## Lever Resultant

A lever is a rigid bar, straight or curved, capable of being rotated around a fixed point (fulcrum). When a fulcrum and a bar are used, two different forces exist, the applied force (Fa) and the resultant force (Fr). The forces, bar, and fulcrum can be used in three ways, called classes, Figure 4.1.

FIGURE 4.1. Three classes of levers.

FIGURE 4.1. Three classes of levers.

The principle of levers can be expressed mathematically as:

/ Force \ / Arm \ / Force \ / Arm \ V Applied V Applied \ Resultant/ \ Resultant/

4.3.1. Class One Lever

Class one levers are used primarily for their mechanical advantage. The mechanical advantage for a first-class lever is the ratio of the lengths of the two arms. In our discussion of simple machines, mechanical advantage will be defined as the increase of force that occurs through the use of a lever. Expressed mathematically:

Force arm length

Mechanical advantage =

Resultant arm length The principles of a class one lever are illustrated by the problem in Figure 4.2.

Problem: How much weight can a 140.0-lb person lift with a class one lever if the force arm is 4.0 ft long, and the resultant arm is 1.0 ft long?

Solution: In this problem three of the variables are known: Fa = 140 lb, Aa = 4 ft, and Ar = 1 ft. To solve the problem, we must use one of the techniques of problem solvingâ€”rearranging an equation. In this example we need to rearrange the equation to solve for Fr and then insert the values.

Fa x Aa 140.0 lb x 4.0 ft Fr = â€”-a =-= 560 lb r Ar 1.0 ft

[Note: In this example two significant figures were used. This is an example where the significance of the zero in the number would be ambiguous unless the reader had excess to the entire problem. To remove this ambiguity the answer should be written as 5.5 E2.]

FIGURE 4.3. Example of the use of a class one lever.

With this lever, 140 lb of applied force is capable of lifting 560 lb. This demonstrates the mechanical advantage of the class one lever. The source of the mechanical advantage is clearer if the equation is written as:

When the equation is arranged in this manner, it is easy to see that the increase in force or mechanical advantage is the ratio of the lengths of the two arms. In this example, the amount of force the person could produce (mechanical advantage) was increased 4/1 or 4 times.

In addition to the mechanical advantage, the distance moved and the speed of movement for the two ends of the bar also can be determined. Calculations will show that the distance moved is proportional to the ratio of the length of the resultant arm to the length of the force arm. The speed of movement is proportional to the ratio of the length of the force arm to the length of the resultant arm.

An example of the use of a class one lever is a wrecking bar pulling a nail, Figure 4.3.

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