CHAPTER XXIX

MAN'S SIMPLE MACHINES

272. How Does Man Lighten His Work? - A few generations ago, if you had gone into a cornfield in the spring, you would have seen oxen pulling a crude wooden plow (see Fig. 2, § 5) which just stirred the soil of one row. The farmer himself, probably stooped and tired, would have been walking beside the team. plow is a steel machine (see § 183, Fig. 98) deep and turns over the soil of several rows. The farmer rides comfortably in a seat which is provided with springs. Perhaps four horses or a tractor are pulling the plow. This is only one way in which man has made his work easier.

Today the which digs

Man has within himself energy, or the power to do work; this is derived from the oxidation of his food (see § 188). But as he became more and more civilized, he found that there were many devices, or tools, with which he could do his work without using so much of his own energy. He could also do much greater tasks than his own strength made possible. We have already spoken of the plow. When man wanted to lift a load of hay into a hayloft (Fig. 195), he learned to use a pulley and rope. It is easier to pull down on the rope than to push up on

the weight. Why? Does a man's own weight help him? Man also learned to pry a stone out of the ground with a crowbar (Fig. 196), instead of lifting it out. He learned to split logs with an ax and a wedge (Fig. 210, § 279).

FIG. 195. - - By using a pulley and a rope, a man can lift a weight more easily than by carrying it. Can a man lift more than his own weight in this way?

If he wished to move a heavy load, he learned to put rollers under it, instead of trying to drag it along the ground.

273. What Advantage Do We Get from Machines? Let us think of this problem: How can we get a 200pound barrel of flour into a wagon without lifting the

whole weight of the barrel? See Fig. 197. Suppose that we use a plank 15 feet long, and that the higher end, which rests on the wagon, is 3 feet above the ground. How does this help us? We roll the barrel 15 feet up the

FIG. 196. By using a crowbar with a support a man can lift a heavy stone from the ground.

plank to raise it 3 feet from the ground; that is, we roll it five times as far as we need to lift it. What is the value of doing this? The value is that we need exert only as much force as we should use to lift the barrel

FIG. 197. By rolling a barrel up a long, inclined plank a man need not exert nearly the force he would need to lift it into the wagon.

directly into the wagon. So a force of 40 pounds will roll a 200-pound barrel up such a plank. Now a grown man can easily exert a force of 40 pounds, although he might not be able to exert one of 200 pounds.

Do we use the principle of the inclined plane in other

ways? Think how much easier it is for us to climb a gradual slope than a steep one, or a stairway with low "risers" rather than high ones. Whenever we climb a sloping ladder, or a train climbs a grade in the mountains, or a horse pulls a load up a hill, the inclined plane is being used. But in going up a slope, we make an exchange: we go farther than if we went straight up.

Have you ever seen some of the famous railway grades, like the letter-S curve of the Pennsylvania Railroad near Altoona?

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274. Is a Teeter a Machine? Let us think of another problem: Suppose that you weighed 50 pounds, and that you made a teeter 15 feet long (Fig. 198).

FIG. 198.—The weight of the child, multiplied

by its distance from the support on which the teeter

turns, is equal to the weight of the man multiplied by his distance from the support.

If your father, weighing 200 pounds, were on one end, how much force must you use on the other end to lift him? Everything will depend, will it not, upon where

you put the log under the teeter board? If you put the middle of the board over the log, you will need to weigh a little more than 200 pounds yourself, to be able to bring your end of the board down. But you are supposed to weigh only 50 pounds. If you should put the log 5 feet from your father's end of the teeter, and 10 feet from your end, you would need to weigh 100 pounds to lift

your father. That is, as your distance from the log would be twice your father's you must weigh at least half as much as he to lift him. But if the log is 3 feet from your father's end of the board, and 12 feet from your end, you, with your 50 pounds, could balance your father, who weighs 200 pounds. However, note one thing carefully: Suppose you and he teeter up and down, how far must you move downward to lift your father one foot? You must go down 4 feet, must you not? To put it in another way, he by going down one foot can raise you 4 feet. Which gets the longer ride on the teeter, the heavy person, or the light one?

As you first think of these two cases of the sloping board and the teeter, you may imagine that in some mysterious way you have made energy; if not, how is it that you, weighing only 50 pounds, can lift your father, who weighs 200 pounds; or how can a man who exerts a force of only 40 pounds, push up a barrel weighing 200 pounds? But if you think of the matter more deeply, you will see that you have made no energy. You push the barrel a greater distance along the board so as to lift it a short vertical distance. In the teeter you go down a greater distance to let your father go up a shorter distance. These facts show us what the law of machines is: The power put forth, multiplied by the distance the power moves, is equal to the weight lifted, multiplied by the distance the weight moves. In using machines, then, we make an exchange of energy; we never get something for nothing. 275. How Many Machines Do We Use? This question does not mean how many pieces of machinery are