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 1-2, part C, the fulcrum is at one end of the lever, and the
Figure 1-4.-This makes it easier.
Figure 1-5.-A third-class 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 third-class levers because you will find the effort applied between the fulcrum and the
resistance. Look at figure 1-5. 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. 1-6) is a third-class 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 18-inch 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 donít use third-class levers to do heavy jobs; you use them to gain speed.
Figure 1-6.-Your arm is a lever.
Figure 1-7.-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 1-7. This bar is 9 feet long, and you want to use it to raise a 300-pound 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 fulcrum-a wooden block-beneath 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 100-pound force will just fit the crate when the fulcrum is 2 feet from the center of the crate. That leaves a 6-foot length of bar from the fulcrum to the point where you pushdown. The 6-foot 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 thelength 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
length of effort arm,
l= length of resistance arm,
R =resistance weight or force, and
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 letís take another problem and see how it works out. Suppose you want to pry up the lid of a paint can (fig. 1-8) with a 6-inch 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,
l= 1 inch
R =50 pounds, and
Then, substituting the numbers in their proper places, we have
= 10 pounds
You will need to apply a force of only 10 pounds.
Figure 1-8.-A first-class 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 wheelówhich is the fulcrum-to the grip is 4 feet. How long is the effort arm? Youíre right, itís 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,
E =50 pounds.
Now for the third-class 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,
E =18 x 10 = 180 pounds.
Your muscle must exert a 180-pound pull to hold up a 10-pound projectile. Our muscles are poorly arranged for lifting or pulling-and thatís why some work seems pretty tough. But remember, third-class levers are used primarily to speed up the motion of the resistance.