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 they pinch hard enough to hurt?
Fig. 32. His hand goes down as far as the pail goes up.
Experiment 22. Put a spool over the nail which was your fulcrum in the first two experiments. (Take the stick off the nail first, of course.) Use this spool as a pulley. Put a string over it and fasten one end of your string to the pail (Fig. 32). Lift the pail by pulling down on the other end of the string. Notice that it is not harder or easier to move the pail when it is near the nail than when it is near the floor. When your hand moves down from the nail to the floor, how far up does the pail move? Does the pail move a greater or less distance than your hand, or does it move the same distance?
Fig. 33. With this arrangement the pail travels more slowly than the hand. Will it seem heavier or lighter than with the arrangement shown in Figure 32?
Next fasten one end of the string to the nail. Set the pail on the floor. Pass the string through the handle of the pail and up over the spool (Fig. 33). Pull down on the loose end of the string. Is the pail easier to lift in this way or in the way you first tried? As you pull down with your hand, notice whether your hand moves farther than the pail, not so far as the pail, or the same distance. Is the greater amount of motion in your hand or in the pail? Then where would you expect the greater amount of force?
The whole idea of the lever can be summed up like this: one end of the contrivance moves more than the other. But energy cannot be lost; so to make up for this extra motion at one end more force is always exerted at the other.
This rule is true for all kinds of levers, blocks and tackles or pulley systems, automobile and bicycle gears, belt systems, cog systems, derricks, crowbars, and every kind of machine. In most machines you either put in more force than you get out and gain motion, or you put in more motion than you get out and gain force. In the following examples of the lever see if you can tell whether you are applying more force and obtaining more motion, or whether you are putting in more motion and obtaining more force:
Cracking nuts with a nut cracker.
Beating eggs with a Dover egg beater.
Going up a hill in an automobile on low gear.
Speeding on high gear.
Cutting cloth with the points of shears.
Cutting near the angle of the shears.
Turning a door knob.
Picking up sugar with sugar tongs.
Pinching your finger in the crack of a door on the hinge side.
Application 16. Suppose you wanted to lift a heavy frying pan off the stove. You have a cloth to keep it from burning your hand. Would it be easier to lift it by the end of the handle or by the part of the handle nearest the pan?
Application 17. A boy was going to wheel his little sister in a wheelbarrow. She wanted to sit in the middle of the wheelbarrow; her brother thought she should sit as near the handles as possible so that she would be nearer his hands. Another boy thought she should sit as near the wheel as possible. Who was right?
Application 18. James McDougal lived in a hilly place. He was going to buy a bicycle. "I want one that will take the hills easily," he said. The dealer showed him two bicycles. On one the back wheel went around three times while the pedals went around once; on the other the back wheel went around four and a half times while the pedals went around once. Which bicycle should James have chosen? If he had wanted the bicycle for racing, which should he have chosen?
Application 19. A wagon stuck in the mud. The driver got out and tried to help the horse by grasping the spokes and turning the wheel. Should he have grasped the spokes near the hub, near the rim, or in the middle?
Inference Exercise
Explain
