Practical Education, Volume II. Edgeworth Maria
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or thirty feet long, upon which a small sledge loaded with different weights may be drawn. Plate 2. Fig. 1.
F. F. The frame.
b. b. Braces to keep the frame steady.
a. a. a. Angular braces to strengthen the transom; and also a king-post.
S. A round, taper shaft, strengthened above and below the mortises with iron hoops.
L L. Two arms, or levers, by which the shaft, &c. are to be moved round.
D D. The drum, which has two rims of different circumferences.
R. The roller to conduct the rope.
P. The pulley, round which the rope passes to the larger drum.
P 2. Another pulley to answer to the smaller drum.
P 3. A pulley through which the rope passes when experiments are tried with levers, &c.
P 4. Another pulley through which the rope passes when the sledge is used.
Ro. The road of deal boards for the sledge to move on.
Sl. The sledge, with pieces of hard wood attached to it, to guide it on the road.
As this machine is to be moved by the force of men or children, and as their force varies not only with the strength and weight of each individual, but also according to the different manner in which that strength or weight is applied; it is, in the first place, requisite to establish one determinate mode of applying human force to the machine; and also a method of determining the relative force of each individual whose strength is applied to it.
Hang a common long scale-beam (without scales or chains) from the top or transom of the frame, so as that one end of it may come within an inch of one side or post of the machine. Tie a rope to the hook of the scale-beam, where the chains of the scale are usually hung, and pass it through the pulley P 3, which is about four feet from the ground; let the person pull this rope from 1 towards 2, turning his back to the machine, and pulling the rope over his shoulder – Pl. 2. Fig. 6. As the pulley may be either too high or too low to permit the rope to be horizontal, the person who pulls it should be placed ten or fifteen feet from the machine, which will lessen the angular direction of the cord, and the inaccuracy of the experiment. Hang weights to the other end of the scale-beam, until the person who pulls can but just walk forward, pulling fairly without propping his feet against any thing. This weight will estimate the force with which he can draw horizontally by a rope over his shoulder.22 Let a child who tries this, walk on the board with dry shoes; let him afterwards chalk his shoes, and afterwards try it with his shoes soaped: he will find that he can pull with different degrees of force in these different circumstances; but when he tries the following experiments, let his shoes be always dry, that his force may be always the same.
Instead of putting the cord that comes from the scale-beam, as in the last experiment, over the shoulder of the boy, hook it to the end 1 of the lever L, Fig. 2. Plate 2. This lever is passed through a socket – Plate 2. Fig. 3. – in which it can be shifted from one of its ends towards the other, and can be fastened at any place by the screw of the socket. This socket has two gudgeons, upon which it, and the lever which it contains, can turn. This socket and its gudgeons can be lifted out of the holes in which it plays, between the rail R R, Plate 2. Fig. 2. and may be put into other holes at R R, Fig. 5. Loop another rope to the other end of this lever, and let the boy pull as before. Perhaps it should be pointed out, that the boy must walk in a direction contrary to that in which he walked before, viz. from 1 towards 3. The height to which the weight ascends, and the distance to which the boy advances, should be carefully marked and measured; and it will be found, that he can raise the weight to the same height, advancing through the same space as in the former experiment. In this case, as both ends of the lever moved through equal spaces, the lever only changed the direction of the motion, and added no mechanical power to the direct strength of the boy.
Shift the lever to its extremity in the socket; the middle of the lever will be now opposite to the pulley, Pl. 2. Fig. 4. – hook to it the rope that goes through the pulley P 3, and fasten to the other end of the lever the rope by which the boy is to pull. This will be a lever of the second kind, as it is called in books of mechanics; in using which, the resistance is placed between the centre of motion or fulcrum, and the moving power. He will now raise double the weight that he did in Experiment II, and he will advance through double the space.
Shift the lever, and the socket which forms the axis (without shifting the lever from the place in which it was in the socket in the last experiment) to the holes that are prepared for it at R R, Plate 2. Fig. 5. The free end of the lever E will now be opposite to the rope, and to the pulley (over which the rope comes from the scale-beam.) Hook this rope to it, and hook the rope by which the boy pulls, to the middle of the lever. The effect will now be different from what it was in the two last experiments; the boy will advance only half as far, and will raise only half as much weight as before. This is called a lever of the third sort. The first and second kinds of levers are used in quarrying; and the operations of many tools may be referred to them. The third kind of lever is employed but seldom, but its properties may be observed with advantage whilst a long ladder is raised, as the man who raises it, is obliged to exert an increasing force until the ladder is nearly perpendicular. When this lever is used, it is obvious, from what has been said, that the power must always pass through less space than the thing which is to be moved; it can never, therefore, be of service in gaining power. But the object of some machines, is to increase velocity, instead of obtaining power, as in a sledge-hammer moved by mill-work. (V. the plates in Emerson's Mechanics, No. 236.)
The experiments upon levers may be varied at pleasure, increasing or diminishing the mechanical advantage, so as to balance the power and the resistance, to accustom the learners to calculate the relation between the power and the effect in different circumstances; always pointing out, that whatever excess there is in the power,23 or in the resistance, is always compensated by the difference of space through which the inferiour passes.
The experiments which we have mentioned, are sufficiently satisfactory to a pupil, as to the immediate relation between the power and the resistance; but the different spaces through which the power and the resistance move when one exceeds the other, cannot be obvious, without they pass through much larger spaces than levers will permit.
Place the sledge on the farthest end of the wooden road – Plate 2. Fig. 1. – fasten a rope to the sledge, and conduct it through the lowest pulley P 4, and through the pulley P 3, so as that the boy may be enabled to draw it by the rope passed over his shoulder. The sledge must now be loaded, until the boy can but just advance with short steps steadily upon the wooden road; this must be done with care, as there will be but just room for him beside the rope. He will meet the sledge exactly on the middle of the road, from which he must step aside to pass the sledge. Let the time of this experiment be noted. It is obvious that the boy and the sledge move with equal velocity; there is, therefore, no mechanical advantage obtained by the pulleys. The weight that he can draw will be about half a hundred, if he weigh about nine stone; but the exact force with which the boy draws, is to be known by Experiment I.
This organ is usually called in mechanics, The axis in peritrochio. A hard name, which might well be spared, as the word windlass or capstan would convey a more distinct idea to our pupils.
To the largest drum, Plate 2. Fig. 1. fasten a cord, and pass it through the pulley P downwards, and through the pulley P 4 to the sledge placed at the end of the wooden road, which is farthest from the machine. Let the boy, by a rope fastened to the extremity of one of the arms of the capstan, and passed over his shoulder, draw the capstan round; he will wind the rope round the drum, and draw the sledge upon its road. To make the sledge advance twenty-four feet upon its road, the boy must have
Were it thought necessary to make these experiments perfectly accurate, a segment of a pulley, the radius of which is half the length of the scale-beam, should be attached to the end of the beam; upon which the cord may apply itself, and the pulley (P 3) should be raised or lowered, to bring the rope horizontally from the man's shoulder when in the attitude of drawing.
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