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Third Class Sometimes you will want to speed up the movement of the resistance even though you have to use a large amount of effort. Levers that help you accomplish this are in the third class of levers. As shown in figure 12, part C, the fulcrum is at one end of the lever, and the Figure 14.This makes it easier. Figure 15.A thirdclass lever. weight or resistance to be overcome is at the other end, with the effort applied at some point between. You can always spot the thirdclass levers because you will find the effort applied between the fulcrum and the resistance. Look at figure 15. It is easy to see that while E moved the short distance (e), the resistance (R) was moved a greater distance (r). The speed of R must have been greater than that of E, since R covered a greater distance in the same length of time. Your arm (fig. 16) is a thirdclass lever. It is this lever action that makes it possible for you to flex your arms so quickly. Your elbow is the fulcrum. Your biceps muscle, which ties onto your forearm about an inch below the elbow, applies the effort; your hand is the resistance, located about 18 inches from the fulcrum. In the split second it takes your biceps muscle to contract an inch, your hand has moved through an 18inch arc. You know from experience that it takes a big pull at E to overcome a relatively small resistance at R. Just to experience this principle, try closing a door by pushing on it about 3 or 4 inches from the hinges (fulcrum). The moral is, you don’t use thirdclass levers to do heavy jobs; you use them to gain speed. Figure 16.Your arm is a lever. Figure 17.Easy does it. One convenience of machines is that you can determine in advance the forces required for their operation, as well as the forces they will exert. Consider for a moment the first class of levers. Suppose you have an iron bar, like the one shown in figure 17. This bar is 9 feet long, and you want to use it to raise a 300pound crate off the deck while you slide a dolly under the crate; but you can exert only 100 pounds to lift the crate. So, you place the fulcruma wooden blockbeneath one end of the bar and force that end of the bar under the crate. Then, you push down on the other end of the bar. After a few adjustments of the position of the fulcrum, you will find that your 100pound force will just fit the crate when the fulcrum is 2 feet from the center of the crate. That leaves a 6foot length of bar from the fulcrum to the point where you pushdown. The 6foot portion is three times as long as the distance from the fulcrum to the center of the crate. And you lifted a load three times as great as the force you applied (3 x 100 = 300 pounds). Here is a sign of a direct relationship between the length of the lever arm and the force acting on that arm. You can state this relationship in general terms by saying: the length of the effort arm is the same number of times greater than the length of the resistance arm as the resistance to be overcome is greater than the effort you must apply. Writing these words as a mathematical equation, we have
where
Remember that all distances must be in the same units, such as feet, and that all forces must be in the same units, such as pounds. Now let’s take another problem and see how it works out. Suppose you want to pry up the lid of a paint can (fig. 18) with a 6inch file scraper, and you know that the average force holding the lid is 50 pounds. If the distance from the edge of the paint can to the edge of the cover is 1 inch, what force will you have to apply on the end of the file scraper? According to the formula,
here,
Then, substituting the numbers in their proper places, we have
and = 10 pounds You will need to apply a force of only 10 pounds. Figure 18.A firstclass job. The same general formula applies for the second class of levers; but you must be careful to measure the proper lengths of the effort arm and the resistance arm. Looking back at the wheelbarrow problem, assume that the length of the handles from the axle of the wheel—which is the fulcrumto the grip is 4 feet. How long is the effort arm? You’re right, it’s 4 feet. If the center of the load of sand is 1 foot from the axle, then the length of the resistance arm is 1 foot. By substituting in the formula,
and E = 50 pounds. Now for the thirdclass lever. With one hand, you lift a projectile weighing approximately 10 pounds. If your biceps muscle attaches to your forearm 1 inch below your elbow and the distance from the elbow to the palm of your hand is 18 inches, what pull must your muscle exert to hold the projectile and flex your arm at the elbow? By substituting in the formula,
it becomes and E = 18 x 10 = 180 pounds. Your muscle must exert a 180pound pull to hold up a 10pound projectile. Our muscles are poorly arranged for lifting or pullingand that’s why some work seems pretty tough. But remember, thirdclass levers are used primarily to speed up the motion of the resistance. 

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