Curved Lever Arms

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Third Class

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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 sailors 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 =

Thus, in the case of the wheelbarrow,

This rulemechanical 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:

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.

Figure 1-10.-Its a dog.