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The Mechanical Powers. A machine is an instrument by means of which force is applied to the performance of work, generally by changing the direction of the forceas the capstan, by which sailors raise the anchor; the crane, by which stones or other heavy weights are raised ; or the lever, by which a heavy object is moved upwards by pressing down the other end. Such contrivances do not increase the force applied, but merely afford the means by which it may be directed more advantageously to the end in view. The simple machines used for this purpose, or the MECHANICAL POWERS, as they have been called, are usually considered to be six in number—the Lever, the Wheel and Axle, the Pulley, the Inclined Plane, the Screw, and the Wedge.

I.-The Lever. A lever, from Latin levo, to raise, means that which raises or lifts. It is a body of any form fixed at a point about which it can move, called the centre of motion, or the fulcrum [Latin, “a prop ']; thus, when the fire is stirred with a poker, the poker is, for the time being, a lever, and the bar on which it rests is the centre of motion, or fulcrum. Levers are distinguished into three classes.

A (1) The first class of lever (fig. 2) has the fulcrum between the force applied and the weight to be raised, or the resistance to be overcome, as in the case of a poker when

NUK stirring the fire. The common balance and

Fig. 2. a pair of scissors—the latter being double- AB, the lever ; F, the fulcrum;

W, the weight; P, the are both examples of this class of lever.

power or force. (2) The second class of lever has the weight between the power and the fulcrum (fig. 3). The common wheelbarrow is a lever of this class; an oar is another example—the man pulling being the power, the water taken hold of by the blade being the fulcrum, and the boat the resistance.

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Fig. 4. (3) The third class of lever has the power between the fulcrum and

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the weight (fig. 4). A man pushing open a gate by applying his hand near the hinges, gives an example of a lever of this class ; another is furnished by the common fire-tongs, the fulcrum being at the joint, and the lever being double, as in the case of the scissors.

Having now described the different kinds of levers, we proceed to explain the principle upon which they work ; and although the practical use of a lever is to move a weight, yet, to calculate accurately its manner of working, we must consider it in that state in which the power balances the weight, which is called the state of equilibrium (Latin, æquus, equal, libra, a balance). The whole principle will be understood at once if it

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the means of applying it. Let the lever AB (fig. 5), which is

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on the fulcrum F, with two

feet of its length on one side, AF, and one foot, FB, on the other; and let a weight of four pounds be suspended at B, and one of two pounds at A. These two weights balance each other—that is, the lever is in equilibrium. But suppose it to move into another position, CD. By a simple proposition in mathematics, we know that AF, being twice as great as FB, the distance AC, through which the small weight moves, is twice as great as BD, the distance through which В moves.

We see, then, that the reason why a smaller weight or force is equivalent to a greater weight is, that the smaller force is exerted over a larger space. Thus, when a man wishes to overturn a large stone, and, finding that it is too heavy for him, takes a lever to assist him, he does not get any additional strength from the lever; it merely enables him to concentrate the strength he has. If his strength be sufficient to enable him to press down the end of the lever, the raising power at the other end will be greater exactly in the proportion that the distance through which the one end is pushed down is greater than the distance through which the other end is moved, or in the proportion that the end of the lever next him is longer than the end next the stone. The principle of the lever then is, that the farther from the fulcrum the force is applied, the less it requires to be; and this principle applies to all kinds of levers.

Sometimes the object in making use of a lever is not to get a greater power applied, as when a man wishes to raise a stone as described above, but to get greater speed of motion. It will be observed that in fig. 5, the long end of the lever A, since it moves through a distance twice as great as that moved by the short end B, must move twice as fast. If then speed

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of motion be desired, it may be gained by means of a lever, at the expense of a greater force than is required ; and it is to this end that the third kind of lever is applied (see fig. 4). On this principle the foot-board of a turning-lathe is constructed (fig. 6). The fulcrum of the lever is the hinge at the toe of the man's left foot; the power is the man's right foot, which presses down the treadle, thus communicating motion to the string S; and although the power communicated to the string is not so great as that of the pressure of the foot, the velocity is many times greater. Driving nails with a hammer is another example of gain of velocity at the expense of strength or force. The fulcrum is the elbow-joint; the power is exerted by the muscles attached near the wrist; and although the exertion

Fig. 6. of the muscles is greater than the power communicated to the hammer, yet the velocity gained is very great.

