Part 3 (1/2)
In this simple transformation the motion of the pendulum about the axis of suspension may be either vibratory or circular, according to the amount of energy externally applied. In each case, every periodic movement of the apparatus ill.u.s.trates the whole energy operation. The general conditions of the process are almost identical with those in the case of the upward movement of a ma.s.s against gravity (-- 20).
Gravitation is the incepting energy influence of the operation. If the pendulum simply vibrates through a small arc, then, at the highest points of its flight, it is instantaneously at rest. Its energy of motion is here, therefore, zero; its energy of position is a maximum. At the lowest point of its flight, the conditions are exactly reversed.
Here its energy of motion is a maximum, while its energy of position pa.s.ses through a minimum value. The same general conditions hold when the pendulum performs complete revolutions about the central axis. If the energy of motion applied is just sufficient to raise it to the highest point E (Fig. 2), the ma.s.s will there again be instantaneously at rest with maximum energy of position. As the ma.s.s falls downwards in completing the circular movement, its energy of position once more a.s.sumes the kinetic form, and reaches its maximum value at C (Fig. 2), the lowest position. The moving pendulum ma.s.s, so far as its energy properties are concerned, behaves in precisely the same manner as a body vertically projected in the field of the gravitative attraction (-- 20).
This simple energy operation of the pendulum is perhaps one of the most familiar of energy processes. By its means, however, it is possible to ill.u.s.trate certain general features of energy reactions of great importance to the author's scheme.
The energy processes of the pendulum system are carried out through the medium of the material pendulum machine, and are limited, both in nature and degree, by the properties of that machine. As the pendulum vibrates, the transformation of energy of motion to energy of position or vice versa is an example of a reversible energy operation. The energy active in this operation continually alternates between two forms of energy: transformation is continually followed by a corresponding return.
Neglecting in the meantime all frictional and other effects, we will a.s.sume complete reversibility, or that the energy of motion of the pendulum, after pa.s.sing completely into the form of energy of position at the highest point, is again completely returned, in its original form, in the descent. Now, for any given pendulum, the amount of energy which can thus operate in the system depends on two factors, namely, the ma.s.s of the pendulum and the vertical height through which it rises in vibration. If the ma.s.s is fixed, then the maximum amount of energy will be operating in the reversible cycle when the pendulum is performing complete revolutions round its axis of suspension. The maximum height through which the pendulum can rise, or the maximum amount of energy of position which the system can acquire, is thus dependent on the length of the pendulum arm. These two factors, then, the ma.s.s and the length of the pendulum arm, are simply properties of this pendulum machine, properties by which its energy compa.s.s is restricted. Let us now examine these limiting factors more minutely.
It is obvious that energy could readily be applied to the pendulum system in such a degree as to cause it to rotate with considerable angular velocity about the axis of suspension. Now the motion of the pendulum ma.s.s in the lines of the gravitation field, although productive of the same transformation process, differs from that of a body moving vertically upward in that, while the latter has a linear movement, the former is constrained into a circular path. This restraint is imposed in virtue of the cohesive properties of the material of the pendulum arm, and it is the presence of this restraining influence that really distinguishes the pendulum machine from the machine in which the moving ma.s.s is constrained by gravity alone (-- 20). It has been shown that the energy capacity of a body projected vertically against gravity is limited by its ma.s.s only; the energy capacity of the pendulum machine may be likewise limited by its ma.s.s, but the additional restraining factor of cohesion also imposes another limit. In the course of rotation, energy is stored in the material of the pendulum against the internal forces of cohesion. The action is simply that of what is usually termed centrifugal force. As the velocity increases, the pendulum arm lengthens correspondingly until the elastic limit of the material in tension is reached. At this point, the pendulum may be said to have reached the maximum length at which it can operate in that reversible process of transformation in which energy of motion is converted into energy of position. The amount of energy which would now be working in that process may be termed the limiting energy for reversibility. This limiting energy is the absolute maximum amount of energy which can operate in the reversible cycle. It is coincident with the maximum length of the pendulum arm in distortion. When the stress in the material of that arm reaches the elastic limit, it is clear that the transformation against cohesion will also have attained its limiting value for reversibility. This transformation, if the velocity of the pendulum is constant, is of the nature of a storage of energy. So long as the velocity is constant the energy stored is constant. If the elastic limiting stress of the material has not been exceeded, this energy--neglecting certain minor processes (---- 15, 29)--will be returned in its original form as the velocity decreases. If, however, the material be stressed beyond its elastic powers, the excess energy applied will simply lead to permanent distortion or disruption of the pendulum arm, and to a complete breakdown and change in the character of the machine and the a.s.sociated energy processes (-- 5). The physical properties of the material thus limit the energy capacity of the machine. This limiting feature, as already indicated, is not peculiar to the pendulum machine alone. Every energy process embodied in a material machine is limited in a similar fas.h.i.+on by the peculiar properties of the acting materials. Every reversible process is carried out within limits thus clearly defined. Nature presents no exception to this rule, no example of a reversible energy system on which energy may be impressed in unlimited amount. On the contrary, all the evidence points to limitation of the strictest order in such processes.
