whence X = 2. If there were no loss by friction, B would therefore be
raised 2'; but owing to friction, and doubtless also to the imperfect
flexibility of the rope, the effect is not so great. We may regard
the work done in raising A as so much energy stored up, and when A is
allowed to fall, the energy is reproduced in a modified form.
539. Let us apply the principle of energy to the pile-driving engine to
which we have referred (Art. 536); we shall then be able to find the
magnitude of the force developed in producing the blow. Suppose the
“monkey,” that is the heavy hammer-head, weighs 560 lbs. (a quarter
of a ton). A couple of men raise this by means of a small winch to a
height of 15'. It takes them a few minutes to do so; their energy is
then saved up, and they have accumulated a store of 560 × 15 = 8,400
units. When the monkey falls upon the top of the pile it transfers
thereto nearly the whole of the 8,400 units of energy, and this is
expended in forcing the pile into the ground. Suppose the pile to enter
one inch, the reaction of the pile upon the monkey must be so great
that the number of units of energy consumed in one inch is 8,400. Hence
this reaction must be 8,400 × 12 = 100,800 lbs. If the reaction did not
reach this amount, the monkey could not be brought to rest in so short
a distance. The reaction of the pile upon the monkey, and therefore
the action of the monkey upon the pile, is about 45 tons. This is the
actual pressure exerted.
540. If the soil which the pile is penetrating be more resisting than
that which we have supposed,—for example, if the pile require a direct
pressure of 100 tons to force it in,—the same monkey with the same fall
would still be sufficient, but the pile would not be driven so far with
each blow. The pressure required is 224,000 lbs.: this exerted over a
space of 0"·45 would be 8,400 units of energy; hence the pile would
be driven 0"·45. The more the resistance, the less the penetration
produced by each blow. A pile intended to bear a very heavy load
permanently must be driven until it enters but little with each blow.
541. We may compare the pile-driver with the mechanical powers in one
respect, and contrast it in another. In each, we have machines which
receive energy and restore it modified into a greater power exerted
through a smaller distance; but while the mechanical powers restore the
energy at one end of the machine, simultaneously with their reception
of it at the other, the pile-driver is a reservoir for keeping energy
which will restore it in the form wanted.
542. We have, then, a class of mechanical powers, of which a hammer
may be taken as the type, which depend upon the storage of energy; the
power of the arm is accumulated in the hammer throughout its descent,
to be instantly transferred to the nail in the blow. Inertia is the
property of matter which qualifies it for this purpose. Energy is
developed by the explosion of gunpowder in a cannon. This energy is
transferred to the ball, from which it is again in large part passed
on to do work against the object which is struck. Here we see energy
stored in a rapidly moving body, a case to which we shall presently
return.
543. But energy can be stored in many ways; we might almost say that
gunpowder is itself energy in a compact and storable form. The efforts
which we make in forcing air into an air-cane are preserved as energy
there stored to be reproduced in the discharge of a number of bullets.
During the few seconds occupied in winding a watch, a small charge of
energy is given to the spring which it expends economically over the
next twenty-four hours. In using a bow my energy is stored up from the
moment I begin to pull the string until I release the arrow.
544. Many machines in extensive use depend upon these principles.
In the clock or watch the demand for energy to sustain the motion
is constant, while the supply is only occasional; in other cases
the supply is constant, while the demand is only intermittent. We
may mention an illustration of the latter. Suppose it be required
_occasionally_ to hoist heavy weights rapidly up to a height. If an
engine sufficiently powerful to raise the weights be employed, the
engine will be idle except when the weights are being raised; and if
the machinery were to have much idle time, the waste of fuel in keeping
up the fire during the intervals would often make the arrangement
uneconomical. It would be a far better plan to have a smaller engine;
and even though this were not able to raise the weight directly with
sufficient speed, yet by keeping the engine continually working and
storing up its energy, we might produce enough in the twenty-four hours
to raise all the weights which it would be necessary to lift in the
same time.
545. Let us suppose we want to raise slates from the bottom of a quarry
to the surface. A large pulley is mounted at the top of the quarry,
and over this a rope is passed: to each end of the rope a bucket is
attached, so that when one of these is at the bottom the other is at
the top, and their sizes and that of the pulley are so arranged that
they pass each other with safety. A reservoir is established at the
top of the quarry on a level with the pulley, and an engine is set to
work constantly pumping up water from the bottom of the quarry into
the reservoir. Each of the buckets is partly composed of a large tank,
which can be quickly filled or emptied. The lower bucket is loaded with
slates, and when ready for work, the man at the top fills the tank of
the upper bucket with water: this accordingly becomes so heavy that
it descends and raises the slates. When the heavier one reaches the
bottom, the water from its tank is let out into the lower reservoir,
from which the engine pumps, and the slates are removed from the bucket
which has been raised. All is then ready for a repetition of the same
operation. If the slates be raised at intervals of ten minutes, the
energy of the engine will be sufficient when in ten minutes’ work
it can pump up enough water to fill one tank; by the aid of this
contrivance we are therefore able to accumulate for one effort the
whole power of the engine for ten minutes.