Lever, a rigid rod or bar to which a force may be applied to overcome a resistance. The lever is free to turn about a fixed support called the fulcrum. A lever is a simple machine used to gain force, gain speed, or change direction. Crowbars, seesaws, wrenches, wheelbarrows, nutcrackers, hammers, bats, balance scales, and thousands of other things in common use are levers or combinations of levers. Arms, legs, hands, feet, and other parts of the body are also levers.

The Fulcrum

is the fixed support about which the lever moves.

The Force Arm

is the part of the lever to which some kind of force is applied. Its length is equal to the distance from the fulcrum to the point where force is applied.

The Resistance Arm

is the part that moves against a weight or other form of resistance. Its length is equal to the distance from the fulcrum to the point where the resistance is concentrated.

Classes of Levers

There are three basic kinds, or classes, of leversfirst, second, and third. A compound lever is one made up of two or more levers of the same or of different classes.

First Class

The fulcrum is between the force arm and the resistance arm. Seesaws, crowbars, and oars are first-class levers.

Second Class

The resistance is between the force arm and the fulcrum. Wheelbarrows and nutcrackers are second-class levers.

Third Class

The force is applied between the resistance and the fulcrum. Brooms and a kicking leg are third-class levers.

How Levers Work

Some levers reduce the force needed to move weights. They do this by increasing the distance through which the force acts. For example, a 1-kilogram force acting through a distance of 3 meters can move a 3-kilogram weight 1 meter, if friction is ignored. Speed is lost in a lever of this kind. The weight moves only 1/3 as fast as the force arm.

In other levers speed is increased by applying the force through a shorter distance than the resistance is moved. This requires a proportional increase of force. When a bat is swung, for example, the end of the bat moves faster than the hands, but greater force is needed to swing the bat than is needed to move the hands alone.

The Law of Levers

Force (F) multiplied by the length of the force arm (Af) is equal to the resistance (R) multiplied by the length of the resistance arm (Ar). This can be stated as follows:

F X Af = R X Ar

This formula makes it possible to calculate how much force must be applied to a given lever to move a certain resistance. For example: What force must be applied to a 3-meter force arm to move a 3-kilogram weight on a 2-meter resistance arm? Answer:

F X 3 = 3 X 2

3F = 6

F = 2

A force of 2 kilograms balances the 3-kilogram weight. To move the weight a force greater than 2 kilograms is required.

The formula can also be used to calculate the length of the force arm required to move a given resistance with a given amount of force. For example: How long must the force arm be if the force is 5 kilograms, the resistance is 15 kilograms, and the resistance arm is 2 meters long? Answer:

5 X Af = 15 X ?

5Af = 30

Af = 6

A 6-meter force arm is needed to balance the resistance. To move the resistance with the same force requires a longer force arm.