MAN'S WAY OF HELPING HIMSELF
149. Labor-saving Devices. To primitive man belonged more especially the arduous tasks of the out-of-door life: the clearing of paths through the wilderness; the hauling of material; the breaking up of the hard soil of barren fields into soft loam ready to receive the seed; the harvesting of the ripe grain, etc.
FIG. 91.—Prying a stone out of the ground.
The more intelligent races among men soon learned to help themselves in these tasks. For example, our ancestors in the field soon learned to pry stones out of the ground (Fig. 91) rather than to undertake the almost impossible task of lifting them out of the earth in which they were embedded; to swing fallen trees away from a path by means of rope attached to one end rather than to attempt to remove them single-handed; to pitch hay rather than to lift it; to clear a field with a rake rather than with the hands; to carry heavy loads in wheelbarrows (Fig. 92) rather than on the shoulders; to roll barrels up a plank (Fig. 93) and to raise weights by ropes. In every case, whether in the lifting of stones, or the felling of trees, or the transportation of heavy weights, or the digging of the ground, man used his brain in the invention of mechanical devices which would relieve muscular strain and lighten physical labor.
If all mankind had depended upon physical strength only, the world to-day would be in the condition prevalent in parts of Africa, Asia, and South America, where the natives loosen the soil with their hands or with crude implements (Fig. 94), and transport huge weights on their shoulders and heads.
FIG. 92.—The wheelbarrow lightens labor.
Any mechanical device (Figs. 95 and 96), whereby man's work can be more conveniently done, is called a machine; the machine itself never does any work—it merely enables man to use his own efforts to better advantage.
FIG. 93.—Rolling barrels up a plank.
150. When do we Work? Whenever, as a result of effort or force, an object is moved, work is done. If you lift a knapsack from the floor to the table, you do work because you use force and move the knapsack through a distance equal to the height of the table. If the knapsack were twice as heavy, you would exert twice as much force to raise it to the same height, and hence you would do double the work. If you raised the knapsack twice the distance,—say to your shoulders instead of to the level of the table,—you would do twice the work, because while you would exert the same force you would continue it through double the distance.
FIG. 94.—Crude method of farming.
Lifting heavy weights through great distances is not the only way in which work is done. Painting, chopping wood, hammering, plowing, washing, scrubbing, sewing, are all forms of work. In painting, the moving brush spreads paint over a surface; in chopping wood, the descending ax cleaves the wood asunder; in scrubbing, the wet mop rubbed over the floor carries dirt away; in every conceivable form of work, force and motion occur.
A man does work when he walks, a woman does work when she rocks in a chair—although here the work is less than in walking. On a windy day the work done in walking is greater than normal. The wind resists our progress, and we must exert more force in order to cover the same distance. Walking through a plowed or rough field is much more tiring than to walk on a smooth road, because, while the distance covered may be the same, the effort put forth is greater, and hence more work is done. Always the greater the resistance encountered, the greater the force required, and hence the greater the work done.
The work done by a boy who raises a 5-pound knapsack to his shoulder would be 5 × 4, or 20, providing his shoulders were 4 feet from the ground.
The amount of work done depends upon the force used and the distance covered (sometimes called displacement), and hence we can say that
Work = force multiplied by distance,
or W = f × d.
151. Machines. A glance into our machine shops, our factories, and even our homes shows how widespread is the use of complex machinery. But all machines, however complicated in appearance, are in reality but modifications and combinations of one or more of four simple machines devised long ago by our remote ancestors. These simple devices are known to-day, as (1) the lever, represented by a crowbar, a pitchfork; (2) the inclined plane, represented by the plank upon which barrels are rolled into a wagon; (3) the pulley, represented by almost any contrivance for the raising of furniture to upper stories; (4) the wheel and axle, represented by cogwheels and coffee grinders.
FIG. 95.—Primitive method of grinding corn.
