Tension (physics)

“ At every point of the medium there is a state of stress such that there is tension along the lines of force and pressure in all directions at right angles to these lines, the numerical magnitude of the pressure being equal to that of the tension, and both varying as the square of the resultant force at the point. ”

“ Several physical facts appear to indicate that, in a mechanical separation of matter into its smallest particles, if the mass be very small in relation to the surface, the electrical tension may increase sufficiently for the production of light and heat. ”

“ Let us come back to Earth, and return to facts. My studies in physics led me to believe that all natural forces—gravity, centrifugal force, and even capillary attraction—are, like electricity and magnetism, both positive and negative in their action. If they do not normally alternate between a positive and negative current, as electricity does, they can be made to do so. Gravity and capillary attraction, as we know them, always act positively; that is, they always attract. ”

“ If one consequently considers this fundamental assumption as disproved, then the attempt to establish the whole of physics (including electrodynamics and optics) upon the principle of relative motion, has to be denoted as failed for the time being. ”

“ Whatever a priori conceptions may be indulged therefore, as to the natural fitness of a central force having the same tension at all distances, it has been definitely established by two centuries of continuous and irreversible demonstration, that gravity is not such a force. ”

“ After mass and energy there is one physical quantity which plays a very fundamental part in modern physics, known as Action. Action here is a very technical term, and is not to be confused [Pg 153] with Newton’s ‘Action and Reaction.’ In the relativity theory in particular this seems in many respects to be the most fundamental thing of all. ”

“ The tension of the rope is just large enough to effect the acceleration of the body. That which determines the magnitude of the tension of the rope is the inertial mass of the body.” Guided by this example, we see that our extension of the principle of relativity implies the necessity of the law of the equality of inertial and gravitational mass. ”

“ The long and constant persuasion that all the forces of nature are mutually dependent, having one common origin, or rather being different manifestations of one fundamental power, has made me often think upon the possibility of establishing by experiment, a connection between gravity and electricity, and so introducing the former into the group, the chain of which (including magnetism, chemical force, and heat,) binds so many and such varied exhibitions of force together by common relations. ”

“ A few simple experiments will help us to fix in our minds the great fact of the convertibility of force. Starting with actual visible motion, correlation requires that when it disappears as motion, it should reappear as heat, light, or electricity. If the moving body be elastic like this rubber ball, then its motion is not destroyed when it strikes, but is only changed in direction. ”

“ In the phraseology of our mechanics we define matter and force as if they had an independent existence. But we have no conception of inert matter or of disembodied force. All we know of matter is its pressure and its motion. ”

“ 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. ”

“ The laws of electrodynamics require that such a force be generated, and yet no force can be observed; so we must assume that the mysterious compensations that conceal our motion through the ether are of so perfectly general a nature that they affect mechanics as well as electromagnetics and optics. ”

“ The fundamental dynamical idea of matter, as capable by its motion of becoming the recipient of momentum and of energy, is so interwoven with our forms of thought that, when ever we catch a glimpse of it in any part of nature, we feel that a path is before us leading, sooner or later, to the complete understanding of the subject. ”

“ When there are two components, neither of which is confined to the surface of discontinuity, we may regard the tension as a function of the temperature and the pressures in the two homogeneous masses. The values of the differential coefficients of the tension with respect to these variables may be represented in a simple form if we choose such substances for the components that in the particular state considered each mass shall consist of a single component. ”

“ Transformation of momentum, energy and stresses. The transformation formulas for momentum, energy density and the stresses in the passage from one valid reference system to another system , is definitely determined by deriving them from the components of the world tensor . ”

“ 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. ”

“ If we wish to interpret these lines of force to ourselves as something material in the ordinary sense, we are tempted to interpret the dynamic processes as motions of these lines of force, such that each separate line of force is tracked through the course of time. ”

“ As force is thus conceived, not as an absolute entity acting upon matter, but as a condition of the parts of matter itself, and as a condition determined by the relative masses and distances of these parts, any valid hypothesis of a force or of a motion to account for any set of phenomena is thus seen to imply an assertion as to relative masses and distances which can be more or less readily submitted to experiment or observation and analysis. ”

“ Since the time enters to the second power, the product of mass and acceleration is smaller by the ratio than it would be if the system were at rest. And we conclude, therefore, that the unit of force, or the dyne, in a direction transverse to the line of motion is smaller in a moving system than in one at rest by this same ratio. ”

“ And therefore the globe meets with a resistance, which is to the force by which its whole motion may be either taken away or generated in the time in which it describes two thirds of its diameter moving uniformly forwards, as the density of the medium to the density of the globe. ”

“ Of all those that appear incontrollable, one only remains, gravitation. Will it escape us also? The laws of its action incline us to think so. The nature of electricity is another problem which recalls us to the condition of electric and magnetic forces through space. Behind this question arises the most important problem of all, that of the nature and properties of the substance which fills space,—the ether,—its structure, its motion, its limits, if it possesses any. We find this subject of research, day by day, predominating over all others. ”

