simple science

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Simple Science

161. Movable Pulleys
Man's Way of Helping Himself:
By the use of a movable pulley, we are able to support a weight by a force equal to only one half the load. 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 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. - A movable pulley lightens labor.
162. Combination of Pulleys
Man's Way of Helping Himself:
A combination of pulleys called block and tackle is used where very heavy loads are to be moved. In Figure 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.

FIG. - An effective arrangement of pulleys known as block and tackle.
163. Practical Application
Man's Way of Helping Himself:
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
Man's Way of Helping Himself:
The wheel and axle consists of a large wheel and a small axle so fastened that they rotate together.

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.

FIG. - The wheel and axle.
165. Windlass Cogwheels Application
Man's Way of Helping Himself:
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; 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.

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. 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. - Cogwheels.

FIG. - By means of a belt, motion can be transferred from place to place.
166. Compound Machines
Man's Way of Helping Himself:
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 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 .

FIG. - A simple derrick for raising weights.

FIG. - A traveling crane.

FIG. - A farm engine putting in a crop.
167. Measurement of Work
Man's Way of Helping Himself:
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.

168. The Power or the Speed with which Work is Done
Man's Way of Helping Himself:
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
Man's Way of Helping Himself:
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.
170. Man's Strength not Sufficient for Machines
Man's Way of Helping Himself:
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 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. 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.

In the following Chapter will be given an account of water, wind, and fuel as machine feeders.

FIG. - Man's strength is not sufficient for heavy work.

FIG. - The windmill pumps water into the troughs where cattle drink.


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