Science for the School and Family, Part I. Natural Philosophy

by Worthington Hooker

243. The Screw.—This is the sixth mechanical power. The principle of it is essentially that of the inclined plane. The "thread" running around the screw is an inclined plane which is spiral instead of straight, and so is also the corresponding part in the nut an inclined plane running in the opposite direction. In the common screw the nut is fixed, and the screw is made to play up and down in it; but sometimes the screw is fixed, and the nut is made to play around it. The screw acts like a wedge, and has the same relation to a straight wedge that a road winding up a hill has to a straight road of the same length and rise. Especially does the comparison hold when the screw is forced into wood; the wedge goes straight into the wood, but the edge of the screw's thread enters the wood spirally.

Fig. 180.

To estimate the force of the screw we compare the length of one turn of the thread around it with the height to which the thread rises in going round. Let a b, Fig. 180, represent one turn of the thread, and b c the height to which it goes. It is clear from the figure that the principle which applies to the inclined plane and to the wedge applies here also. As the less is the height of the plane the easier it is for a weight to be drawn up it; and as the less is the depth of the wedge the less is it resisted; so, also, the less the height of the turn of the screw's thread the easier is it to move the screw, and the greater is the force which it exerts. Hence the prodigious power of a screw with a thread which rises very slowly in its spiral turns. Screws are much used when great pressure is required, as in pressing oils and juices from vegetable substances, in compressing cotton into bales, in bringing together with firm grasp the jaws of the vice, etc. In turning the screw a bar is used, so that we have in this instrument the combined advantages of the screw and the lever. That you may have some idea of the power of these two instruments acting together I will suppose a case. Let the weight to be raised by a screw be 10,000 pounds. Let a turn of the screw be 10 inches long, and the rise be but one inch. Then, so far as the screw is concerned, the power requisite to raise the 10,000 pounds will be 1000—the ratio of the height of the thread's turn to its length. But the power of the lever is yet to be estimated. Let the length of the lever, passed through the head of the screw so that it is equal on each side, be 30 inches. The diameter of the screw is about three inches, or one-tenth of the diameter of the circle described by the end of the lever. It will now take but a power of 100 pounds to raise the weight, the ratio of the radius of the screw to half the length of the lever.

244. Truly but Three Mechanical Powers.—The Wheel and Axle, you have seen, is merely a modification of the Lever, and the Wedge and the Screw are modifications of the Inclined Plane. The Mechanical Powers are, then, in reality but three—the Lever, Pulley, and Inclined Plane. And these are the elements of all machinery, from the simplest tool that is used for the most common purposes to the most complicated and powerful engine which the ingenuity of man ever designed. The principle upon which a pin is shaped is identical with that of the wedge, by which large masses are cleft in two; and the instrument by which the finest textures are cut by delicate fingers is arranged on the same principle with those varied contrivances by which immense weights are raised by a comparatively small power, viz., the principle of the lever.

245. Friction in Machinery.—You have seen, as we have proceeded, that the Mechanical Powers, though thus named, do not generate power. So far from this, there is really a loss of power in their use, chiefly from friction. In raising a weight, for example, directly by the hand, there is no loss from this cause; but if you use a pulley you have the friction of the cord upon it, and a loss of power in proportion to the amount of friction. In some cases the loss of power from this cause is so great as to call for a considerable variation from such calculations as we have made in this chapter in regard to the relations of power and weight in machinery. In the operations of the screw friction has a great influence in diminishing the power of the instrument.

246. The Real Advantages of the Mechanical Powers.—If there is then no saving, but a loss of power in tools and machinery, what, let us inquire, are their advantages?

If one man can do alone by the aid of some instrument what would otherwise require the exertion of many men, though he be slow in doing it, yet it is a great advantage. Thus one man can with a lever move a stone which perhaps it would require thirty men to move without it, and though it take him thirty times as long, it saves him the trouble of getting a company of men to help him. So if a man can raise his goods by a wheel and axle to the upper loft of his store, though he raise them slower than several men would lift them directly by ropes, it is an advantage to him, as it saves the hiring of a company of laborers. A few men by a capstan can raise an anchor which could be raised without it only by a large company of men.

Another advantage often is that there may be intervals of rest in applying the force without any loss. This is obvious in the case of the pulley, but still more so in the case of the screw. It is friction in both these cases which enables the workman to rest. It saves to him all that he has gained by opposing any tendency to slip back. We see the same thing in the wedge. When this is driven into wood, it remains because it is prevented from returning by the friction of the wood against its sides. It is the same cause which holds a nail in its place, and opposes any effort to draw it out. In driving the wedge the workman can have as long intervals as he pleases between his blows, because friction saves all that is gained. This effect is very well exemplified in the capstan, Fig. 170. It requires but little exertion of the man who sits there to hold the rope, because the few turns of it around the axle prevent its slipping easily.

A third advantage which often attends the use of tools and machines is that force may be made to produce motion at various distances, in various directions, and in various degrees of velocity. Thus as to distance, a man standing on the ground can raise a weight to the top of a house by a pulley. So, also, a water-wheel may by the connections of machinery produce motion at considerable distances from it. Then as to direction, horizontal motion may be converted into vertical, rotary into straight, etc. The velocity of motion is generally varied by cog-wheels. Thus a wheel of 60 cogs revolving once in a minute, playing on a wheel of 10 cogs, will make it revolve once in 6 seconds.