Suppose a 600-pound bowlder which is embedded in the ground is needed for the tower of a building. The problem of the builder is to get the heavy bowlder out of the ground, to load it on a wagon for transportation, and finally to raise it to the tower. Obviously, he cannot do this alone; the greatest amount of force of which he is capable would not suffice to accomplish any one of these tasks. How then does he help himself and perform the impossible? Simply, by the use of some of the machine types mentioned above, illustrations of which are known in a general way to every schoolboy. The very knife with which a stick is whittled is a machine.
FIG. 96.—Separating rice grains by flailing.
FIG. 97.—The principle of the lever.
152. The Lever. Balance a foot rule, containing a hole at its middle point F, as shown in Figure 97. If now a weight of 1 pound is suspended from the bar at some point, say 12, the balance is disturbed, and the bar swings about the point F as a center. The balance can be regained by suspending an equivalent weight at the opposite end of the bar, or by applying a 2-pound weight at a point 3 inches to the left of F. In the latter case a force of 1 pound actually balances a force of 2 pounds, but the 1-pound weight is twice as far from the point of suspension as is the 2-pound weight. The small weight makes up in distance what it lacks in magnitude.
Such an arrangement of a rod or bar is called a lever. In any form of lever there are only three things to be considered: the point where the weight rests, the point where the force acts, and the point called the fulcrum about which the rod rotates.
The distance from the force to the fulcrum is called the force arm. The distance from the weight to the fulcrum is called the weight arm; and it is a law of levers, as well as of all other machines, that the force multiplied by the length of the force arm must equal the weight multiplied by the length of the weight arm.
Force × force arm = weight × weight arm.
A force of 1 pound at a distance of 6, or with a force arm 6, will balance a weight of 2 pounds with a weight arm 3; that is,
1 × 6 = 2 × 3.
Similarly a force of 10 pounds may be made to sustain a weight of 100 pounds, providing the force arm is 10 times longer than the weight arm; and a force arm of 800 pounds, at a distance of 10 feet from the fulcrum, may be made to sustain a weight of 8000 pounds, providing the weight is 1 foot from the fulcrum.
153. Applications of the Lever. By means of a lever, a 600-pound bowlder can be easily pried out of the ground. Let the lever, any strong metal bar, be supported on a stone which serves as fulcrum; then if a man exerts his force at the end of the rod somewhat as in Figure 91 ([p. 154]), the force arm will be the distance from the stone or fulcrum to the end of the bar, and the weight arm will be the distance from the fulcrum to the bowlder itself. The man pushes down with a force of 100 pounds, but with that amount succeeds in prying up the 600-pound bowlder. If, however, you look carefully, you will see that the force arm is 6 times as long as the weight arm, so that the smaller force is compensated for by the greater distance through which it acts.
At first sight it seems as though the man's work were done for him by the machine. But this is not so. The man must lower his end of the lever 3 feet in order to raise the bowlder 6 inches out of the ground. He does not at any time exert a large force, but he accomplishes his purpose by exerting a small force continuously through a correspondingly greater distance. He finds it easier to exert a force of 100 pounds continuously until his end has moved 3 feet rather than to exert a force of 600 pounds on the bowlder and move it 6 inches.
By the time the stone has been raised the man has done as much work as though the stone had been raised directly, but his inability to put forth sufficient muscular force to raise the bowlder directly would have rendered impossible a result which was easily accomplished when through the medium of the lever he could extend his small force through greater distance.
154. The Wheelbarrow as a Lever. The principle of the lever is always the same; but the relative position of the important points may vary. For example, the fulcrum is sometimes at one end, the force at the opposite end, and the weight to be lifted between them.
FIG. 98.—A slightly different form of lever.
Suspend a stick with a hole at its center as in Figure 98, and hang a 4-pound weight at a distance of 1 foot from the fulcrum, supporting the load by means of a spring balance 2 feet from the fulcrum. The pointer on the spring balance shows that the force required to balance the 4-pound load is but 2 pounds.
The force is 2 feet from the fulcrum, and the weight (4) is 1 foot from the fulcrum, so that
Force × distance = Weight × distance,
or 2 × 2 = 4 × 1.
FIG. 99.—The wheelbarrow lightend labor.
