Note 9 — Chapter I · ENERGY IN GENERAL.

We therefore notice that the measures of force and work bring in mass, space, and time. The typical force, weight, is given by w = mg. On the other hand, we have by the laws of falling bodies v = gt; s = 1∕2gt2; whence g = 2s∕t2; w = m(2s∕ t2); or, if F be the force, M the mass, L the space described, and T the time, we have F = MLT-2, which expresses what are called the dimensions of the force—that is to say, the magnitudes with their degree, which enter into its expression. We may thus easily obtain the dimensions of work:—

Work = f × s = mv²∕2 = ML²T^-2.