Simple Machines: Levers (2nd Ed, 1984)

[Music] Suppose you wanted to move a large stone, but it was too heavy. One simple machine that could help is the lever. A lever can be any bar that tips back and forth on a point. The point is called the fulcrum. When you exert a force on one end of the lever, it produces another force here on the other end to lift a load. Suppose the load weighs 25 lb. Then 25 lb of force are needed to lift it. If the fulcrum is in the middle of the lever as it is here, you need to push down with the same amount of force 25 lbs on your end. If the load weighs 50 lb, you need to push down with 50 lb. The amount of force that you apply is the same as the force that acts on the load. The same force you'd need to lift the load without the lever. Notice what distances the two ends of the lever move. If you push your end down a distance of 2 feet, the other end moves 2 feet. If you move your end 3 ft, the other end also moves 3 ft. So when the fulcrum is in the middle, the force is the same at both ends and so is the distance that each end moves. This lever makes your work easier only by changing the direction of force. It allows you to push down to lift something up. If you lift something directly, only your own muscles do the work. But when you push down, your weight can help you. Using your own weight as a force with the lever arranged like this, you can raise something that weighs less than you do, but not something that weighs more. But suppose you move the fulcrum. Now you can lift something that weighs more than you. Why? the load arm, that's the length from the load to the fulcrum, is shorter than the other arm. And now, in order to get the load to move this distance, you have to move your force a greater distance. And in exchange, when you apply your force here, the lever applies a greater force here to raise the load. You trade increased distance at one end of the lever to get increased force at the other end. If you move the fulcrum even further, the load arm is even shorter. You move your force a still greater distance, but the lever applies a still greater force, so you can lift even heavier things. So, here is a simple machine that can help you apply a lot of force where you need it. You often use a lever of this kind when you use a tool. For instance, when you pry up dirt with a shovel, the dirt is the load. This point on the ground is the fulcrum, and you apply your force here. And when you pull a nail with a hammer, you're using another, only now the lever is bent. It still works the same way. The long arm travels a great distance, and the short arm produces a great force. The nail doesn't weigh more than you do, of course, but it would be extremely difficult to pull it out without a lever. You need the extra force. But there are times when increased force is not what you want. When you want to get increased distance instead. In that case, you apply your force here at the short end. You have to apply a large force, but that makes the other end move a large distance. Now you do the opposite of what you did before. You trade force to get distance as you do when you row a boat. A short movement of your hands moves the other ends of the ores a long distance to move the boat. But using levers this way also gives you something else. Speed. Both ends of the lever move back and forth in the same amount of time. But since this end moves farther in that time, it also has to move faster. So with this lever you can make the boat move fast when speed is what you want. Now suppose you take two of these levers and join them this way. That's how the levers are in scissors. The screw is the fulcrum for both levers. In these scissors, the load arms are longer than the other arms. So the force the scissors cut with is smaller than the force you apply here. Is there a way of getting these scissors to cut with more force? You can't move the fulcrum, but you can move the load. Now the load arms from the load to the fulcrum are shorter. The levers work as though these parts were no longer there. You know that the shorter the load arms are compared with the other arms, the more the levers increase force. So the closer you put something to the fulcrum, the more force the scissors can apply and the more easily they cut. Cutting and squeezing tools are made with load arms of various lengths. You can choose the one you need for the job you're doing. These shears, for instance, with the fulcrum near the middle, are good for trimming something easy to cut, like grass. If you need to squeeze something tightly, you might choose these. The load arms are quite a bit shorter than the other arms, so you can get quite a lot of force here. And if you need even more force to cut through a branch, for instance, you might choose these. The load arms are very short compared with the other arms. So these ends move through a great distance. And here you get very great force. But levers with the fulcrum near one end aren't the only kinds of levers that can multiply force. Some levers have the fulcrum at the end. To use this kind of lever, you could put the load here and apply your force at this end. In this case, by lifting. Now, where is the load arm? The rule is that the load arm is always from the load wherever it is to the fulcrum and the other arm is from you to the fulcrum. So in this lever the two arms overlap. If you move your end a large distance the load moves a smaller distance. And in exchange, when you lift with a small force here, the lever applies a larger force here. So once again, you're trading increased distance to get increased force. But notice that with this lever, both forces go the same direction. Suppose you made the load arm longer by moving the load toward you and then even longer and still longer. This way, the lever applies only a small amount of force. You supply the rest. Once again, the shorter the load arm is compared with the other arm, the more force the lever will apply to help you lift. You use this kind of lever when you use a wheelbarrow. This is the fulcrum. The closer you get the load to the fulcrum, that is the shorter the load arm, the more the lever will help you and the more you can lift. You use two of these levers together when you use a nutcracker. The best place to put the nut to get the most force is where the load arms will be as short as possible. [Music] But suppose you use this kind of lever a different way. Suppose you put the load at this end. Now this is the load arm from the load to the fulcrum. In this case, the whole length of the lever. If you apply your force here between the load and the fulcrum, then this is the other arm. You can see that now you have to apply a large force, but that the load moves a large distance. There are many levers of this kind in your own body. For instance, you use one when you swing your arm. From above, you look like this. Here is the load. Here is the fulcrum in your shoulder. And your muscle applies its force here. Your muscle pulls very hard, but only for a short distance, while the load moves a much greater distance and with much more speed than the muscle. You use another of these levers when you lift something this way. Your elbow is the fulcrum. What you have in your hand is the load. And your muscle applies its force here. And when you bite, you're using another. Here's the fulcrum. Here's the load. And here's where your muscle applies its force. So levers are simple machines that can have their fulcrums between the two ends or at one end. And depending on where you place the load and apply your force, you can use a lever to increase force or distance and speed. 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