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of one pound weight, moving at the rate of 32 feet in a second is also 32; and these momentaj are equal to one another.–6. Wherever one body acts upon another, it is met by an equal and contrary reaction ; that is to say, if a body in motion strike another body, the resistance of the struck body is equal to the blow given by the striking body, and in the opposite direction. If I strike a table with my
hand is equally struck by the table. When a horse draws a cart, the horse is as much drawn back by the cart, as the cart is drawn forward by the horse ; for the horse exerting the same strength, wouid have gone to a much greater distance, in the same time, if it had not been impeded by the cart. In playing a game of marbles, where one marble is chucked away by another, that which gave the impulse is itself immediately stopt in its course, by the reaction of the one which it displaces. So also, if two ivory balls be suspended from a beam by threads, in such a manner, that the balls touch each other, and, if one of them be drawn aside, and allowed to fall down upon the other by the force of gravity, the ball struck will immediately fly off to a distance, equal to that through which the other fell; but that which gave the blow will, at the same moment, stand still in consequence of the reaction. If six ivory balls be suspended in the same manner, and one of them be allowed to fall down upon the rest, none of them will appear to move after the collision, except the one which is most remote: for, in this case, the reaction of the second ball, will destroy the motion of the first; the second ball, though it will not appear to move, must strike against the third, and from its reaction be set at rest; and so on, till motion is communicated to the last ball, which, having no reaction to encounter, alone flies off. If, in place of using ivory balls in these experiments, balls of clay, or of any other soft substance, be employed, the result will not be precisely the same, though still equally illustrative of the operation of reaction. If one of these be allowed to fall
another in the manner formerly described, neither the falling body will by the collision be deprived of all its motion, nor the body struck have all that motion communicated to it, as in the former case; but both will move on together in contact, to a distance not so great, as the struck ball did in the former case. --Thecause of this difference arises entirely from the difference in point of elasticity, between the ivory and the clay. By elasticity is meant that property, by means of which bodies, when compressed or dilated, return to their former state. You have all seen its operation in the case of a bit of sponge or ball of cotton when compressed, and Indian rubber when dilated. Of all bodies air is the most elastic, and hence is distinguished by the name of elastic fuid. Hard bodies are next in point of elasticity. When two balls of metal or of ivory strike each other, the parts at which they touch yield to the stroke, and are pressed inwards; but, in consequenceof elasticity, they instantly return to their former situation, so instantaneously indeed and effectually, as to destroy all trace of their compressed state. Soft bodies, such as clay, butter, tallow, &c., have little elasticity, and liquids least of all. Without an acquaintance with that law of motion, by which action is always accompanied by a contrary reaction, you would be quite at a loss to explain how a bird is enabled to support itself in the air. This is owing entirely to the reaction of the air, when struck by the wings of the bird. If the force, with which the bird strikes the air below it, be equal to the weight of its own body, it will remain stationary ; if it be greater, it will rise; if less, it will fall.
LAWS OF MOTION—(continued). In the last article, we considered the circumstances connected with motion, when occasioned by the operation of a single force once exerted. We are now to turnour attention to those motions, which are produced either by the incessant exertion of the same force, or by the com ned exertions of different forces.-1. If the force, which set a body in motion, do not cease to exert itself at the moment when the body is set in motion, but continue in a state of incessant exertion during the whole of its course, the motion then will not be uniform, but continually accelerated; or, in other words, the velocity of the body will become every moment greater and greater. This will explain to you the reason, why a falling body descends with so much greater velocity at the end, than at the beginning of its fall. This does not arise (as perhaps at first you might be disposed to think) from the circumstance of the body at the close of its fall being nearer the centre of attraction, than at its commencement; because the difference arising from this cause is so trifling, at any small distance from the earth, as to be scarcely perceptible. The cause of the accelerated motion of the falling body is this.