Move the 4-pound weight so that it is very near the fulcrum, say but 6 inches from it; then the spring balance registers a force only one fourth as great as the weight which it suspends. In other words a force of 1 at a distance of 24 inches (2 feet) is equivalent to a force of 4 at a distance of 6 inches.
FIG. 100.—A modified wheelbarrow.
One of the most useful levers of this type is the wheelbarrow (Fig. 99). The fulcrum is at the wheel, the force is at the handles, the weight is on the wheelbarrow. If the load is halfway from the fulcrum to the man's hands, the man will have to lift with a force equal to one half the load. If the load is one fourth as far from the fulcrum as the man's hands, he will need to lift with a force only one fourth as great as that of the load.
This shows that in loading a wheelbarrow, it is important to arrange the load as near to the wheel as possible.
FIG. 101.—The nutcracker is a lever.
The nutcracker (Fig. 101) is an illustration of a double lever of the wheelbarrow kind; the nearer the nut is to the fulcrum, the easier the cracking.
FIG. 102.—The hand exerts a small force over a long distance and draws out a nail.
Hammers (Fig. 102), tack-lifters, scissors, forceps, are important levers, and if you will notice how many different levers (fig. 103) are used by all classes of men, you will understand how valuable a machine this simple device is.
155. The Inclined Plane. A man wishes to load the 600-pound bowlder on a wagon, and proceeds to do it by means of a plank, as in Figure 93. Such an arrangement is called an inclined plane.
The advantage of an inclined plane can be seen by the following experiment. Select a smooth board 4 feet long and prop it so that the end A (Fig. 104) is 1 foot above the level of the table; the length of the incline is then 4 times as great as its height. Fasten a metal roller to a spring balance and observe its weight. Then pull the roller uniformly upward along the plank and notice what the pull is on the balance, being careful always to hold the balance parallel to the incline.
When the roller is raised along the incline, the balance registers a pull only one fourth as great as the actual weight of the roller. That is, when the roller weighs 12, a force of 3 suffices to raise it to the height A along the incline; but the smaller force must be applied throughout the entire length of the incline. In many cases, it is preferable to exert a force of 30 pounds, for example, over the distance CA than a force of 120 pounds over the shorter distance BA.
FIG. 103.—Primitive man tried to lighten his task by balancing his burden.
Prop the board so that the end A is 2 feet above the table level; that is, arrange the inclined plane in such a way that its length is twice as great as its height. In that case the steady pull on the balance will be one half the weight of the roller; or a force of 6 pounds will suffice to raise the 12-pound roller.
FIG. 104.—Less force is required to raise the roller along the incline than to raise it to A directly.
The steeper the incline, the more force necessary to raise a weight; whereas if the incline is small, the necessary lifting force is greatly reduced. On an inclined plane whose length is ten times its height, the lifting force is reduced to one tenth the weight of the load. The advantage of an incline depends upon the relative length and height, or is equal to the ratio of the length to the height.
156. Application. By the use of an inclined plank a strong man can load the 600-pound bowlder on a wagon. Suppose the floor of the wagon is 2 feet above the ground, then if a 6-foot plank is used, 200 pounds of force will suffice to raise the bowlder; but the man will have to push with this force against the bowlder while it moves over the entire length of the plank.
Since work is equal to force multiplied by distance, the man has done work represented by 200 × 6, or 1200. This is exactly the amount of work which would have been necessary to raise the bowlder directly. A man of even enormous strength could not lift such a weight (600 lb.) even an inch directly, but a strong man can furnish the smaller force (200) over a distance of 6 feet; hence, while the machine does not lessen the total amount of work required of a man, it creates a new distribution of work and makes possible, and even easy, results which otherwise would be impossible by human agency.
157. Railroads and Highways. The problem of the incline is an important one to engineers who have under their direction the construction of our highways and the laying of our railroad tracks. It requires tremendous force to pull a load up grade, and most of us are familiar with the struggling horse and the puffing locomotive. For this reason engineers, wherever possible, level down the steep places, and reduce the strain as far as possible.
FIG. 105.—A well-graded railroad bed.
