# Acceleration

## weight, motion, velocity, body, axis, equal, force, stage, time and wheel

ACCELERATION is the increase of velocity in a moving body, caused by the continued action of the motive force. When bodies in motion pass through equal spaces in equal times, or, in other words, when the velocity of the body is the same during the period that the body is in motion, it is termed uniform motion, of which we have a familiar instance in the motion of the hands of a clock over the face of it ; but a more correct illustration is the revolution of the earth on its axis. In the case of a body moving through unequal spaces in equal times, or with a varying velocity, if the velocity increase with the duration of the motion, it is termed accelerated motion ; but if it decrease with the duration of the motion, it is termed retarded motion. A stone thrown up in the air, affords an illustration of both these cases, the motion during the ascent being retarded by the force of gravity, and accelerated by the same during the descent of the stone. All bodies have a tendency to preserve their state, either of rest or of motion; so that if a body were set in motion, and the moving force were withdrawn, the body, if unopposed by any force, would continue to move with the same velocity it had acquired at the instant the moving force was withdrawn. And if a body in motion be acted upon by a con stant force (as the force of gravity), the motion becomes accelerated, the velocity increasing as the times, and the whole spaces passed through increasing as the square of the times ; whilst the proportional spaces passed through during passed equal portionsof time, will be as the odd numbers, I, 3, 5, 7, &c. ; and the space over in any portion of time, will be equal to half the velocity acquired at the end of such time, which results will be better brought to view in the follow ing Table.

Times. Velocities. Spaces for each Time. Total Space.

I 1 1 1 1=1' 2 2 3 3 + 1=4=--2 3 3 5 5 + 3 + 1=9=3' '4 4 7 7 +5 +3 It has been ascertained by experiment, that a body falling freely by its own weight from a state of rest, will descend through 164 feet in the first second of time, and will have acquired a velocity of 32; feet; but from the rapidity with which the velocity increases, we cannot extend the experiment, for in only four seconds, a body falling freely would pass through a space of 256 feet. But by an ingenious contrivance of the late Mr. Attwood, of Cambridge, the laws of motion above laid down may be verified experimentally. The machine is called " Attwood's machine," after the name of the inventor ; and the principle of its action consists in counteracting a portion of the gravitating power of a body, by the gravitating power of a smaller body ; so that the absolute velocity, and the spaces passed through, shall be less than in the case of bodies descending freely, whilst, as the force is constant, the same ratio of progression will hold in both cases. The annexed figure represents one of these machines, as constructed by Mr. Toplis. a a a is a triangular frame, upon three moveable legs ; 11, a small platform suspended from it by a universal joint cc, and supporting two upright standards d d, in which the axis of a light brass wheel e revolves with very little friction. Over a groove in the periphery of the wheel, passes a very light and pliable silk thread, from the ends of which hang two equal weights f, g. Into the under side of b is screwed a square rod h, descending to the floor, • to which it is secured, in a perpendicular position, by small pins passing through holes in the claws at i i. On the face of the rod is a scale of inches. k is a brass guide, fixed at the upper part of the rod h, so that when the to of the weight g touches the lower side of k, the under side of g is on a level with the top, or commencement of the scale ; 1 is a small stage, movable along the rod h, and having a hole in it sufficiently large for the weight g to pass : on one side is a tightening screw m. n is another movable stage, fitted with a tightening screw o, as also a fork p, turning upon a hinge. The experiments are conducted as follows :—A small cir cular weight is placed upon g, which is pulled up to the top of the scale, and the stage a is screwed to the rod h, on a level with the lower part of the weight f, which is held down upon it by the fork p. Upon

releasing f from the fork, the weight g descends with a slow, but gradually acce lerated motion, and the number of inches the weight has descended, at each erne cessive beat of a pendulum (suspended fiom another triangle) is observed upon the scale ; and if the additional weight be such as to cause g to descend through three inches in the first second, then it will cause it to descend through 1 foot in two seconds, and through 6-1 feet in five seconds. If the additional weight be removed, and a small bar of equal weight, but of a length exceeding the diameter of the hole in 1, be placed upon g, and the stage 1 be set at any division of the scale, at which the weight would, arrive at the end of any number of seconds, the stage will intercept the bar in its descent, and the weight will continue to descend with the velocity it had acquired upon reaching 1. Thus if the velocity at the end of the second second be two feet, in which case the weight would have descended one foot in that time, if the stage be set at one foot upon the scale, it will intercept the bar at the end of the second second, and the weight g will move with a uniform velocity of two feet per second, through the remaining portion of its descent. If it is required to illustrate the case of retarded motion, the small circular weight is placed upon the weights, and a similar small weight upon the weight f, so that g, still outweighing f, will descend; but as soon as the stage 1 intercepts the bar with the small weight upon it, f becomes the heaviest, and g will descend with a velocity decreasing as the squares of the times, counted from the time of g passing the stage 1. To diminish as much as possible the friction of the axis of the wheel e, which carries the line from which the weights hang, Mr. Attwood, instead of causing the axis to turn in fixed bearings, supported it upon the peripheries of four anti-friction wheels, fixed upon the ends of two spindles placed parallel to each other, and as close together as the diameters of the wheels would allow. The sliding or rubbing motion of the axis of the wheel e, is by this means transferred to the spindles of the anti friction wheels, (for the axis does not slide, but it rolls over their peripheries,) and the amount of the friction becomes diminished in the proportion of the dia meter of the axis of the wheel e, to the diameter of the anti-friction wheels. This is an extremely beautiful and effectual arrangement, but requires great care and nicety of execution; it also enhances greatly the cost of the Instrument. Mr. Top lis's method of supporting the axis of the wheel is less complex and costly, whilst it is attended with very little friction, owing to the extremely small quantity of rubbing surface. His plan is as follows: the axis consists of a short piece of steel, not equal in length to the distance between the two standards, between which it is supported. In each end of the axis a conical recess is formed, terminated by a short cylindrical one; these conical recesses receive the ends of two studs or pivots, supported by the vertical standards, and formed into cones more acute than the conical recesses. By this means the rubbing surfaces are reduced to a mere Iine, forming a species of knife-edge support; the axis is kept steady by the different obliquities of the external and internal cone ; and the end of the pivot cannot wear down, as it does not reach the bottom of the cylindrical part of the recess. For the ate of portability, the legs of the triangle, and the square rod h, are jointed in the middle, and the wheel, stages, &c. can be packed separately in a small case. Altogether we think Mr. Toplis has rendered the instrument much more portable, and less liable to injury, whilst he has very much diminished the cost without impairing its efficiency.