CONVERSATION V.

CONTINUED.

ON THE MECHANICAL POWERS.

OF THE PULLEY.-OF THE WHEEL AND AXLE.—OF THE INCLINED PLANE. OF THE WEDGE. OF THE SCREW.

MRS. B.

THE pulley is the second mechanical power we are to examine. You both, I suppose, have seen a pulley? Caroline. Yes frequently: it is a circular and fat piece of wood or metal, with a string which runs in a groove round it; by means of which, a weight may be pulled up; thus pulleys are used for drawing up cur

tains.

Mrs. B. Yes; but in that instance the pulleys are fixed, and do not increase the power to raise the weights, as you will perceive by this figure. (plate V. fig. 1.) Observe that the fixed pulley is on the same principle as the lever of a pair of scales, in which the fulcrum F being in the centre of gravity, the power P and the weight W, are equally distant from it, and no advantage is gained.

Emily. Certainly; if P represents the power employed to raise the weight W, the power must be greater than the weight in order to move it. But of what use then are pulleys in mechanics? Mrs. B. The next figure represents a pulley which

is not fixed, (fig. 2.) and thus situated you will perceive that it affords us mechanical assistance. In order to raise the weight (W) one inch, P, the power, must draw the strings B and C one inch each; the whole string is therefore shortened two inches, while the weight is raised only one.

Emily. That I understand: if P drew the string but one inch, the weight would be raised only half an inch, because it would shorten the strings B and C half an inch each, and consequently the pulley with the weight attached to it, can be raised only half an inch.

Caroline. I am ashamed of my stupidity; but I confess that I do not understand this; it appears to me that the weight would be raised as much as the string is shortened by the power.

Mrs. B. I will endeavour to explain it more clearly. I fasten this string to a chair and draw it towards me; I have now shortened the string, by the act of drawing it, one yard.

Caroline. And the chair, as I supposed, has advanced one yard.

Mrs. B. This exemplifies the nature of a single fixed pulley only. Now unfasten the string, and replace the chair where it stood before. In order to represent the moveable pulley, we must draw the chair forwards by putting the string round it; one end of the string may be fastened to the leg of the table, and I shall draw the chair by the other end of the string. I have again shortened the string one yard; how much has the chair advanced?

Caroline. I now understand it; the chair represents the weight to which the moveable pulley is attached; and it is very clear that the weight can be drawn only half the length you draw the string. I believe the cir cumstance that perplexed me was, that I did not observe the difference that results from the weight being attached to the pulley, instead of being fastened to the string, as is the case in the fixed pulley.

Emily. But I do not yet understand the advantage

of pulleys; they seem to me to increase rather than diminish the difficulty of raising weights, since you must draw the string double the length that you raise the weight; whilst with a single pulley, or without any pulley, the weight is raised as much as the string is shortened.

Mrs. B. The advantage of a moveable pulley consists in dividing the difficulty; we must draw, it is true, twice the length of the string, but then only half the strength is required that would be necessary to raise the weight without the assistance of a moveable pulley. Emily. So that the difficulty is overcome in the same manner as it would be, by dividing the weight into two equal parts, and raising them successively.

Mrs. B. Exactly. You must observe, that with a moveable pulley the velocity of the power is double that of the weight, since the power P (fig. 2.) moves two inches whilst the weight W moves one inch; therefore the power need not be more than half the weight to make their momentums equal.

Caroline. Pulleys act then on the same principle as the lever, the deficiency of strength of the power being compensated by its superior velocity.

Mrs. B. You will find, that all mechanical power is founded on the same principle.

Emily. But may it not be objected to pulleys, that a longer time is required to raise a weight by their aid than without it; for what you gain in power you lose in time?

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Mrs. B. That, my dear, is the fundamental law in mechanics it is the case with the lever as well as the pulley; and you will find it to be so with all the other mechanical powers.

Caroline. I do not see any advantage in the mechanical powers then, if what we gain by them one way is lost another.

Mrs. B. Since we are not able to increase our natural strength, is not that science of wonderful utility, by means of which we may reduce the resistance or

weight of any body to the level of our strength? This the mechanical powers enable us to accomplish, by dividing the resistance of a body into parts which we can successively overcome. It is true, as you observe, that it requires a sacrifice of time to attain this end, but you must be sensible how very advantageously it is exchanged for power: the utmost exertion we can make adds but little to our natural strength, whilst we have a much more unlimited command of time. You can now understand, that the greater the number of pulleys connected by a string, the more easily the weight is raised, as the difficulty is divided amongst the number of strings, or rather of parts into which the string is divided by the pulleys. Several pulleys thus connected, form what is called a system, or tackle of pulleys. (fig. 3.) You may have seen them suspended from cranes to raise goods into warehouses, and in ships to draw up the sails.

Emily. But since a fixed pulley affords us no mechanical aid, why is it ever used?

Mrs. B. Though it does not increase our power, it is frequently useful for altering its direction. A single pulley enables us to draw up a curtain, by drawing down the string connected with it; and we should be much at a loss to accomplish this simple operation without its

assistance.

Caroline. There would certainly be some difficulty in ascending to the head of the curtain, in order to draw it up. Indeed, I now recollect having seen workmen raise small weights by this means, which seemed to answer a very useful purpose.

Mrs. B. In shipping, both the advantages of an increase of power and a change of direction, by means of pulleys, are united: for the sails are raised up the masts by the sailors on deck, from the change of direc tion which the pulley effects, and the labour is facilitated by the mechanical power of a combination of pulleys.

Emily. But the pulleys on ship-board do not appear to me to be united in the manner you have shown us.