it becomes
1
10
—=—
18
E
and
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 that’s why some work seems
pretty tough. But remember, third-class levers are used
primarily to speed up the motion of the resistance.
Curved Lever Arms
Up to this point, you have been looking at levers
with straight arms. In every case, the direction in which
the resistance acts is parallel to the direction in which
the effort is exerted. However, not all levers are straight.
You ’ll need to learn to recognize all types of levers and
to understand their operation.
Look at figure 1-9. You may wonder how to measure
the length of the effort arm, which is represented by the
curved pump handle. You do not measure around the
curve; you still use a straight-line distance. To determine
the length of the effort arm, draw a straight line (AB)
through the point where the effort is applied and in the
direction that it is applied. From point E on this line,
draw a second line (EF) that passes through the fulcrum
and is perpendicular to line AB. The length of line EF is
the actual length (L) of the effort arm.
To find the length of the resistance arm, use the same
method. Draw a line (MN) in the direction that the
resistance is operating and through the point where the
resistance is attached to the other end of the handle.
From point R on this line, draw a line (RF) perpendicular
to MN so that it passes through the fulcrum. The length
of RF is the length (l) of the resistance arm.
Regardless of the curvature of the handle, this
method can be used to find lengths L and l. Then, curved
levers are solved just like straight levers.
MECHANICAL ADVANTAGE
There is another thing about the first and second
classes of levers that you have probably noticed by now.
Since they can be used to magnify the applied force, they
provide positive mechanical advantages. The third-class
lever provides what is called a fractional mechanical
advantage, which is really a mechanical disadvantage—
you use more force than the force of the load you lift.
In the wheelbarrow problem, you saw that a
50-pound pull actually overcame the 200-pound weight
Figure 1-9.-A curved lever arm.
of the sand. The sailor’s effort was magnified four times,
so you may say that the mechanical advantage of the
wheelbarrow is 4. Expressing the same idea in
mathematical terms,
MECHANICAL ADVANTAGE =
RESISTANCE
EFFORT
or
Thus, in the case of the wheelbarrow,
This rule—mechanical advantage equals resistance
divided by effort —applies to all machines.
The mechanical advantage of a lever may also be
found by dividing the length of effort arm A by the length
of resistance arm a. Stated as a formula, this reads:
or
How does this apply to third-class levers? Your
muscle pulls with a force of 1,800 pounds to lift a
100-pound projectile. So you have a mechanical
advantage of
which is fractional-less than 1.
1-5
