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
L = length of effort
arm,
l = length of
resistance arm,
R = resistance weight
or force, and
E= effort force.
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,
L = 5 inches
l = 1 inch
R = 50 pounds, and
E is unknown.
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.
