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COMPOUND MOTION. 37
by the stroke of its wings, is able to support its weight in the air. If the force with which it strikes the air below it, is equal to the weight of its body, then the re-action of the air upwards is likewise equal to it, and the bird being acted upon by two equal forces in contrary directions, will rest between them. If the force of the stroke is greater than its weight, the bird will rise with the difference of these two forces; and if the stroke be less than its weight, then it will sink with the difference. In the act of rowing, the water is struck with the oars, in a direction opposite to that in which the boat is required to move; and the boat is driven along by the reaction of the water on the oars.
Questions.—1. When is a body in motion? 2. What is force? 3. What are the motive powers? 4. In what direction is the motion of a body acted upon by a single force? 5. What is velocity? 6. To what is the velocity of a moving body proportioned? 7. How do you calculate the velocity of a moving body? 8. What is uniform motion? 9. Accelerated? 10. Retarded? 11. Why cannot perpetun1 motion-"" be produced by art? 12. When a stone falls from a height iw does gravity accelerate its motion? 13. What is said of the listances through which heavy bodies fall in successive seconds of time? 14. What is an instance of retarded motion? 15. What is the momentum of a body? 16. Of what composed? 17. Why is it so important with respect to mechanics? 18. What is meant by the term reaction? 19. To what is reaction equal? 20. Explain the manner in which birds support themselves in the air.
Projec'tile, impelled forward in a right line.
If a body be struck by two equal forces in opposite directions, it will not move at all; but if the forces, instead of acting on the body in opposition, strike it in two directions inclined to each other, it will follow the direction of neither of the forces, but will move in a line between them. There are many instances in nature, of motion produced by several powers acting at the same time. If a ship at sea sail before the wind directly east, and a current set from the north, it will be driven in a direction between the south and east
A ball fired from a cannon is acted upon by two forces, the one is that occasioned by the powder, the other is the force of gravity.
Circular motion is the result of two forces on a body, by one of which it is projected forward in a right line, whilst by the other it is confined to a fixed point. When you whirl a ball, for instance, which is fastened to your hand with a string, the ball moves in a circular direction; because it is acted upon by two forces, that given it by yourself, which represents the force of projection, and that of the string which confines it to your hand. If during its motion the string were suddenly to break, the ball would fly off in a straight line; being released from confinement to the fixed point, it would be acted on but by one force, and motion produced by one force is always in a right line. The force which confines a body to a centre round which it moves, is called the centrip'etal force; and that force which impels a body to fly from the centre, is called the centrifugal force. In circular motion these two forces constantly balance each other, otherwise the revolving body would either approach the centre, or recede from it, according as the one or the other prevailed. If any cause should destroy the centripetal force, the centrifugal force would alone impel the body, and it would fly off in a right line in the direction in which it was moving, at the instant of its release. When a stone, whirled round in a sling, gets loose, it flies off in a right line, called a tangent, because it touches the circumference of the circle in which the stone was revolving.
It is by the laws of circular motion that the moon and all the planets revolve in their orbits. The moon, for instance, has a constant tendency to the earth, by the attraction of gravitation, and it has also a tendency to proceed in a right line, by that projectile force impressed upon it by the Creator; now, by the joint action of these two forces it describes a circular motion. If the projectile force were to cease, the moon must fall to the earth; and if the force of gravity were to cease acting upon the moon, it would fly off into infinite space.
When you throw a ball in a horizontal or oblique direction, it describes a curve line in falling, and is acted upon by three forces; the force of projection, which you communicated to it; the resistance of the air, which diminishes its
THE PENDULUM. 39
velocity, without changing its direction; and the force of gravity, which finally brings it to the ground. The curve line which the ball describes is called in geometry a.parab'ola.
A pendulum consists of a line, or rod, to one end of which a weight is attached, and it is suspended by the other to a fixed point, about which it is made to vibrate. Without being put in motion, a pendulum, like a plumb line, hangs perpendicularly to the general surface of the earth, by which it is attracted; but if you raise a pendulum, gravity will bring it back to its perpendicular position. It will, however, not remain stationary there, for the velocity it has received during its descent will impel it onwards, and it will rise on the opposite side to an equal height; from thence it is brought back by its gravity, and again driven by the impulse of its velocity. Were it possible to remove the obstacles occasioned by the resistance of the air, and by the friction ofthe part by which it is suspended, the motion of a pendulum would be perpetual, and its vibrations perfectly regular; being of equal distances, and performed in equal times. The metallic rods of pendulums are expanded by heat and contracted by cold; clocks therefore will go faster in winter, and slower in summer, for the longer a pendulum is, the slower are its vibrations. The common remedy for this inconvenience is raising or lowering the weight of the pendulum, by means of a screw, as occasion may require. Pendulums vibrate faster towards the poles, and slowest at the equator. This is accounted for by the earth's diameter being greater through the equator than through the poles. All bodies on the earth's surface are drawn to its centre by the force of gravity; and more powerfully as the square of their distance is less. Hence, if one portion of the earth's surface be farther from its centre than another, the force of gravity on a pendulum in one place must be less than in another; and consequently the pendulum will vibrate slower or faster according to its situation. And this is found to be actually the case.