“ This is the fundamental conception (not hypothesis) of the theory.... Now in a system of atoms as above defined, let the centers be of equal mass and at equal distances; there will be no difference of pressure on any one center, no moving force will be developed, and the conditions of equilibrium will be satisfied. ”

“ 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. ”

“ Surely no more rigid, constant and unalterable cause could be conceived of than that of the normal motion of the particles of a medium among themselves, which, by an inevitable automatic adjustment arrange their motions so as to produce the effects of gravity. ”

“ Together with inertial forces, something comes into light which was until now be interpreted as the "geometrical structure": the "guidance field", as something real, as an acting power of shaking force in some cases. ”

“ We are dissatisfied with the explanation founded on the hypothesis of attractive and repellent forces directed towards the magnetic poles, even though we may have satisfied ourselves that the phenomenon is in strict accordance with that hypothesis, and we cannot help thinking that in every place where we find these lines of force, some physical state or action must exist in sufficient energy to produce the actual phenomena. ”

“ He says: "Contemplating pure force, we are irresistibly compelled by the relativity of our thought to vaguely conceive some unknown force as the correlative of the known force." This unknown or imperceptible force I contend is electricity and the mental force back of it. All our ideas of matter and motion, he says, are ideas of force. The demonstrated fact of the indestructibility of matter is but another name for the indestructibility of force. ”

“ Now, in establishing by mathematical reasoning the well-known principle of the conservation of energy, it is generally assumed that the force acting between two particles is a function of the distance only, and it is commonly stated that if it is a function of anything else, such as the time, or the velocity of the particles, the proof would not hold. ”

“ Now the conduction of heat is supposed to proceed by an action between contiguous parts of a medium, while the force of attraction is a relation between distant bodies, and yet, if we knew nothing more than is expressed in the mathematical formulae, there would be nothing to distinguish between the one set of phenomena and the other. ”

“ But, these motions remaining the same, their circuits of motion are reduced, the frequency of contact is increased, and heat and light are evolved from the friction. The tendency of all matter under the law of gravitation, considered as an unexplained fact, is toward concentration. The evolution of heat is rather the check put upon this tendency, and, in so far as it exerts any influence, it exerts it in a direction the reverse of gravitation. There is a perpetual and rhythmic antagonism between the forces of integration and disintegration. ”

“ 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 ”

“ Just as the geometrician formulates the properties of lines and surfaces, independently of the irregularities and thicknesses of lines and surfaces as they really exist; so the physicist and the chemist formulate the manifestations of each mode of force, independently of the disturbances in its manifestations which other modes of force cause in every actual case. In works on Mechanics, the laws of motion are expressed without reference to friction and resistance of the medium. Not what motion ever really is, but what it would be if retarding forces were absent, is asserted. ”

“ The word force is foreign to the subject. Yet we find that the mathematical laws of the uniform motion of heat in homogeneous media are identical in form with those of attractions varying inversely as the square of the distance. We have only to substitute source of heat for centre of attraction, flow of heat for accelerating effect of attraction at any point, and temperature for potential, and the solution of a problem in attractions is transformed into that of a problem in heat. ”

“ In other words, the components of the force at any point are determined from the components of acceleration in all parts of the field by the same process by which (in the theories of gravitation, etc.) the value of the potential at any point is determined from the density of matter in all parts of space, except that the sign is to be reversed. Adopting this law, provisionally at leasts we may express it by saying that the components of electrodynamic force are equal to the potentials taken negatively of the components of acceleration of electrical flux. ”

“ Force, when manifested by the mutual approach or cohesion of bodies, is also called attraction, and it is variously denominated, according to the circumstances under which it is observed to act. Thus, the force which holds together the atoms of solid bodies is called cohesive attraction. The force which draws bodies to the surface of the earth, when placed above it, is called the attraction of gravitation. The force which is exhibited by the mutual approach, or adhesion, of the loadstone and iron, is called magnetic attraction, and so on. ”

“ Every particle of matter of which we have any knowledge attracts every other particle in conformity to the law of gravitation; and every material element exerts chemical, electrical, magnetic, thermic, and similar forces upon other elements which in respect to these forces are its correlates. The whole presence of matter to the senses consists in the manifestation of power, in the exhibition of force. All this has been very clearly seen and very explicitly stated by numerous physicists ”

“ If the conception of a material connecting-link throughout space may be supposed to rest on a perception of physical fitness or necessity in such a transmitter of energy, this gives no physical reason to believe the origin of force resident in the one form of matter rather than in the other. ”

“ The beautiful illustration of the presence of magnetic force afforded by this experiment, naturally tends to make us think of the lines of force as something real, and as indicating something more than the mere resultant of two forces, whose seat of action is at a distance, and which do not exist there at all until a magnet is placed in that part of the field. ”