The slope of the road is called its grade, and the grade itself is simply the number of feet the hill rises per mile. A road a mile long (5280 feet) has a grade of 132 if the crest of the hill is 132 feet above the level at which the road started.
FIG. 106.—A long, gradual ascent is better than a shorter, steeper one.
In such an incline, the ratio of length to height is 5280 ÷ 132, or 40; and hence in order to pull a train of cars to the summit, the engine would need to exert a continuous pull equal to one fortieth of the combined weight of the train.
If, on the other hand, the ascent had been gradual, so that the grade was 66 feet per mile, a pull from the engine of one eightieth of the combined weight would have sufficed to land the train of cars at the crest of the grade.
Because of these facts, engineers spend great sums in grading down railroad beds, making them as nearly level as possible. In mountainous regions, the topography of the land prevents the elimination of all steep grades, but nevertheless the attempt is always made to follow the easiest grades.
158. The Wedge. If an inclined plane is pushed underneath or within an object, it serves as a wedge. Usually a wedge consists of two inclined planes (Fig. 107).
FIG. 107.—By means of a wedge, the stump is split.
A chisel and an ax are illustrations of wedges. Perhaps the most universal form of a wedge is our common pin. Can you explain how this is a wedge?
159. The Screw. Another valuable and indispensable form of the inclined plane is the screw. This consists of a metal rod around which passes a ridge, and Figure 108 shows clearly that a screw is simply a rod around which (in effect) an inclined plane has been wrapped.
FIG. 108—A screw as a simple machine.
The ridge encircling the screw is called the thread, and the distance between two successive threads is called the pitch. It is easy to see that the closer the threads and the smaller the pitch, the greater the advantage of the screw, and hence the less force needed in overcoming resistance. A corkscrew is a familiar illustration of the screw.
160. Pulleys. The pulley, another of the machines, is merely a grooved wheel around which a cord passes. It is sometimes more convenient to move a load in one direction rather than in another, and the pulley in its simplest form enables us to do this. In order to raise a flag to the top of a mast, it is not necessary to climb the mast, and so pull up the flag; the same result is accomplished much more easily by attaching the flag to a movable string, somewhat as in Figure 109, and pulling from below. As the string is pulled down, the flag rises and ultimately reaches the desired position.
If we employ a stationary pulley, as in Figure 109, we do not change the force, because the force required to balance the load is as large as the load itself. The only advantage is that a force in one direction may be used to produce motion in another direction. Such a pulley is known as a fixed pulley.
FIG. 109.—By means of a pulley, a force in one direction produces motion in the opposite direction.
161. Movable Pulleys. By the use of a movable pulley, we are able to support a weight by a force equal to only one half the load. In Figure 109, the downward pull of the weight and the downward pull of the hand are equal; in Figure 110, the spring balance supports only one half the entire load, the remaining half being borne by the hook to which the string is attached. The weight is divided equally between the two parts of the string which passes around the pulley, so that each strand bears only one half of the burden.
We have seen in our study of the lever and the inclined plane that an increase in force is always accompanied by a decrease in distance, and in the case of the pulley we naturally look for a similar result. If you raise the balance (Fig. 110) 12 feet, you will find that the weight rises only 6 feet; if you raise the balance 24 inches, you will find that the weight rises 12 inches. You must exercise a force of 100 pounds over 12 feet of space in order to raise a weight of 200 pounds a distance of 6 feet. When we raise 100 pounds through 12 feet or 200 pounds through 6 feet the total work done is the same; but the pulley enables those who cannot furnish a force of 200 pounds for the space of 6 feet to accomplish the task by furnishing 100 pounds for the space of 12 feet.
FIG. 110.—A movable pulley lightens labor.
FIG. 111.—An effective arrangement of pulleys known as block and tackle.
162. Combination of Pulleys. A combination of pulleys called block and tackle is used where very heavy loads are to be moved. In Figure 111 the upper block of pulleys is fixed, the lower block is movable, and one continuous rope passes around the various pulleys. The load is supported by 6 strands, and each strand bears one sixth of the load. If the hand pulls with a force of 1 pound at P, it can raise a load of 6 pounds at W, but the hand will have to pull downward 6 feet at P in order to raise the load at W 1 foot. If 8 pulleys were used, a force equivalent to one eighth of the load would suffice to move W, but this force would have to be exerted over a distance 8 times as great as that through which W was raised.
