How can a man lift up a heavy automobile by using a jack?
Why can you crack a hard nut with a nutcracker when you cannot crack it by squeezing it between two pieces of iron?
"Give me a lever, long enough and strong enough, and something to rest it on, and I can lift the whole world," said an old Greek philosopher. And as a philosopher he was right; theoretically it would be possible. But since he needed a lever that would have been as long as from here to the farthest star whose distance has ever been measured, and since he would have had to push his end of the lever something like a quintillion (1,000,000,000,000,000,000) miles to lift the earth one inch, his proposition was hardly a practical one.
But levers are practical. Without them there would be none of our modern machines. No locomotives could speed across the continents; no derricks could lift great weights; no automobiles or bicycles would quicken our travel; our very bodies would be completely paralyzed. Yet the law back of all these things is really simple.
You have often noticed on the see-saw that a small child at one end can be balanced by a larger child at the other end, provided that the larger child sits nearer the middle. Why should it matter where the larger child sits? He is always heavier—why doesn't he overbalance the small child? It is because when the small child moves up and down he goes a longer distance than the large child does. In Figure 26 the large boy moves up and down only half as far as the little girl does. She weighs only half as much as he, yet she balances him.
Fig. 26. The little girl raises the big boy, but in doing it she moves twice as far as he does.
You will begin to get a general understanding of levers and how they work by doing the following experiment:
Experiment 18. For this experiment there will be needed a small pail filled with something heavy (sand or stones will do), a yardstick with a hole through the middle and another hole near one end and with notches cut here and there along the edge, and a post or table corner with a heavy nail driven into it to within an inch of the head. The holes in the yardstick must be large enough to let the head of this nail through.
Put the middle hole of the yardstick over the nail, as is shown in Figure 27. The nail is the fulcrum of your lever. Now hang the pail on one of the notches about halfway between the fulcrum and the end of the stick and put your hand on the opposite side of the yardstick at about the same distance as the pail is from the fulcrum. Raise and lower the pail several times by moving the opposite end of the lever up and down. See how much force it takes to move the pail.
Now slide your hand toward the fulcrum and lower and raise the pail from that position. Is it harder or easier to lift the pail from here than from the first position? Which moves farther up and down, your hand or the pail?
Next, slide your hand all the way out to the end of the yardstick and raise and lower the pail from there. Is the pail harder or easier to lift? Does the pail move a longer or a shorter distance up and down than your hand?
If you wanted to move the pail a long way without moving your hand as far, would you put your hand nearer to the fulcrum or farther from it than the pail is?
Fig. 27. The yardstick is a lever by which he lifts the pail.
Fig. 28. A lever with the weight between the fulcrum and the force.
Suppose you wanted to lift the pail with the least possible effort, where would you put your hand?
Notice another fact: when your hand is at the end of the yardstick, it takes the same length of time to move a long way as the pail takes to move a short way. Then which is moving faster, your hand or the pail?
Experiment 19. Put the end hole of the yardstick on the nail, as shown in Figure 28. The nail is still the fulcrum of your lever. Put the pail about halfway between the fulcrum and the other end of the stick, and hold the end of the stick in your hands.
Raise and lower your hand to see how hard or how easy it is to lift the pail from this position. Which is moving farther, your hand or the pail? Which is moving faster?
Now put your hand about halfway between the fulcrum and the pail and raise and lower it. Is it harder or easier to raise than before? Which moves farther this time, your hand or the pail? Which moves faster?
If you wanted to make the pail move farther and faster than your hand, would you put your hand nearer to the fulcrum than the pail is, or farther from the fulcrum than the pail? If you wanted to move the pail with the least effort, where would you put your hand?
Experiment 20. Use a pair of long-bladed shears and fold a piece of cardboard once to lie astride your own or some one else's finger. Put the finger, protected by the cardboard, between the two points of the shears. Then squeeze the handles of the shears together. See if you can bring the handles together hard enough to hurt the finger between the points.
Now watch the shears as you open and close the blades. Which move farther, the points of the shears or the handles? Which move faster?
Next, put the finger, still protected by the cardboard, between the handles of the shears and press the points together. Can you pinch the finger this way harder or less hard than in the way you first tried?
Fig. 29. You cannot pinch hard enough this way to hurt.
Fig. 30. But this is quite different.
Do the points or handles move farther as you close the shears? Which part closes with the greater force?
Experiment 21. Use a Dover egg beater. Fasten a small piece of string to one of the blades, so that you can tell how many times it goes around. Turn the handle of the beater around once slowly and count how many times the blade goes around. Which moves faster, the handle or the blade? Where would you expect to find more force, in the cogs or in the blades? Test your conclusion this way: Put your finger between the blades and try to pinch it by turning the handle; then place your finger so that the skin is caught between the cogs and try to pinch the finger by turning the blades. Where is there more force? Where is there more motion?
Fig. 31. When the handle is turned the blades of the egg beater move much more rapidly than the hand. Will