DYNAMIC UNITS are units for measuring forces and their effects. It is an axiom of mechanics that if a body at rest be impressed by a force, and meet no resistance other than its own inertia, it will move in a straight line with a velocity which varies as the force; e.g., twice the force will develop twice the velocity. Also, if the mass of the body be increased, the force must be increased in like ratio to maintain the same velocity; e.g., double the mass will require double the force; or, if the force remain unchanged, double the mass will move with half the velocity. Combining the two statements, we find that the velocity varies directly as the force, and inversely as the mass; velocity equals force divided by mass, or v -4 From this we have F = Mv. The unit of force is that force which will impart a unit of velocity to a unit of mass; that is, which will cause a unit of mass to move through a unit of space in a unit of time. If the force considered be that of gravitation, whose action in the same place is practically uniform, and if we remember that the measure of the force of gravitation in a body is the weight of the body, we have W = Mv. But if the mass be submitted to the force of gravitation, that is, if it be permitted to fall freely in a vacuum, it traverses a space of 32.16 ft. in one second,
at New York, approximately. We have then, by experiment, a value for v which makes our equation W = M X 32.16, whence M =Wą32.16. The English or American unit of force is one pound avoirdupois; and the corresponding unit of mass is 1 lb. divided by 32.16.
The unit of work is the force which will raise a unit of weight through a unit of space. The two items are indicated in the name foot-pound, which by analogy might be exchanged in proper ratio for inch-ounce, ton-mile, etc. The corresponding French unit of work is the kilogram-meter. More generally the foot-pound is the work of a unit of force acting through a unit of space. The horse-power is an arbitrary unit, being the force required to perfom 33,000 units of work in one minute. It may be called the unit of the rate of working. The French cheval a vapeur is 75 kilogram-meters per second, and is equal to 32.550 foot-pounds per minute, or a little less than our horse-power. The theoretical horse-power is merely a conventional quantity, the actual work of horses averaging about 17,000, and rarely exceeding 22,000 foot-pounds per minute.