163. Practical Application. In our childhood many of us saw with wonder the appearance and disappearance of flags flying at the tops of high masts, but observation soon taught us that the flags were raised by pulleys. In tenements, where there is no yard for the family washing, clothes often appear flapping in mid-air. This seems most marvelous until we learn that the lines are pulled back and forth by pulleys at the window and at a distant support. By means of pulleys, awnings are raised and lowered, and the use of pulleys by furniture movers, etc., is familiar to every wide-awake observer on the streets.
164. Wheel and Axle. The wheel and axle consists of a large wheel and a small axle so fastened that they rotate together.
FIG. 112.—The wheel and axle.
When the large wheel makes one revolution, P falls a distance equal to the circumference of the wheel. While P moves downward, W likewise moves, but its motion is upward, and the distance it moves is small, being equal only to the circumference of the small axle. But a small force at P will sustain a larger force at W; if the circumference of the large wheel is 40 inches, and that of the small wheel 10 inches, a load of 100 at W can be sustained by a force of 25 at P. The increase in force of the wheel and axle depends upon the relative size of the two parts, that is, upon the circumference of wheel as compared with circumference of axle, and since the ratio between circumference and radius is constant, the ratio of the wheel and axle combination is the ratio of the long radius to the short radius.
For example, in a wheel and axle of radii 20 and 4, respectively, a given weight at P would balance 5 times as great a load at W.
165. Application. Windlass, Cogwheels. In the old-fashioned windlass used in farming districts, the large wheel is replaced by a handle which, when turned, describes a circle. Such an arrangement is equivalent to wheel and axle (Fig. 112); the capstan used on shipboard for raising the anchor has the same principle. The kitchen coffee grinder and the meat chopper are other familiar illustrations.
Cogwheels are modifications of the wheel and axle. Teeth cut in A fit into similar teeth cut in B, and hence rotation of A causes rotation of B. Several revolutions of the smaller wheel, however, are necessary in order to turn the larger wheel through one complete revolution; if the radius of A is one half that of B, two revolutions of A will correspond to one of B; if the radius of A is one third that of B, three revolutions of A will correspond to one of B.
FIG. 113.—Cogwheels.
Experiment demonstrates that a weight W attached to a cogwheel of radius 3 can be raised by a force P, equal to one third of W applied to a cogwheel of radius 1. There is thus a great increase in force. But the speed with which W is raised is only one third the speed with which the small wheel rotates, or increase in power has been at the decrease of speed.
This is a very common method for raising heavy weights by small force.
Cogwheels can be made to give speed at the decrease of force. A heavy weight W attached to B will in its slow fall cause rapid rotation of A, and hence rapid rise of P. It is true that P, the load raised, will be less than W, the force exerted, but if speed is our aim, this machine serves our purpose admirably.
An extremely important form of wheel and axle is that in which the two wheels are connected by belts as in Figure 114. Rotation of W induces rotation of w, and a small force at W is able to overcome a large force at w. An advantage of the belt connection is that power at one place can be transmitted over a considerable distance and utilized in another place.
FIG. 114.—By means of a belt, motion can be transferred from place to place.
166. Compound Machines. Out of the few simple machines mentioned in the preceding Sections has developed the complex machinery of to-day. By a combination of screw and lever, for example, we obtain the advantage due to each device, and some compound machines have been made which combine all the various kinds of simple machines, and in this way multiply their mechanical advantage many fold.
A relatively simple complex machine called the crane (Fig. 116) maybe seen almost any day on the street, or wherever heavy weights are being lifted. It is clear that a force applied to turn wheel 1 causes a slower rotation of wheel 3, and a still slower rotation of wheel 4, but as 4 rotates it winds up a chain and slowly raises Q. A very complex machine is that seen in Figure 117.
FIG. 115.—A simple derrick for raising weights.
FIG. 116.—A traveling crane.
