Lever

I. Introduction

Lever, simple machine consisting of a rigid bar that rotates about a fixed point, called a fulcrum. Levers affect the effort, or force, needed to do a certain amount of work, and are used to lift heavy objects. To move an object with a lever, force is applied to one end of the lever, and the object to be moved (referred to as the resistance or load) is usually located at the other end of the lever, with the fulcrum somewhere between the two. By varying the distances between the force and the fulcrum and between the load and the fulcrum, the amount of effort needed to move the load can be decreased, making the job easier.

Physicists classify the lever as one of the four simple machines used to do work. (The other three are the pulley, the wheel and axle, and the inclined plane.) Work is defined in physics as the result of a force, such as a person lifting, that moves an object over a distance. A common example of a lever is the seesaw. The human arm is also a lever, where the elbow is the fulcrum and the muscles apply the force.

II. Work and Mechanical Advantage

A lever makes work easier by reducing the force needed to move a load. Work, in physics, is the product of the force used to lift a load multiplied by the distance the force, or effort, is applied. This relationship can be written mathematically as:

Work = Force ¥ Distance

The amount of work needed to move an object a given distance always remains the same except when friction is present. The lever, like all simple machines, makes doing work easier by reducing the force needed to move an object. In order to reduce the force needed, the distance over which the force is applied must be increased.

To increase this distance, the load to be moved must be close to the fulcrum and the force must be applied far from the fulcrum. A good example is a claw hammer used to pry nails loose. The user's hand applies force to the handle at one end of the lever. The head of the hammer is the fulcrum, and the nail at the other end of the lever is the load to be moved. The nail is much closer to the fulcrum than is the hand applying the force. Since the hand is farther away from the fulcrum, the force travels a greater distance than does the load as the nail is pried loose. The same amount of work would have been done if the nail had been pulled directly out by hand. However, by using the lever the force was spread out over a greater distance, and so less force was needed. Another example is a seesaw. The force of a smaller person can balance and even lift the load of a larger person as the smaller person moves farther away from the fulcrum.

The mechanical advantage (MA) of a lever tells how much the lever magnifies effort. The greater the MA, the less the effort needed to move a load. The MA of a lever is the ratio of the distance the force travels to the distance the load travels. In practical terms, the MA is the distance of the force to the fulcrum divided by the distance of the load to the fulcrum. Depending on the class of lever and the location of the fulcrum, the MA may be less than or greater than 1.

III. Types of Levers

There are three different classes of levers, depending on the arrangement of the force, the load, and the fulcrum along the lever bar. Each class of lever affects force in a different way, and each class has different applications.

A. Class 1 Levers

The class 1 lever has the fulcrum between the force and the load, as in a seesaw. When two people of equal weight use the seesaw, they position themselves an equal distance from the fulcrum, and the system is balanced. When a heavier person sits on one end, that person usually moves toward the center, which gives a mechanical advantage to the lighter person so that the system is again in balance. It is possible for a class 1 lever to have a significant mechanical advantage.

B. Class 2 Levers

The class 2 lever has the fulcrum at one end, the force at the other end, and the load in the middle. A common example is the wheelbarrow, where the wheel is the fulcrum, the load rests within the box, and the force is the lift supplied by the user. A class 2 lever always has a mechanical advantage of greater than 1. To reduce the force required by the user even more, the best wheelbarrow design is one where the wheel is directly under the load, reducing the distance from the load to the fulcrum almost to zero. Many wheelbarrows and garden carts are designed in that manner to make them easy for the user to move.

C. Class 3 Levers

A class 3 lever has the fulcrum at one end, the load at the other end, and the force in the middle. The human forearm is a class 3 lever. The elbow is the fulcrum, and the muscles of the forearm apply the force between the elbow and the hand. The class 3 lever always has a mechanical advantage of less than 1, because the load travels a greater distance than the force travels. Consequently, the work requires more effort than would ordinarily be needed. Although they boost the amount of effort needed, class 3 levers are useful for increasing the speed at which a load is moved. A baseball bat and a broom are also examples of class 3 levers, with which a greater effort results in a smaller load moving at a greater speed.

IV. History

The first levers were probably branches or logs used to lift heavy objects, followed by sticks used to till soil for planting crops. In both of those applications, the lever magnifies the force applied by a human. Learning to use those simple tools led to the development of other applications of the lever.

In addition to using human power as the force applied to the lever, people added weights so that the force they had to exert was lessened. These weights are called counterweights. A counterbalanced lever called a shadoof was used in ancient Egypt for lifting irrigation water from the Nile River up onto land, and it is still used today. During the Middle Ages, attacking armies used a similar device for lifting soldiers over fortress walls. The principle of the lever was often utilized through the rotary motion of the wheel and axle. Waterwheels installed near waterfalls used the continuous force of moving water to provide the necessary leverage to turn large grindstones for grinding grain into flour.

A crowbar and the claw of a hammer used to pry loose nails are both common examples of levers in action. Balance scales use levers to find the mass of an object. Complex machines often use a series of levers to transfer force. The keys of a piano use levers to transmit force from the keys to the hammers that strike the strings.

Contributed By:

Odis Hayden Griffin, Jr., B.S., M.S., Ph.D.

Director and Professor, Division of Engineering Fundamentals, Virginia Polytechnic Institute and State University.