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velocity of the little child must be than that of the bigger one. Enormous weights may be raised by levers of this description, for the longer the acting part of the lever is in comparison to the resisting part, the greater is the effect produced by it; because the greater is the velocity of the power compared to that of the weights.
We have all seen a heavy barrel or tun rolled over 29V19097T Sponges by thrusting the end of a Bemagidadod strong stick beneath it and gode resting it against a log of of bus wood, or any wood, or any other object OR which can give it support, near the end in contact with the barrel. The stick, in this case, is a lever, the support, the prop or fulcrum; and the nearer the latter is to the resistance, the more easily will the power be able to move it.
There are three different kinds of levers; in the first, which comprehends the several levers we have described, the fulcrum is between the power and the weight. When the fulcrum is situated equally between the power and the weight, as in the balance, the power must be greater than the weight, in order to move it; for nothing can in this case be gained by velocity. The two arms of the lever being equal, the velocity of their extremities must be so likewise. The balance is therefore of no assistance as a mechanical power, but it is extremely useful to estimate the respective weights of bodies. But when the fulcrum, F, of a lever is not equally distant from the power and the weight, and that the power, P, acts at the extremity of the longer arm, the power may then be less than the weight, w, its deficiency being compensated by its greater velocity; as we observed in describing the see-saw'. Therefore, when a great weight is to be raised, it must be fastened to the shorter arm of a lever, and the power applied to
the longer arm. But, if the case will admit of putting the end of the lever under the weight, no fastening will be required, as you may perceive by stirring the fire. The poker is a lever of the first kind: the point, where it rests against the bars of the grate, whilst stirring the fire, is the fulcrum; the short arm, or resisting part of the lever, is employed in lifting the weight, which is the coals; and the hand is the power, applied to the longer arm, or acting part of the lever. A pair of scissors is an instrument composed of two levers, united in one common fulcrum; the point at which the two levers are screwed together, is the fulcrum; the handles to which the power of the fingers is applied, are the extremities of the acting part of the levers; and the cutting parts of the scissors are the resisting parts of the levers therefore, the longer the handles, and the shorter the points of the scissors, the more easily will they cut. Thus, when pasteboard, or any hard substance is to be cut, that part of the scissors nearest the screw or rivet is used. Snuffers, and most kinds of pincers, are levers of a similar description, the great force of which consists in the resisting part of the lever being very short in comparison of the acting part.
In levers of the second kind, the weight, instead of being at one end, is situated between the power and the fulcrum. In moving it, the velocity of the power must necessarily be greater than that of the weight, as it is more distant from the centre of motion. We may sometimes see a barrel moved by means of a lever of the second kind, as well as by one of the first. The end of the stick that is thrust under the barrel rests on a ya ye the ground, which becomes the fulcrum; the barrel is the weight to be yo moved, and the power the hands applied to the other
end of the lever. In this instance there is an immense difference in the length of the arms of the lever, the weight being almost close to the fulcrum, and the advantage gained is proportional. The most common example that we have of levers of the second kind is in the doors of our apartments; in these the hinges represent the fulcrum; the hand, the power applied to the other end of the lever; and the door, or rather its inertia, is the weight which occupies the whole of the space between the power and the fulcrum. Another very common instance is found in an oar; the blade is kept in the same place by the resistance of the water, and becomes the fulcrum, the resistance is applied where the oar passes over the side of the boat: and the hands at the handle are the power. Nut-crackers are double levers of this kind: the hinge is the fulcrum; the nut-crackers the resistance, and the hands the power.
In levers of the third kind, the fulcrum is also at one of the extremities, the weight or resistance at the other, and the power is applied between the fulcrum and the resistance. Thus the fulcrum, the weight, and the power, each in its turn, occupies some part of the lever between its extremities. But in this third kind of lever, the weight being further from the centre of motion than the power, the difficulty of raising it, instead of being diminished is increased. Levers of this description are used when the object is to produce great velocity. The aim of mechanics, in general, is to gain force by exchanging it for time; but it is sometimes desirable to produce great velocity by an expenditure of force. The treddle of the common turning lathe affords an example of a lever of the third kind employed in gaining time, or velocity, at the expense of force. A man, in raising a long ladder perpendicularly against a wall, cannot place his hands on the upper part of the ladder; the power
therefore, is necessarily placed nearer the fulcrum than the weight, for the hands are the power, the ground, the fulcrum, and the ladder the weight, which, in this, as well as in the door, may be considered as collected in the centre of gravity of the ladder, about half way up it, and consequently beyond the point where the hands are applied. This kind of lever is employed in the structure of the human frame. In lifting a weight with the hand, the lower part of the arm becomes a lever of the third kind; the elbow is the fulcrum; the muscles which move the arm, the power; and as these are nearer to the elbow, than the hand is, it is necessary that their power should exceed the weight to be raised. It is of more consequence that we should be able to move our limbs nimbly, than that we should be able to overcome great resistance; for it is comparatively seldom that we meet with great obstacles, and when we do, they can be overcome by
The pulley, which is the second mechanical power we are to examine, is a circular flat piece of wood or metal, with a string running in a groove round it, by means of which a weight may be pulled up. Thus pulleys are used for drawing up curtains, the sails of a ship, &c. When the pulley is fixed, it does not increase the power to raise the weight. If P represent the power to raise the weight w, it is evident that the power must be greater than the weight in order to move it. A fixed pulley is useful, therefore, only in altering the direction of the power and its most frequent practical application is to enable us to draw up a weight by drawing down the string, connected with the pulley. But a moveable pulley affords mechanical assistance. The hand which sustains the cask by means of the
cord D E, passing round the moveable pulley A C, does it more easily than if it held the cask suspended to a cord without a pulley; for the fixed hook н, to which one end of the cord is fastened, bearing one half of the weight of the cask, the hand has only the other half to sustain.
Now, it is evident, that the hook affords the same assistance in raising, as in sustaining the cask, so that the hand will have only one-half of the weight to raise. But observe, that the velocity of the hand must be double that of the cask; for in order to raise the latter one inch, the hand must draw the two strings (or rather the two parts, D and E, into which the string is divided by the pulley,) one inch each; the whole string being shortened two inches, while the cask is raised only one. Thus the advantage of a moveable pulley consists in dividing the difficulty. Twice the length of string, it is true, must be drawn, but one-half the strength is required which would be necessary to raise the weight without such assistance; 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. The pulley, therefore, acts on the same principle as the lever, the deficiency of strength of the power being compensated by superior velocity; and it is on this principle that all mechanical power is founded. In the fixed pulley, [p. 281,] the line A c may be considered as a lever, and B the fulcrum: then the two arms A B and B c being equal, the lever will afford no aid as a mechanical power; since the power must be equal to the weight in order to balance it, and superior to the weight in order to raise it. In the moveable pulley you must consider the point a as the fulcrum; A B, or half the diameter of the pulley, as the shorter arm; and a C, or the whole diameter, as the