kinetic energy has also the capacity for doing work, for, in order to bring it to rest, the amount of work given by the formula $$Fs = \tfrac{1}{2}mv^2$$ must be done upon it.

The unit of work and energy is the work done by a unit force upon a particle while it is displaced in the direction of the force through unit distance.

The dimensions of energy are $$M L^2 T^{-2}$$, the same as those of work. Since the square of a length cannot involve direction, it follows that energy is a quantity independent of direction and is not a vector quantity.

The practical unit of work and energy is the erg.

It is the work done by a force of one dyne, in moving its point of application in the line of the force through a space of one centimetre:

Or, it is the energy of a body so conditioned that it can exert the force of one dyne through a space of one centimetre:

Or, it is the energy of a mass of two grams moving with unit velocity.

29. Bodies, Density.— The particle with which we have been dealing hitherto has no counterpart in Nature. In our experience we have to deal with extended bodies or systems of bodies, and the description of their motions and of the way in which forces act on them is more complicated than the corresponding description for the ideal particle. The notion of the particle is nevertheless of great utility: we may in the first place consider bodies as composed of numbers of these particles or as being systems of particles; and, in the second place, we may to some extent describe the motion of bodies by comparison with the motion of a particle. It is, however, often convenient to be able to represent the mass of a body as distributed continuously throughout its volume. In that case we make use of a special concept, the density. To define it we suppose the particles of the body so distributed that each unit volume in the body contains the same number of them.