The common balance is a familiar application of the lever. Since it is used to weigh quantities of articles equal to certain weights, it will be readily understood, from what has been said, that it is absolutely necessary that the arms of the balance be of equal length, because a smaller weight at the end of a longer arm would balance a greater weight at the end of a shorter arm. This is one way by which persons selling articles requiring to be weighed could cheat their customers, although their weights were quite correct; for, if one arm of the balance were shorter than the other, by putting the weights at that side, a less quantity than the just weight would balance them.

A few words will now be sufficient to explain the principle of the steelyard, another application of the lever (fig. 7). In the figure, C is the fulcrum or pivot on which it is suspended, CA is the distance from the fulcrum to the point at which the article to be weighed is suspended. The longer arm of the instrument is divided into equal lengths,

Fig. 7. marked 1, 2, 3, &c.; and the great convenience of this is, that many different quantities can be weighed with one weight. For instance, if the weight used be one pound, and it is required to weigh two pounds, the one - pound weight is placed at the division marked 2, and there, as was seen

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in fig. 5, it will balance two pounds in the scale ; and so for any other number of pounds, because, if the distance of the small weight from the fulcrum be three, four, or five times greater than the distance of the other weight, that weight must be three, four, or five times greater than the weight at the longer end.

II.-The Wheel and Axle. This machine, although apparently very different from the lever, is in reality constructed on the same principle. In fig. 8, we see an arrangement by which a small weight, P, balances a much greater one, W. Now, if we

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take a section of this machine (fig. 9), we see at once how it acts like a lever. Although the machine might be turned round, yet, in every position, the weights act at right angles to the diameters of the wheel and of the axle ; and as the machine is perfectly rigid, it is easily seen that it is simply a lever, with F, the centre of the axle, for its fulcrum, and having on one side half the diameter of the wheel, and on the other half the diameter of the axle. If the half-diameter, FA, were six times greater than the half-diameter FB, the weight, P, would

balance a weight six times greater than itself. What has been said applies to the machine in a state of equilibrium; for practical purposes, however, the weight on the wheel is not used, the axle being turned by a winch, H (fig. 8). The strength of a man pressing round the handle, acts like the weight on the circumference of the wheel.

The capstan, used on board ships for heaving Fig. 10.

the anchor, is on the same principle (fig. 10). The fulcrum is the centre of the machine; the short end of the lever, with the heavier weight, is half the diameter of the part round which the cable is wound; while the longer arm, on which the power acts, is the distance from the centre to the part of the spokes on which the sailors press.

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III.-The Pulley. A pulley consists of a small wheel, with a grooved rim, fixed in a block so as to move freely on its axis, and having a cord passing over the rim, with weights attached to each end. There are two kinds of pulleys, one the fixed pulley, as in fig. 11, the other the movable pulley, as B, fig. 12.

It is clear, that if P is to balance W in fig. 11, the weights must be equal, because the wheel simply acts like a lever with equal arms, as was seen in describing the wheel and axle ; so that a fixed pulley does not give any increase of strength, but merely changes the direction of application of the force. For example, if a man wished to raise something heavy to a considerable height, he might find the greatest difficulty in lifting what he could raise with ease by pulling a rope attached to the article over a pulley.

Ow By means of a movable pulley, however, as in fig.

Fig. 11. 12, a man may exert a power greater than his own strength. But, just as in the case of the lever, it is a mistake to suppose that the pulley gives rise to any power in itself; it merely affords the means by which power may be concentrated. The parts of the string in the figure, between A and B, and between B and C, support each one half of the weight of W. And as the effect of C is simply to change the direction of the force, and the tension of the string being the same throughout, it is evident that the hand at P must be pulling with a force equal to half the weight of W. Thus, by means of a movable pulley, a weight or power at the end of a cord is able to balance a weight twice as great. It will readily be seen how it is so. Suppose the cord to be pulled so as to raise W one inch. In order to do this, one inch of cord must

Fig. 12. be taken up on both sides of the pulley B. The inch on the side of AB will be pulled over the pulley B, and then two inches must be pulled over the pulley C; so that, in order to raise W one inch, the hand at P must descend two inches. Thus, exactly as in the case of the lever, although the work done at one end of the machine seems to be greater than that done at the other, it is not really so; for, at the other end, the work is merely spread over a larger space.

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