When a body falls from a height, the force of gravity, which sets it in motion at the first instant of its fall, would be sufficient to bring it to the ground with a uniform motion, though that force had instantly ceased. But the force of gravity operates, not in the first instant merely, but in every succeeding instant of the body's fall. The force, therefore, which it receives at the second instant, is added to that of the first ; and the force, with which it falls in the last instant, is composed of all the forces, which it received in every instant of its fall. It has accordingly been ascertained, that heavy bodies descending from a height, by the force of gravity, fall 16 feet the first second of time, three times that distance in the next second, five times that distance in the third, and so forth in progression, according to the odd numbers 7, 9, 11, &c. Hence the height of a precipice, or the depth of a well, may be measured by the time, in which a heavy body falls from the top to the bottom. Thus, if a stone have taken 7 seconds to descend from a height, that height, according to this mode of calculation, is 784 feet. For it fell, during the first second,
16 feet. during the next, 3 times 16 or
48 during the third, 5 times 16 or
80 during the fourth, 7 times 16 or
112 during the fifth, 9 times 16 or
144 during the sixth, 11 times 16 or
176 and, during the seventh, 13 times 16 or 208
In all such cases, however, the arithmetical process may be greatly abridged: for if, instead of calculating the height, which the body fell, during each separate second, and then adding the whole together, you multiply the whole number of seconds by itself, and that product by 16, the result will be precisely the same. Thus, in the foregoing instance, if you multiply 7 by itself, the product is 49, and, if you farther multiply that product by 16, the result will be 784 as before. 2. If a body be, at the same instant, acted upon by two equal and opposite forces, as neither of these can prevail over the other, the body will of course remain stationary.-3. If a body be, at the same instant, acted upon by two opposite but unequal forces, it will move in the direction of the stronger force, but with a velocity diminished in proportion to the other.-4. If a body be put in motion by a force which instantly ceases, and be, at the same time, acted upon by an opposite force, which originally is not sufficient to prevail over the other, but continues in constant exertion, the body will have a continually retarded motion, or, in other words, its velocity will be every moment diminished; till, at last, the counteracting and incessant force will completely predominate, and the movement will take place under its influence in the opposite direction. Thus, if a stone be thrown up perpendicularly from the earth, its motion will, in consequence of the force of gravity, be more and more retarded, until at length, in place of ascending, it falls back to the ground in the same line by which it rose. It is a circumstance well worthy of attention, that the stone descends in precisely the same time in which it ascended. It has been proved by experiment, that the force requisite to throw up a heavy body sixteen feet from the earth, will make it ascend so high in one second, which you precisely the time of its descent. If it were thrown up with greater force, it would ascend higher, and of course would take longer time also to descend; if thrown up with less force, it would not ascend so high, and would descend the sooner. Hence, we may calculate the height, to which a body has ascended, when projected
have seen is
perpendicularly from the earth. If an arrow, thus shot up, continue ten seconds in motion, it has, for the reason now assigned, been five seconds on its descent: therefore, according to the method of calculation formerly suggested; multiplying five by itself, we obtain the product 25, and, multiplying this product by 16, we find 400 feet to have been the height ascended.5. If a body be, at the same instant, acted upon by two different but not directly opposing forces, its motion will not be entirely in the direction of either, but compound. ed as it were of both, and the body will accordingly move in a line between the two. Thus, if a body be at once acted upon by two equal forces, one of which would carry it directly south, and the other directly east, it will actually move in a south-east direction. To explain the same thing by a diagram. If a ball, placed at the point A, be at the same moment impelled by two equal forces, one of which, if operating by itself, would, in a second of time, carry it to the point B, in the direction AB, and the other would, in the same time, carry it to the point C in the direction AC, it will move in the direction of the intermediate line AD (which is called a diagonal), and arrive in a second at the point D. Let us next suppose the two forces to be unequal, and that the force impelling the ball in the direction AB is double the force impelling it in the direction AC. Here it is plain, that, if the former force had acted alone, the ball would have reached the point E, in the same time that the latter force, if acting alone, would have carried it to the point C, which is only half the distance. Now, when both forces act together, the ball is, in the same time, moved to the point F in the diagonal AF. An attentive examination of the diagram will show, that, in combination, no less than while the forces acted separately, one of them has precisely double the effect of the other. The distance which the ball has moved, from its original situation, by the force impelling it in the direction AE, is obviously twice as great as the distance which it has moved by the force impelling it in the direction AC. It will also be seen,