24. _Transformations of the Moving Pendulum--b. Frictional Transformation at the Bearing Surfaces_
The motion of the pendulum, whether it be completely rotatory or merely vibratory in nature, invariably gives rise to heating at the bearings or supporting points. Since the heating effect is only evident when motion is taking place, and since the heat can only make its appearance as the result of some energy process, it would appear that this persistent heat phenomenon is the result of a transformation of the original energy of motion of the pendulum.
The general energy conditions of the apparatus already adverted to (-- 21) still hold, and the lubricating oil employed in the apparatus being a.s.sumed to have sufficient capillarity or adhesive power to separate the metallic surfaces of bearings and journals at all velocities, then every action of the spindle on the bearings must be transmitted through the lubricant. The latter is, therefore, strained or distorted against the internal cohesive or viscous forces of its material. The general effect of the rotatory motion of the spindle will be to produce a motion of the material of the lubricant in the field of these incepting forces.
To this motion the heat transformation is primarily due. Other conditions being the same, the extent of the transformation taking place, in any given case, is dependent on the physical properties of the lubricant, such as its viscosity, its cohesive or capillary power, always provided that the metallic surfaces are separated, so that the action is really carried out in the lines or field of the internal cohesive forces of the lubricant. In itself, this transformation is not a reversible process; no mechanism appears by which this heat energy evolved at the bearing surfaces could be returned once more to its original form of energy of motion. It may be, in fact, communicated by conduction to the metallic ma.s.ses of the bearings, and thence, by conduction and radiation, to the air ma.s.ses surrounding the apparatus.
Its action in these ma.s.ses is dealt with below (-- 29). The operation of bearing friction, though in itself not a reversible process, really forms one link of a complete chain (-- 9) of secondary operations (transmissions and transformations) which together form a comprehensive and complete cyclical energy process (-- 32).
When no lubricant is used in the apparatus, so that the metallic surfaces of bearings and journals are in contact, the heat process is of a precisely similar nature to that described above (see also -- 16).
Distortion of the metals in contact takes place in the surface regions, so that the material is strained against its internal cohesive forces.
The transformation will thus depend on the physical properties of these metals, and will be limited by these properties. Different metallic or other combinations will consequently give rise to quite different results with respect to the amounts of heat energy evolved.
25. _Stability of Energy Systems_
The ratio of the maximum or limiting energy for reversibility to the total energy of the system may vary in value. If the pendulum vibrates only through a very small arc, then, neglecting the minor processes (---- 24, 29), practically the whole energy of the system operates in the reversible transformation. This condition is maintained as the length of the arc of vibration increases, until the pendulum is just performing complete revolutions about the central axis. After this, the ratio will alter in value, because the greater part of any further increment of energy does not enter into the reversible cyclical process, but merely goes to increase the velocity of rotation and the total energy of the system. The small amount of energy which thus enters the reversible cycle as the velocity increases, does so in virtue of the increasing length of the pendulum arm in distortion. To produce even a slight distortion of the arm, a large amount of energy will require to be applied to and stored in the system, and thus, at high velocities of rotation, the energy which operates in the reversible cycle, even at its limiting value, may form only a very small proportion of the total energy of the system. At low velocities or low values of the total energy, say when the pendulum is not performing complete rotations, practically the whole energy of the system is working in the reversible cycle; but, in these circ.u.mstances, it is clear that the total energy of the system, which, in this case, is all working in the reversible process, is much less than the maximum or limiting amount of energy which might so work in that process. Under these conditions, when the total energy of the system is less than the limiting value for reversibility, so that this total energy in its entirety is free to take part in the reversible process, then the energy system may be termed stable with respect to that process. Stability, in an energy system, thus implies that the operation considered is not being, as it were, carried out at full energy capacity, but within certain reversible energy limits.
