The Energy System of Matter: A Deduction from Terrestrial Energy PhenomenaWeir, James, active 1883-1912
Science
The Energy System of Matter: A Deduction from Terrestrial Energy Phenomena
Weir, James, active 1883-1912
Force and energy
It will be readily seen, however, that the working of this rotating
pendulum machine, when considered as a whole, is of a nature somewhat
different from that of the simple pendulum machine in that the energy of
position of the former (as measured by the vertical displacement of M
and M{1} in rotation) and its energy of rotation must increase
concurrently, and also in that the absolute maximum value of this energy
of position will be attained when the pendulum masses reach merely the
horizontal level HL in rotation. The machines are alike, however, in
this respect, that the transformation of energy of motion into energy of
position is in each case a completely reversible process. In the working
of the rotating pendulums the limiting amount of energy which can
operate in this reversible process is dependent on and rigidly defined
by the maximum length of the pendulum arms; the longer the arms, the
greater is the possible height through which the masses at their
extremities must rise to attain the horizontal position in rotation. It
will be clear also that it is not possible for the whole energy of the
rotating system to work in the reversible process as in the case of the
simple pendulum. As the pendulum masses rise, the ratio of the limiting
energy for reversibility to the total energy of the system becomes in
fact smaller and smaller, until at the horizontal or position of maximum
energy it reaches a minimum value. This is merely an aspect of the
experimental fact that, as the pendulum masses approach the ultimate
horizontal position, a much greater increment of energy to the system is
necessary for their elevation through a given vertical distance than at
the lower levels. A larger proportion of the applied energy is, in fact,
stored in the material of the system in the form of energy of strain or
distortion.
The two points which this system is designed to illustrate, and which
it is desirable to emphasise, are thus as follows. Firstly, as the whole
system rotates, the movement of the pendulum masses M and M{1} from the
lower to the higher levels, or from the regions of low to those of
higher velocity, is productive of a transformation of the rotatory
energy of the system into energy of position--a transformation of the
same nature as in the case of the simple pendulum system. Neglecting the
minor transformations (§§ 24, 29), this energy process is a reversible
one, and consequently, the return of the masses from the higher to the
lower positions will be accompanied by the complete return of the
transformed energy in its original form of energy of rotation. Secondly,
the maximum amount of energy which can work in this reversible process
is always less than the total energy of the system. The latter,
therefore, conforms to the general condition of stability (§ 25).
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