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of the same length vibrate in the same time however different in weight.
QUESTIONS.—1. In what direction will a body movè when impel. led 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 ofi 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 slated by some to be 34 miles, and by others to be 26 miles longer than the polar diameter. 16. Illustratē by figure 1. the composition and resolution of motion.
Centre of motion is that point which remains at rest while all
the uther parts of a body move round it. Axis of motion is the line about which a revolving body moves. Equilib'rium, equipoise, equality of weight.
The mechanical powers are simple instruments or ma.. chines 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 rea sistance, which must depend upon their respective distances
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 to the bone about one-tenth part as far below the elbow as the hand
is. The elbow being the centre round which the lower part of the arm turns, the muscle, therefore, must exert a force ten times as great as the weight to be raised. At first view this may appear a disadvantage, but the loss of power
is compensated by the gain of velocity, and by the beauty and compactness of the limb.
Questions.-1. What are mechanical powers ? 2. What four things are necessary to be considered in order to understand the pow. er of a machine ? 3. When do the power and weight balance each other? 4. What is a lever? 3. Describe the lever of the first kind. 6. What are some instances of it, and to what purposes are they applicable? 7. What is said of a balance ? 8. Describe the second kind of lever. 9. What does it explain ? 10. What is the third kind of lever? 11. Show how the bones of a man's arm make a lever of this kind. 12. How is the loss of power compensated ? 13. Give an illustration by fig. 7. of the first kind of lever. 14. Of the second kind, by figures 9' and 5. 15. Of the third kind, by figures 10 and 2.
The Pulley, Wheel and Axle, and Inclined Plane. The pulley is formed by a small wheel, made of wood or metal, with a groove in its circumference, which is placed in a frame and turns on an axis. The wheel is usually called a sheeve, and is so fixed in the frame, or block, as to move round a pin passing through its centre. Pullies are of two kinds ; fixed, which do not move out of their places; and moveable, which rise and fall with the weight. A single fixed pulley gives no mechanical advantage, but it is of great importance in changing the direction of power, and is much used in buildings for drawing up small weights, for a man may raise a weight to any height without the fatigue of ascending a ladder. In the single moveable pulley, the advantage gained is as two to one ; that is, a power exerted by the hand of ten pounds will balance a weight of twenty pounds. In a system of pullies, the power gained must be estimated, by doubling the number of pullies in the lower or moveable block. So that when the fixed block contains two pullies which only turn on their axes, and the lower block also contains two, which not only turn on their axes, but rise with the weight, the advantage gained is as four to one.
THE INCLINED PLANE.
example of this kind, you will perceive, that by raising the weight an inch, there are four ropes shortened each an inch, and therefore the hand must have passed through four inches of space in raising the weight a single inch; which establishes the maxim, that what is gained in power is lost in space.
The next mechanical power is the wheel and axle, which consists of a cylinder, and a wheel fastened to it, or of a cylinder with projecting spokes. The power being applied at the circumference of the wheel, the weight to be raised is fastened to a rope that coils round the axle. The advantage gained is in proportion as the diameter of the wheel exceeds that of the axle. Suppose a wheel to be twelve feet diameter, and the axle one foot, the power acting at the circumference of the wheel moves over twelve times the space which the circumference of the axle does. Hence, twelve hundred weight may be raised with the power of one hundred weight. The wheel and axle may be considered as a perpetual lever, the centre of the le being the fulcrum, half the diameter of the wheel the long arm, and half the diameter of the axle the short arm. Now, from this it is evident, that the greater the diameter of the wheel, and the smaller the diameter of the axle, the stronger is the power of this machine ; but then the weight must rise slower in proportion. A useful application of the wheel and axle is the crane used on wharfs for drawing goods up from a ship. A man sets a great wheel in motion by pressing on the spokes at the rim, and the rope to which the goods are attached is wound round the axle. The wheel is sometimes put in motion by a man in the inside, who is in an upright position, and keeps walking on the bars, as if ascending stairs, which keeps the wheel revolving.
The inclined plane is nothing more than a slope, or declivity, frequently used to facilitate the drawing up of weights. The increase of the power is in the proportion of the length of the plane to its height; that is, the more the plane is lengthened, or its height shortened, the less is the resistance to be overcome. If a plane be twenty feet long, and the perpendicular height be four feet, or one-fifth of the length, then five hundred pounds would be balanced on it by one hundred, because the plane is five times the length of the perpendicular height to which the weight is to be raised. If the height be two feet, or one-tenth of the length, then fifty
THE WEDGE AND SCREW.
pounds will balance the five hundred. It is much less laboria ous to ascend a hill by a winding gentle ascent than to climb up a steep declivity. In addition to there being a greater force required in ascending a hill, horses, that draw a load, are placed in a position in which they can exert but a small part of their usual strength. The principle of the inclined plane is applied to the construction of carriage-ways, for the conveyance of heavy loads up steep elevations. It is applied also in rail-ways, the use of which has been hitherto confined, almost exclusively, to coal-works, and other mines. Inventions, whose only recommendations are simplicity and usefulness, are often suffered to lie long in a state of public neglect, while others of more imposing aspect are readily adopted. It has been remarked with respect to Great Britain, that the time has at length arrived, when carriages moving on level surfaces, or on gently inclining planes, with little friction, and without obstructions, are fast spreading over the face of the country.
Questions.-1. How is the pulley formed ? 2. What are the two kinds of pullies? 3. What is said of the single fixed pulley ? 4. What advantage is gained in a single moveable pulley? 5. How is the power gained to be estimated in a system of pullies ? 6. How is this explained and what maxim does it establish ?' 7. Describe the wheel and axle. 8. In what proportion is advantage gained in this mecha. nical power ? 9. What is the example? 10. Why may the wheel and axle be considered as a perpetual lever ? 11. What application is made of this power? 12. What is an inclined plane? 13. In what proportion is the increase of power? 14. What is the example for illustrating this? 15. What application is made of the principle of the inclined plane ? 16. What has been remarked concerning the use of rail-ways ? 17. With respect to Great Britain ? 18. Explain the single moveable pulley by fig. 13.-system of pullies by fig. 15. 19. Illustrate the power of the wheel and axle by fig. 11. 20. Inclined plane by fig. 8.
The Wedge and Screw.
upon another, or the shock of two bodies in motion. Sili'ceous, flinty; see Lesson 63. The wedge may be considered as two equally inclined planes united at their bases. The advantage gained by it is