ATWOOD'S MACHINE, an instrument for illustrating the relations of time, space, and velocity in the motion of a body falling under the action of gravity. It was invented by George' Atwood or Attwood, a mathematician of sonic eminence, who was b. in 1745, educated at Cambridge, became fellow and tutor of Trinity college in that university, g published a few treatises on mechanics and engineering, and died in 1807. It is found that a body falling freely, passes through 16 ft. in the second, 64 ft. in the first two seconds, 144 ft. in the first three seconds, and so on. Now, as these spaces are so large, we should require a machine of impracticable size to illustrate the relations just men tioned. The object of A. M. is to reduce the scale on which gravity acts without in any way altering its essential features as an accelerating force. The machine consists essen tially of a pulley, P (see fig. 1), moving on its axis With very little friction, with a fine silk cord passing over it, sustaining two equal cylindrical weights, p and g, at its extremities. The pulley rests on a square wooden pillar, graduated on one side in feet and inches, which can be placed in a vertical position by the leveling-screws of the sole on which it stands. Two stages, A. and B, slide along the pillar, and can be fixed at any part of it by means of fixing-screws. One of thesestages, A, has a circular hole cut into it, so as to allow the cylinder, p, to pass freely through it; the other is unbroken, and intercepts the passage of the weight. A series of smaller weights, partly bar-shaped, partly circular, maybe placed on the cylinders in the way repre sented in figs. 2 and 3. A. pendulum usually accompanies the machine, to beat seconds of time. The weight of the cylinders, 0 p and g, equal, they have no tendency to rise or• fall, but are reduced, as it were, to masses without weight. When 1 2 a bar is placed od p, the motion that ensues is due only to the t action of gravity upon it, so that the motion of the whole must be considerably slower than that of the bar falling freely. Sup a pose, for instance, that p and g are each 71 ozs. in weight, and 1 ' that the bar is 1 oz., the force acting on the system—leaving the friction and inertia of the pulley out of account—would. be -h 1 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 4 5 or moving force would bring its own mass through 16 ft. the first second; but when placed on p, this force is exerted not I ... only on the mass of the bar, but on that of p and g, which is 15 PI -11,;,1 times ,greater, so that it has altogether 16 times more matter in the second case to move than in the first, and must, in eon 1 : sequence, move it 16 times more slowly. By a proper
adjustment of weights, the rate of motion may be made as small as we please, or we can reduce the accelerating force to a any fraction of gravity. Suppose the weights to he so adjusted iv that under the moving force of the bar or circular weight the whole moves through 1 in. in the first second, we may tute the following simple experiments: Experiment 1.—Place the tpi. bar on p, and put the two in such a position that the lower sur- face of the bar shall be horizontally in the same plane as the 0 _ . 4' .14 point of the scale, and fix the stage A at 1 inch. When allowed - to descend, the bar will accompany the weight, p, during one second and for 1 in., when it will be arrested by the stage A, after which p and g will continue to move from the momentum Atwood's machine. they have acquired in passing through the first inch Their velocity will now be found to be quite uniform, being 2 in. per second, illustrating the principle that a body itc tuires, at the end of the first second, a velocity per second equal to twice the space it has fallen through. Erp: instead of the bar, the circular weight, place the bottom of p in a line with the 0 point, and put the stage Bat 64 in. 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 let off, the bottom of the cylinder, p, reaches 1 in. in 1 second, 4 in. in 2 seconds, 9 in. in 3 seconds, 16 in. in 4 seconds, 25 in. in 5 seconds, 49 in. in 7 seconds, and 64 in. and the stage in 8 seconds—showing that the spaces described are as the squares of the times. Flip. 3— If the bar be placed as in exp. 1, and the stage A be fixed at 4 in., the bar will accom pany the weight, p, daring 2 seconds, and the velocity acquired in that time by p and will be 4 in. per second, or twice what it was before. In the same manner. if the stage A be placed at 9. 16, 25, etc. in., the velocities acquired in falling through these spaces would be respectively 6, 8, 10, etc. in.-2 in. 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 increments of velocity in equal times. By III :ans 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 question it, as it were, as to the velocity it has acquired.