It was from observing the difference in the vibrations of pendulums of the same length, that the difference of gravity was discovered, and the true figure of the earth ascertained. Pendulums vibrating seconds, at London, are thirty-nine inches and two-tenths in length; but at the equator about thirty-nine inches and one-tenth. Pendulums
40 MECHANICAL POWERS.
of the same length vibrate in the same time however different in weight.
QUESTIONS.—1. In what direction will a body move when impelled by two forces? 2. Describe the motion of a ship as impelled by the wind and a current. 3. What is circular motion? 4. The example? 5. Centripetal force? 6. Centrifugal? 7. What is said of these two forces? 8. What is a tangent? 9. What is said of the motion of the moon? 10. What is a parabola? 11. A pendulum? 12. Describe the manner in which a pendulum vibrates. 13. Why is not the motion of a pendulum perpetual? 14. Why do clocks go faster in winter than in summer? 15. Why do pendulums vibrate faster towards the poles than at the equator?
NOTE. The centrifugal force is stronger at the equator than at the poles; and as it tends to drive bodies from the centre, it is necessarily opposed to, and must lessen the power of gravity, which attracts them towards the centre. The equatorial diameter of the earth is stated by some to be 34 miles, and by others to be 26 miles longer than the polar diameter. 16. Illustrate by figure 1. the composition and resolution of motion.
Mechanical Powers.Centre of motion is that point which remains at rest while all
the other parts of a body move round it. Axis of motion is the line about which a revolving body moves. Equilibrium, equipoise, equality of weight.
THE mechanical powers are simple instruments or machines in the hands of man, by which he is enabled to raise great weights, and overcome such resistances as his natural strength could never effect without them. They are six in number, the lever, the pulley, the wheel and axle, the inclined plane, the wedge, and the screw, one or more of which enters into the composition of every machine. In order to understand the power of a machine, four things are to be considered; the power that acts, which consists in the effort of men or horses, of weights, springs, running waters, wind, and steam; the resistance which is to be overcome by the power, which is generally a weight to be moved; the centre of motion, or, as it is termed in mechanics, the fulcrum, which is the point about which all the parts of a body move; and lastly, the respective velocities of the power, and of the resistance, which must depend upon their respective distances
*HE LEVER. 41
from the axis of motion. The power and weight are said to balance each other, or to be in equilibrium, when the effort of the one to produce motion in one direction, is equal to the effort of the other to produce it in the opposite direction. The power of a machine is calculated, when it is in a state of equilibrium, that is, when the power just balances the resistance opposed, and the momentum of each is equal.
The lever is any inflexible bar of iron, wood, or other material, which serves to raise weights, while it is supported at a point by a prop or fulcrum, on which, as the centre of motion, all the other parts turn. There are three different kinds of levers. The first kind has the fulcrum between the weight and the power, as in steelyards and scissors. It is the most common kind, and is chiefly used for loosening large rocks; or for raising great weights to small heights, in order to place ropes under them. Let it be required to raise a body which weighs ten hundred pounds, by the strength of a man equal to a hundred pounds weight. Now as the man's strength is only equal to the tenth part of the weight of the body to be raised, the arm of the lever, to which his strength is to be applied, must be ten times as long as the other, in order that the power and weight may be in equilibrium. A balance is a lever of this kind, with equal arms; but if one arm be four times the length of the other, then it is a lever which gains power in the proportion of four to one, and a single pound weight, put into the scale which is suspended from the long arm, will balance four pounds in the other. The second kind of lever is when the prop is at one end, the power at the other, and the weight between them. It explains why two men carrying a burden upon a pole, may bear unequal shares according to their strength, by placing it nearer to the one than the other. He, to whom the burden is five times the nearest, will have to bear five times as much weight as the other. In the case of two horses of unequal strength the beam may be so divided, that they shall draw in proportion to their respective ability. The third kind of lever is when the prop is at one end, the weight at the other, and the power applied between them. To this kind are generally referred the bones of a man's arm, for when he lifts a weight by the hand, the muscle that-exerts its force to raise that weight, is fixed toihe bone about one-tenth part as far below the elbow as the hand