36 THE LAWS OF MOTION. that human powers can produce. Accelerated motion takes place, when the motive power continues to act upon any body, so that its motion is continually increased. When a stone falls from a height, the impulse which it receives from gravity during the first instant of its fall, would be sufficient to bring it to the ground with a uniform velocity; but the stone is not acted upon by gravity merely at the first instant of its fall,-this power continues to impel it during the whole of its descent, and it is this continued impulse which accelerates its motion. It has been found by experiment that heavy bodies, descending from a height by the force of gravity, fall sixteen feet the first second of time, three times that distance in the next, five times in the third second, seven times in the fourth, and so on, regularly increasing their velocities according to the number of seconds during which the body has been falling. Retarded motion is that of a body which moves every moment slower and slower; and it is produced by some force acting upon a body in a direction opposite to that which first put it in motion, as when a stone is thrown upwards, its velocity is gradually diminished by the power of gravity. The force, or power, with which a body in motion strikes against another body, is called its momentum. It is composed of its quantity of matter, multiplied by its quantity of motion; or in other words, its weight and its velocity. A small body may have a greater momentum than a large one, provided its velocity be sufficiently greater; the momentum of an arrow shot from a bow, for instance, must be greater than a stone thrown by the hand. The momentum of bodies is one of the most important points in mechanics; for you will find, that it is from opposing motion to matter, that machines derive their powers. When a body in motion strikes against another body, it meets with resistance from it; and the resistance of the body at rest will be equal to the blow struck by the body in motion; or to express the same in philosophical language, action and re-action will be equal and in opposite directions. It appears, therefore, that one body acting upon another, loses as much motion as it communicates, and that the sum of the motions of any two bodies in the same line of direction, cannot be changed by their mutual action. From the action and re-action of bodies we may learn in what manner a bird, 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 perpetua' motion be produced by art? 12. When a stone falls from a height >w does gravity accelerate its motion? 13. What is said of the stances 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. LESSON 19. Compound Motion. Projec'tile, impelled forward in a right line. Oblique', not direct, not perpendicular, not parallel. 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. 38 COMPOUND MOTION. 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 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 im pulse of its velocity. Were it possible to remove the obstacles occasioned by the resistance of the air, and by the friction of the 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. LESSON 20. Mechanical Powers. Centre of motion is that point which remains at rest while all Axis of motion is the line about which a revolving body moves. 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 |