ATWOOD'S MACHINE, ma-shiin'. An in strument for illustrating the relations of time, space, and velocity in the motion of a body fall ing under the action of gravity, invented by George Atwood (q.v.). It is known that a body falling freely passes through 16 feet in the first second, 64 feet in the first two sec onds, 144 feet in the first three seconds, and so on. Nov, as these spaces are so large, it would require a machine of impracticable size to illus trate the relations just mentioned. The object of Atwood's machine is to reduce the scale on which gravity acts without in any way altering its essential features as an accelerating force. The machine consists essemtially of a pulley, P ( see the cut), moving on its axis with very little friction, with a line silk cord passing over it, sustaining two equal cylindrical weights, p and g, at its extremities. The pulley rests on a graduated wooden pillar, which is placed in a vertical position by leveling screws. Two stages, A and B, slide along the pillar, and be fixed _ .
at any part of it by means of clamps. One of these stages, A, has a circular hole cut in it, so as to allow the cylinder, p, to pass freely through it; the other is un broken, and intercepts the passage of the weight. A pendulum, chronograph, or other device is used with the machine to measure time. The weight of the cylinders, p and g, being equal, they have no tendency to rise or fall, but arc reduced, as it were, to masses without weight. When a bar is placed on p, the motion that ensues is due only to the action of gravity upon it, so that the motion of the whole _ _ must be considerably slower than that of the bar falling freely. Suppose, foe in stance, that p and g are each ounces in weight, and that the bar is 1 ounce, the force acting on the system— leaving the friction and inertia of the pulley out of account—would be 1-16 of gravity, or the whole would move only 1 foot in the first second, instead of 16. If the bar be left free to fall, its weight or moving force would bring its own mass through 16 feet the first second ; but when placed on p, this force is exerted not only on the mass of the bar, but on that of p and y, which is 15 times greater, so that it has altogether 16 times more matter in the second case to move than in the first, and must, in consequence, move it 16 times more slowly. By a proper adjust ment of weights, the rate of motion may be made as small as we please, or we can reduce the ac .celerating force to any fraction of gravity. Sup pose the weights to be so adjusted that under the moving force of the bar or circular weight the whole moves through 1 inch in the first second, we may make the following simple experiments: Experiment I.—Place the bar on p, and put
the weight in such a position that the lower sur face of the bar shall be horizontally in the same plane as the 0 point of the scale, and fix the stage A at 1 inch. When allowed to descend, the bar will accompany the weight, p, during 1 second and for 1 inch, when it will be arrested by the stage A, after which p and g will con tinue to move from the momentum they have ac quired in passing through the first inch. Their velocity will now be found to be quite uniform, being 2 inches per second, illustrating the prin ciple that a falling body acquires, at the end of the first second, a velocity per second equal to twice the space it has fallen through. Experi ment II.—Take, instead of the bar, the circular weight, place the bottom of p in a line with the 0 point, and put the stage B at 64 inches. Since the weight accompanies p throughout its fall, we have in this experiment the same conditions as in the ordinary fall of a body. When released, the bottom of the cylinder, p, reaches 1 ihch in 1 second, 4 inches in 2 seconds, 9 inches in 3 seconds, 16 inches in 4 seconds, 25 inches in 5 seconds, 49 inches in 7 seconds, and 64 inches and the stage in 8 secomls—showing that the spaces described are as the squares of time times. Experiment 111.-1f the bar be placed as in Ex periment I., and the stage A he fixed at 4 inches, the bar will accompany the weight, p, during 2 seconds, and the velocity acquired in that time by p and g will be 4 inches per second, or twice what it was before. In the same manner, if the stage A be placed at 9, 1G, 25, etc. inches, the velocities acquired in falling through these spaces would he respectively 6, 8, 10, etc. inches —2 inches of velocity being acquired in each second of the fall. From this it is manifest that the force under which bodies fall is a uniformly accelerating force—that is. adds equal incre ments of velocity in equal times. By means of the bar and the stage A, we are thus enabled to remove the accelerating force from the falling body at any point of its fall, and then determine the velocity it has acquired.
Atwood's machine will he found described and explained in almost any treatise on physics, and complete directions for performing the experi ments are given in Glazebrook and Shaw's Prac tical Physics (New York, 1893).