Deceleration

“ In a railroad-train standing still or moving at a uniform speed, the passengers are comfortable; but if that same train is suddenly brought to rest when going at a high speed, say by collision, the consequences are horrible in the extreme, and the horror is caused simply by the suddenness of the change. The same is true all through nature and human nature. Any sudden change in the velocity of any mass has its exact counterpart in any sudden change in the conditions of living of any man or woman, or any sudden change in the conditions under which any organization must carry on its business. ”

“ That which we call acceleration pertains wholly to deflection, or in very small part to speed, as loss of speed by one and gain by another.
There is still another set of relations to be considered. A body is composed of particles; in order that they should remain within the sphere of the body their paths must be composite, and in order that their paths may be composite there must be a sufficient number of internal collisions to deflect them and retain them within that sphere. If the body itself is moved the paths of the several particles in the average must thus be rendered less composite ”

“ So, in the revolution of the sun and the earth about a common axis, acceleration is chiefly deflection, being positive at perihelion and negative at aphelion. Thus we have a well-known astronomical example of acceleration, and find it deflection and increase or decrease of bodily speed, and now we must refer this acceleration of speed in the body to deflection in the particles of which it is composed. ”

“ If, however, we push it rapidly forward, the resistance greatly increases, for the air-molecules must have time to change their position, and we encounter them in their passage. If, now, we increase the velocity of the motion to the highest speed ever attained by a locomotive—say, one and one-fifth mile per minute—we should encounter still more particles, and find a resistance which no human muscle could overcome. Increase that velocity ten times, to twelve miles a minute, the velocity of sound, and the air would oppose such a resistance that our wooden board would be shivered into splinters. ”

“ Furthermore we may remark that any velocity once imparted to a moving body will be rigidly maintained as long as the external causes of acceleration or retardation are removed, a condition which is found only on horizontal planes; for in the case of planes which slope downwards there is already present a cause of acceleration, while on planes sloping upward there is retardation; from this it follows that motion along a horizontal plane is perpetual; for, if the velocity be uniform, it cannot be diminished or slackened, much less destroyed. ”

“ No one is likely to suggest a theory that man’s convenience had been consulted by Nature at any time, or that Nature has consulted the convenience of any of her creations, except perhaps the Terebratula. In every age man has bitterly and justly complained that Nature hurried and hustled him, for inertia almost invariably has ended in tragedy. Resistance is its law, and resistance to superior mass is futile and fatal.
Fifty years ago, science took for granted that the rate of acceleration could not last. ”

“ So that if the excess of motion or velocity in the power is so great as to overcome all that resistance which commonly arises from the friction or attraction of contiguous bodies, as they slide by one another, or from the cohesion of bodies that are to be separated, or from the weights of bodies that are to be raised: the excess of the force remaining, after all these resistances are overcome, will produce an acceleration of motion thereto, as well in the parts of the machine, as in the resisting body. ”

“ However, the effects of this wave of acceleration, in particular the corresponding loss of energy, are in most cases negligible, that is to say not only in ordinary mechanics and in the motions of the heavenly bodies, but even in the radium rays, where the velocity is very great without the acceleration being so. We may then confine ourselves to applying the laws of mechanics, putting the force equal to the product of acceleration by mass, this mass, however, varying with the velocity according to the laws explained above. ”

“ Why does the velocity of its "violent" motion decrease as it rises, while that of its "natural" fall increases as it descends. If we mark closely the relation between these two facts, the problem will solve itself. We shall see, as Galileo did, that the decrease of velocity in rising and the increase of velocity in falling are one and the same phenomenon, viz., an increase of velocity towards the earth. Accordingly, it is not a place that is assigned to the body, but an increase of velocity towards the earth. ”

“ A.--All bodies fall with the same velocity, when there is no resistance from the atmosphere, as is shown by the experiment of letting fall, from the top of a tall exhausted receiver, a feather and a guinea, which reach the bottom at the same time. The velocity of falling bodies is one that is accelerated uniformly, according to a known law. When the height from which a body falls is given, the velocity acquired at the end of the descent can be easily computed. It has been found by experiment that the square root of the height in feet multiplied by 8.021 will give the velocity. ”

“ As to the wave of acceleration, this is a perturbation altogether analogous to light waves, which starts from the electron at the instant when it undergoes an acceleration, and which is then propagated by successive spherical waves with the velocity of light. Whence follows: in a straight and uniform motion, the energy is wholly conserved; but, when there is an acceleration, there is loss of energy, which is dissipated under the form of luminous waves and goes out to infinity across the ether. ”

“ Velocity is the rate of motion of a body in a given direction. For example, a bullet may have a velocity of 1300 ft. a [Pg 87] second upwards. Acceleration is the rate of change of velocity in a given direction, or the change of velocity in a unit of time. A train starting from a station gradually increases its speed. The gain in velocity during one second is its acceleration. When the velocity is decreasing, as when a train is slowing down, the acceleration is opposite in direction to the velocity. A falling body falls faster and faster. ”

“ These accelerations are objective in that they exist to the same degree for all observers in the objective space and time world of science. To take a simple case, if we allow a stone to fall on our foot, its velocity of impact will vary with the height whence it was released. We cannot say that these variations in velocity are to be ascribed to a mere optical distortion of the light rays reflected from the stone. We know, indeed, that quite aside from any visual image of motion, the pain we experience will tell the tale. ”