167. Measurement of Work. In Section 150, we learned that the amount of work done depends upon the force exerted, and the distance covered, or that W = force × distance. A man who raises 5 pounds a height of 5 feet does far more work than a man who raises 5 ounces a height of 5 inches, but the product of force by distance is 25 in each case. There is difficulty because we have not selected an arbitrary unit of work. The unit of work chosen and in use in practical affairs is the foot pound, and is defined as the work done when a force of 1 pound acts through a distance of 1 foot. A man who moves 8 pounds through 6 feet does 48 foot pounds of work, while a man who moves 8 ounces (1/2 pound) through 6 inches (1/2 foot) does only one fourth of a foot pound of work.
FIG. 117.—A farm engine putting in a crop.
168. The Power or the Speed with which Work is Done. A man can load a wagon more quickly than a growing boy. The work done by the one is equal to the work done by the other, but the man is more powerful, because the time required for a given task is very important. An engine which hoists a 50-pound weight in 1 second is much more powerful than a man who requires 50 seconds for the same task; hence in estimating the value of a working agent, whether animal or mechanical, we must consider not only the work done, but the speed with which it is done.
The rate at which a machine is able to accomplish a unit of work is called power, and the unit of power customarily used is the horse power. Any power which can do 550 foot pounds of work per second is said to be one horse power (H.P.). This unit was chosen by James Watt, the inventor of a steam engine, when he was in need of a unit with which to compare the new source of power, the engine, with his old source of power, the horse. Although called a horse power it is greater than the power of an average horse.
An ordinary man can do one sixth of a horse power. The average locomotive of a railroad has more than 500 H.P., while the engines of an ocean liner may have as high as 70,000 H.P.
169. Waste Work and Efficient Work. In our study of machines we omitted a factor which in practical cases cannot be ignored, namely, friction. No surface can be made perfectly smooth, and when a barrel rolls over an incline, or a rope passes over a pulley, or a cogwheel turns its neighbor, there is rubbing and slipping and sliding. Motion is thus hindered, and the effective value of the acting force is lessened. In order to secure the desired result it is necessary to apply a force in excess of that calculated. This extra force, which must be supplied if friction is to be counteracted, is in reality waste work.
If the force required by a machine is 150 pounds, while that calculated as necessary is 100 pounds, the loss due to friction is 50 pounds, and the machine, instead of being thoroughly efficient, is only two thirds efficient.
Machinists make every effort to eliminate from a machine the waste due to friction, leveling and grinding to the most perfect smoothness and adjustment every part of the machine. When the machine is in use, friction may be further reduced by the use of lubricating oil. Friction can never be totally eliminated, however, and machines of even the finest construction lose by friction some of their efficiency, while poorly constructed ones lose by friction as much as one half of their efficiency.
FIG. 118.—Man's strength is not sufficient for heavy work.
170. Man's Strength not Sufficient for Machines. A machine, an inert mass of metal and wood, cannot of itself do any work, but can only distribute the energy which is brought to it. Fortunately it is not necessary that this energy should be contributed by man alone, because the store of energy possessed by him is very small in comparison with the energy required to run locomotives, automobiles, sawmills, etc. Perhaps the greatest value of machines lies in the fact that they enable man to perform work by the use of energy other than his own.
Figure 118 shows one way in which a horse's energy can be utilized in lifting heavy loads. Even the fleeting wind has been harnessed by man, and, as in the windmill, made to work for him (Fig. 119). One sees dotted over the country windmills large and small, and in Holland, the country of windmills, the landowner who does not possess a windmill is poor indeed.
For generations running water from rivers, streams, and falls has served man by carrying his logs downstream, by turning the wheels of his mill, etc.; and in our own day running water is used as an indirect source of electric lights for street and house, the energy of the falling water serving to rotate the armature of a dynamo (Section 310).
A more constant source of energy is that available from the burning of fuel, such as coal and oil. The former is the source of energy in locomotives, the latter in most automobiles.
FIG. 119.—The windmill pumps water into the troughs where cattle drink.
In the following Chapter will be given an account of water, wind, and fuel as machine feeders.