Kinetics

“ Introduction.—The First Law of Motion.—The Experiment of Galileo from the Tower of Pisa.—The Space is proportional to the Square of the Time.—A Body falls 16' in the First Second.—The Action of Gravity is independent of the Motion of the Body.—How the Force of Gravity is defined.—The Path of a Projectile is a Parabola.
INTRODUCTION.
483. Kinetics is that branch of mechanics which treats of the action of forces in the production of motion. We shall find it rather more difficult than the subjects with which we have been hitherto occupied ”

“ Every action of our body as a motive apparatus depends not less but more upon the proper co-operation of the muscles than upon the force of their contraction. In order to execute a composite motion, like a leap, the muscles must begin to work in the proper order, and the energy of each one of them must increase, halt, and diminish, according to a certain law, so that the result shall be the proper position of the limbs, and the proper velocity of the center of gravity in the proper direction. ”

“ The Idea of Energy Derived from the Kinetic Theory.—The notion of energy is not less clear than the notion of matter, it is only more novel to our minds. We are led to it by the mechanical conception which now dominates the whole of physics, the kinetic conception, according to which in the sensible universe there are no phenomena but those of motion. Heat, sound, light, with all their manifestations so complex and so varied, may, according to this theory, be explained by motion. ”

“ But to treat of Mechanics is not my present business. I was only willing to show by those examples the great extent and certainty of the third Law of motion. For if we estimate the action of the agent from its force and velocity conjunctly; and likewise the reaction of the impediment conjunctly from the velocities of its several parts, and from the forces of resistance arising from the attrition, cohesion, weight, and acceleration of those parts; the action and re-action in the use of all sorts of Machines will be found always equal to one another. ”

“ If T denote the kinetic energy, we may say then that the sum T + V is in any interval of time increased by an amount equal to the work done by the extraneous forces. In particular, if there are no extraneous forces T + V is constant. Again, if some of the extraneous forces are due to a conservative field of force, the work which they do may be reckoned as a diminution of the potential energy relative to the field as in § 13. ”

“ And so, summing up our conclusions regarding Force and Energy and Motion in Inorganic Substance—and then in Organic Substance—we arrive at an understanding of the Basic Proposition of the Theory of Dynamic Thought, which is as follows:
Basic Proposition.—That All forms and exhibition of Force, Energy, Motion and Power are manifestations of Vital-Mental Action. And that, consequently, at the last there is no Force but Vital-Mental Force; no Energy but Vital-Mental Energy; no Motion but Vital-Mental Motion; no Power but Vital-Mental Power. ”

“ Now it is proved by experiment, that an impulse requisite to project a body sixteen feet upwards, will make it ascend that height in one second of time; here, then, the times of ascent and descent are equal. But, supposing it be required to throw a stone twice that height, the force must be proportionally greater. You see, then, that the impulse of projection, in throwing a body upwards, is always equal to the action of the force of gravity during its descent ”

“ Another form of kinetic energy is called Potential Energy, which is in reality the capacity of a body for doing work owing to its position. For example we may take an ordinary eight-day clock. When the weights are wound up, they have a certain amount of potential energy stored up, which will counteract the friction of the wheels and the resistance of the air on the pendulum. Or, again, we have the example of a water-wheel: first the water in the reservoir, being higher than the wheel, has an amount of potential energy. ”

“ Caroline. Yes; I have the most weight, he the greatest velocity; so that upon the whole our momentums are equal. But you said, Mrs. B., that the power should be greater than the resistance, to put the machine in motion; how then can the plank move if the momentums of the persons who ride are equal?
Mrs. B. Because each person at his descent touches and pushes against the ground with his feet; the reaction of which gives him an impulse which produces the motion; this spring is requisite to destroy the equilibrium of the power and the resistance, otherwise the plank would not move. ”

“ Seymour; “viz. some exertion which is called Force; thus the force of my hand put your ball in motion; while gravitation was the force which made it fall to the earth; and I must, moreover, inform you, that a body always moves in the direction of the force which impels it, and with a velocity, or rate of motion, which is proportional to its degree, or strength; and, were there no other forces in action but that which originally produced the motion, the body would proceed onwards in a right line, and with a uniform velocity for ever.” ”

“ The force exercised by the human hand in lifting a weight either with or without rope and pulley is, in every definitional sense of the word, mechanical force. For the arm and hand are only the implements, or mechanical contrivances of nature, by which the will-power transmutes itself into work, or, more properly speaking, transmits itself from the point of force-generation to that of force-expenditure. And this is precisely the office performed by all mechanical contrivances for the transmission--not transmutation--of force. ”

“ It is an universal law of nature that action and reaction are equal and opposite. Hence when any agent acts to set a body in motion, or to modify its motion in any way, the body reacts on the agent, and this force has been called the Kinetic reaction. ”

“ You are quite right; and the return of the ball, after having struck the wall, affords an example of what is termed reflected motion, upon which I shall have to remark when we come to the interesting subject of ‘Compound Forces;’ but at present, my only wish is to render the property of elasticity intelligible to you. It is a force of very extensive application; there is scarcely a machine wherein the elasticity of one or more solids is not essentially concerned. Nature, also, avails herself of this property to accomplish many of her purposes. ”

“ But our muscular sense is not limited to the perception of free motion: we constantly find it restricted or forcibly resisted. This "muscular action impeded" is another direct sense, that of "force"; and attempts to analyse it into anything simpler than itself have hitherto resulted only in confusion. By "force" is meant primarily muscular action not accompanied by motion. Our sense of this teaches us that space, though roomy, is not empty: it gives us our second scientific inference—what we call "matter." ”

