Page:Elementary Text-book of Physics (Anthony, 1897).djvu/39

[§ 22 bodies can exert force on one another. This conclusion is not strictly justifiable, and our comparison of the action of one body on another to the action of our muscles may be only a convenient analogy.

If we throw a weight by exerting a certain effort for a short time, and then by exerting an equal effort for a longer time, we find that the velocity acquired by the weight is greater in the latter case. If we apply different efforts for the same time in throwing the same weight, we find that the effort which we are conscious of as greater gives the weight a greater velocity than that effort which we are conscious of as less. We may substitute for the forces exerted by our muscles those forces which we have assumed by analogy to act between bodies. Relying upon the uniformity with which these forces act, as determined by universal experience, we can exhibit, more precisely than by the use of our muscular effort, the relations which obtain between the force exerted and the motion caused by it. As our experiments increase in precision, and as one disturbing cause after another is eliminated, we find that the velocity acquired by a given body acted on by a given force increases in proportion to the time during which the force acts, or, as may be said, a constant force produces a uniform acceleration. Further, if different forces act on the same body for the same time, the velocities produced are proportional to the forces. If $$F$$ represent the magnitude of the force, $$t$$ the time during which it acts, $$v$$ the velocity which the body acquires, and $$m$$ a proportional factor, the results of these experiments may be embodied in the formula The factor $$m$$ is called the mass or the inertia of the body. Since $$\frac{v}{t}$$ measures the acceleration of the body, this equation is equivalent to The dimensions of force are $$MLT^{-2}.$$

The practical unit of force is the dyne, which is the force that