We have emphasised this point in order to draw attention to the fact that the great reversible processes which are presented to our notice in natural phenomena are all eminently stable in character. Perhaps the most striking example of a natural reversible process is found in the working of the terrestrial atmospheric machine (---- 10, 38). The energy in this case is limited by the ma.s.s, but in actual operation its amount is well within the maximum limiting value. The machine, in fact, is stable in nature. Other natural operations, such as the orbital movements of planetary ma.s.ses, (-- 8) ill.u.s.trate the same conditions.
Nature, although apparently prodigal of energy in its totality, yet rigidly defines the bounding limits of her active operations.
26. _The Pendulum as a Conservative System_
Under certain conditions the reversible energy cycle produces an important effect on the rotatory motion of the pendulum. For the purpose of ill.u.s.tration, let it be a.s.sumed that the pendulum is an isolated and conservative system endowed with a definite amount of rotatory energy.
In its circular movement, the upward motion of the pendulum ma.s.s is accompanied by a gain in its energy of position. This gain is, in the given circ.u.mstances, obtained solely at the expense of its inherent rotatory energy, which, accordingly, suffers a corresponding decrease.
The manifestation of this decrease will be simply a r.e.t.a.r.dation of the pendulum's rotatory motion. Its angular velocity will, therefore, decrease until the highest alt.i.tude E (Fig. 2) is attained. After this, on the downward path, the process will be reversed. Acceleration will take place from the highest to the lowest point of flight, and the energy stored as energy of position will be completely returned in its original form of energy of motion. The effect of the working of the reversible cycle, then, on the rotatory system, under the given conditions, is simply to produce alternately a r.e.t.a.r.dation and a corresponding acceleration. Now, it is to be particularly noted that these changes in the velocity of the system are produced, not by any abstraction from or return of energy to the system, which is itself conservative, but simply in consequence of the transformation and re-transformation of a certain portion of its inherent rotatory energy in the working of a reversible process embodied in the system. The same features may be observed in other systems where the conditions are somewhat similar.
In the natural world, we find processes of the same general nature in constant operation. When any ma.s.s of material is elevated from the surface of a rotating planetary body against the gravitative attraction, it thereby gains energy of position (-- 20). This energy, on the body's return to the surface in the course of its cycle, reappears in the form of energy of motion. Now the material ma.s.s, in rising from the planetary surface, is not, in reality, separated from the planet. The atmosphere of the planet forms an integral portion of its material, partakes of its rotatory motion, and is bound to the solid core by the mutual gravitative forces. Any ma.s.s, then, on the solid surface of a planet is, in reality, in the planetary interior, and the rising of such a ma.s.s from that surface does not imply any actual separative process, but simply the radial movement, or displacement of a portion of the planetary material from the central axis. If the energy expended in the upraisal of the ma.s.s is derived at the expense of the inherent rotatory energy of the planet, as it would be if the latter were a strictly conservative energy system, then the raising of this portion of planetary material from the surface would have a r.e.t.a.r.ding effect on the planetary motion of rotation. But if, on the other hand, the energy of such a ma.s.s as it fell towards the planetary surface were converted once more into its original form of energy of axial motion, exactly equivalent in amount to its energy of position, it is evident that the process would be productive of an accelerating effect on the planetary motion of rotation, which would in magnitude exactly balance the previous r.e.t.a.r.dation. In such a process it is evident that energy neither enters nor leaves the planet. It simply works in an energy machine embodied in planetary material. This point will be more fully ill.u.s.trated later. The reader will readily see the resemblance of a system of this nature to that which has already been ill.u.s.trated by the rotating pendulum.
In the meantime, it may be pointed out that matter displaced from the planetary surface need not necessarily be matter in the solid form. All the operations mentioned above could be quite readily--in fact, more readily--carried out by the movements of gaseous material, which is admirably adapted for every kind of rising, falling, or flowing motion relative to the planetary surface (-- 13).
27. _Some Phenomena of Transmission Processes--Transmission of Heat Energy by Solid Material_
The pendulum machine described above furnishes certain outstanding examples of the operation of energy transformation. It will be noted, however, that it also portrays certain processes of energy transmission.
In this respect it is not peculiar. Most of the material machines in which energy operates will furnish examples of both energy transmissions and energy transformations. In some instances, the predominant operation seems to be transformation, in others, transmission; and the machines may be cla.s.sified accordingly. It is, however, largely a matter of terminology, since both operations are usually found closely a.s.sociated in one and the same machine. The apparatus now to be considered is designed primarily to ill.u.s.trate the operative features of certain energy transmissions, but the description of the machines with their allied phenomena will show that energy transformations also play a very important part in their const.i.tution and working.
A cylindrical metallic bar about twelve inches long, say, and one inch in diameter, is placed with its ends immersed in water in two separate vessels, A and B, somewhat as shown.