“ General Principles.—In order that the velocity of every piece of a machine may be uniform, it is necessary that the forces acting on each piece should be always exactly balanced. Also, in order that the forces acting on each piece of a machine may be always exactly balanced, it is necessary that the velocity of that piece should be uniform.
An excess of the effort exerted on any piece, above that which is necessary to balance the resistance, is accompanied with acceleration; a deficiency of the effort, with retardation. ”

“ Further, although any velocity which a body may have acquired through natural fall is permanently maintained so far as its own nature [suapte natura] is concerned, yet it must be remembered that if, after descent along a plane inclined downwards, the body is deflected to a plane inclined upward, there is already existing in this latter plane a cause of retardation; for in any such plane this same body is subject to a natural acceleration downwards. ”

“ From observation we now know the greatest acceleration and maximum velocity of an earth particle likely to be encountered; and these are measures of the destructivity. The engineer is therefore dealing with known forces, and he has to bear in mind that these are chiefly applied in a horizontal direction. A formula connecting the acceleration requisite to overturn bodies of different dimensions has been given. The acceleration which will fracture or shatter a column firmly fixed at its foundation to the moving earth may be expressed as follows:—
where
a=the acceleration per sec. ”

“ A is then detached, and a body B is attached to the same thread, and the same or another force is made to act until the increment of length again is α, and the acceleration of B is noted. The experiment is then renewed with both A and B until the increment of length is β. The four accelerations observed should be proportional. Here we have an experimental verification of the law of acceleration enunciated above. Again, we may consider a body under the action of several threads in equal tension, and by experiment we determine the direction of those threads when the body is in equilibrium. ”

“ The real question is this: What is the figure representing the acceleration of the motion of a piston, controlled by a crank which revolves with a uniform velocity? I stated it to be a right-angled triangle, and indicated, as I supposed, clearly enough, a simple method by which this could be shown. Your correspondent claims that the calculation, according to my own rule, gives a figure of a totally different form, and one that shows the acceleration, as well as the motion, to be reduced to zero at the commencement of the stroke. ”

“ On the other hand, a body thrown upward has uniformly retarded motion, that is, its acceleration is downward. The velocity acquired by a falling body in unit time is called its acceleration, or the acceleration due to gravity, and is equal to 32.16 ft. (980 cm.) per second, downward, each second of time. In one second, therefore, a falling body gains a velocity of 32.16 ft. ”

“ Would it not be simpler to consider the law of acceleration as a definition in all cases, and to regard the experiments in question, not as verifications of this law, but as verifications of the principle of reaction, or as demonstrating that the deformations of an elastic body depend only on the forces to which this body is subjected? ”

“ But in this case, each impulse produces its effect instantaneously, and the time is employed, not in the transition from any cause to its effect, but in the intervals between the action of the several causes, during which intervals the body goes on with the velocity already communicated to it. In each impulse, force produces motion: and the motion goes on till a new change takes place, by the same kind of action. The force may be said, in the language employed by the Critic, to be transformed into momentum ”

“ Hence it is clear that equal spaces will be traversed in equal times by two bodies, one of which, starting from rest, moves with a uniform acceleration, while the momentum of the other, moving with uniform speed, is one-half its maximum momentum under accelerated motion. ”

“ It is, however, not difficult to lead any person of a speculative habit 236 of thought to see that the retardation which constantly takes place in the motion of all bodies when left to themselves, is, in reality, the effect of extraneous forces which destroy the velocity. A top ceases to spin because the friction against the ground and the resistance of the air gradually diminish its motion, and not because its motion has any internal principle of decay or fatigue. ”

“ Let us take the problem of a falling stone. There is a relative acceleration of 32 feet per second per second—of the stone relative to ourselves or of ourselves relative to the stone. Which end of the relation must we choose? The one indicated by molecular bombardment? Well, the stone is not bombarded; it is falling freely in vacuo. But we are bombarded by the molecules of the ground on which we stand. Therefore it is we who have the acceleration; the stone has zero acceleration, as the man in the lift supposed. ”

“ Therefore, any speed up to a little below that of light could be obtained, and that bogey man so often ignored in scientifiction, acceleration, was disposed of at the start, since there was nothing that had a tendancy to stay behind. ”

“ It is true that the effects of the wave of acceleration constantly accumulate, but this accumulation itself is so slow that thousands of years of observation would be necessary for it to become sensible. ”

“ After a very short latent period, not yet actually proved but whose existence is highly probable, growth commences with a velocity which very {145} rapidly increases to a maximum. The curve quickly,—almost suddenly,—changes its direction, as the velocity begins to fall; and the rate of fall, that is, the negative acceleration, proceeds at a slower and slower rate, which rate varies inversely as some power of the time, and is found in both of the above-quoted experiments to be very ap­prox­i­mate­ly as 1 ⁄ T2 . ”

“ We daily witness the gradual retardation and final stoppage of things projected from the hand or otherwise impelled; and we equally often witness the change from Rest to Motion produced by the application of force. But truly to represent these transitions in thought, we find impossible. For a breach of the law of continuity seems necessarily involved; and yet no breach of it is conceivable. A body travelling at a given velocity cannot be brought to a state of rest, or no velocity, without passing through all intermediate velocities. ”

“ Hence rigorously uniform movement is limited to infinitesimal time.
Varied movement is that whose rate is continually changing. It is divided into accelerated and retarded; and, when the acceleration or the retardation arises from a constant action which in equal times imparts equal momentums, the movement is said to be uniformly accelerated or retarded.
Epilogue.—The explanation we have given of space, duration, and movement suffices, if we are not mistaken, to show what is the true nature of the only continuous quantities which can be found in the real order of things. ”