Experimental Mechanics / A Course of Lectures Delivered at the Royal College of Science for Ireland

by Robert S. Ball

THE STORING OF ENERGY.

538. Our study of the subject will be facilitated by some considerations founded on the principles of energy. In the experiment of [Fig. 71] let a be 14 lbs., and b, on the ground, be 56 lbs. Since the rope is 15' long, a is 3' from the ground, and therefore 6' from the pulley. I raise a to the pulley, and, in doing so, expend 6 × 14 = 84 units of energy. Energy is never lost, and therefore I shall expect to recover this amount. I allow a to fall; when it has fallen 6', it is then precisely in the same condition as it was before being raised, except that it has a considerable velocity of descent. In fact, the 84 units of energy have been expended in giving velocity to a. b is then lifted to a maximum height x, in which 56 × x units of energy have been consumed. At the instant when b is at the summit x, a must be at a distance of 6 + x feet from the pulley; hence the quantity of work performed by a is 14 × (6 + x). But the work done by a must be equal to that done upon b, and therefore

14(6 + x) = 56 x,

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.