“ At present it is being more and more recognized that it was only an unproved assumption, which the development of science daily proves to be more untenable.
46. Energetic Mechanics. In the light of our previous observations the branch of science traditionally known as mechanics appears as the science of work and of kinetic energy. Furthermore, statics [139] is shown to be the science of work, while dynamics, besides treating of kinetic energy in itself, also treats of the phenomena of the change of work into kinetic energy, and vice versa. ”

“ If our ideas possess a certain degree of artificiality, this is also true of others which have long since been adopted into mechanics. The apparent change in rate of a moving clock, and the apparent change in length and mass of a moving body, are completely analogous to that apparent change in energy of a body in motion, which we have long been accustomed to call its kinetic energy. ”

“ One and the same movement may vary in velocity, as in watching the ascent or descent of a projectile thrown up vertically. So different movements may present a difference of velocity as in the sequences of a ballet. Such contrasts plainly answer to the most favorable mode of expending motor energy. Again, our movement may be followed by another of different direction; that is to say, one that involves the action of fresh muscular elements, or a change in the relative amounts of action of two or more combining muscles. ”

“ From the standpoint of the principle of relativity, one of the most interesting quantities in mechanics is the so-called kinetic energy, which is the increase in energy attributed to a body when it is set in motion with respect to an arbitrarily chosen point of rest. ”

“ Equilibrium.—There are typical examples of almost as striking increase of muscle sensation, or rather of ability to distinguish minute differences in muscular sensation, noted in those who train this faculty carefully. Acrobats succeed in developing wonderful control over muscles and marvelous response to slight disturbance of equilibrium. The ordinary individual has comparatively small balancing powers, but the slack-rope performer seems almost to defy the laws of gravity, because he has learned so to coordinate all muscular action as to enable him to maintain his balance. ”

“ Statics and Dynamics.—We must first turn our attention to a technical distinction of Mechanics into two portions, according as the forces about which we reason produce rest, or motion; the former portion is termed Statics, the latter Dynamics. If a stone fall, or a weight put a machine in motion, the problem belongs to Dynamics; but if the stone rest upon the ground, or a weight be merely supported by a machine, without being raised higher, the question is one of Statics.
3. Equilibrium.—In Statics, forces balance each other, or keep each other in equilibrium. ”

“ Therefore must the muscular force be sufficient for both the weight and the velocity.
Sir Isaac Newton teaches that the motion of an animal is a series of falls, received and prevented by advancing one leg after the other. Since the force of gravity is constant, the velocity does not affect it. ”

“ The kinetic energy, or capacity of a body for doing work against resistance, is found experimentally to be measured by half the square of its velocity multiplied by its mass. It is further found by experiment that, so far as we can measure, the energy of a material system not acted upon from without remains constant. ”

“ It is from our dynamic Activity also that we derive our conception of Force. Force, though it is studied scientifically in the measurement of the great natural forces which operate constantly, is originally known to us in the stress or pressure to which muscular exertion in contact with a material body gives rise. Such a force if it could be correctly measured, would record the rate at which Energy was undergoing transmutation, and it is from such experience of pressure that our idea of Force is originally derived. ”

“ Commencing with the generalization that " a mechanical force, or the cause of a mechanical motion, we know to be in general the condition of a difference of pressure," he infers, "hence it appears that if a general mechanical theory is possible, the ultimate property of matter must be conceived to be a mutual repulsion of its parts, and the indubitable Newtonian law of universal attraction be deduced herefrom, under the actual conditions of the world. ”

“ Bodies are equally incapable of changing their actual state, whether it be of motion or of rest. You know that it requires force to put a body which is at rest in motion; an exertion of strength is also requisite to stop a body which is already in motion. The resistance of the body to a change of state, in either case, arises from its inertia.
Emily. In playing at base-ball I am obliged to use all my strength to give a rapid motion to the ball ”

“ Thus 'tis a Law of Motion, discover'd by Experience, that the Moment or Force of any Body in Motion is in the compound Ratio or Proportion of its solid Contents and its Velocity; and consequently, that a small Force may remove the greatest Obstacle or raise the greatest Weight, if by any Contrivance or Machinery we can encrease the Velocity of that Force, so as to make it an Overmatch for its Antagonist. ”

“ Whatever produces, or tends to produce, motion, or an alteration in its direction, is mechanical force, no matter from what force-centre it may start. When we can definitely determine the centre of vital force, as exercised in building up vital structure, not in wielding pickaxes, it is to be hoped we shall be able to distinguish, by the proper correlates, vital force from that which is mechanical. But the task is manifestly a hopeless one with the materialists. ”

“ But experience furnishes innumerable examples of the production of kinetic energy in a body previously at rest, when no impact is discernible as the cause of that energy. In all such cases, the presence of a second body is a necessary condition; and the amount of kinetic energy, which its presence enables the first to gain, is strictly dependent on the relative positions of the two. Hence the phrase energy of position, which is frequently used as equivalent to potential energy. ”

“ Look here, Phil, I’ll tell you something that I’m beginning to get hold of which isn’t to be got from any book, and yet is a fundamental principle of athletics. In every exercise that requires a skilled motion or great speed, you’ll find that there’s a peculiar kind of final snap or twist that gives the motion or the speed; and you’ve got to master this if you want the highest results. Without it a strong man is powerless, and with it a weak man often slips to the front. ”

“ We are accustomed to regard the whole energy of a moving ponderable body as additively composed of a part, which varies only (regardless of the internal state of the body) with its speed: the energy of the kinetic motion, and a second part which (regardless of the speed) only depends on the internal state, namely on the density, temperature and chemical composition: the internal energy of the body. ”