Theory of operation

The principle of leverage can be derived using Newton's laws of motion, and modern statics. It is important to note that the amount of work done is given by force times distance. For instance, to use a lever to lift a certain unit of weight with a force of half a unit, the distance from the fulcrum to the spot where force is applied must be twice the distance between the weight and the fulcrum. For example, to cut in half the force required to lift a weight resting 1 meter from the fulcrum, we would need to apply force 2 meters from the other side of the fulcrum. The amount of work done is always the same and independent of the dimensions of the lever (in an ideal lever). The lever only allows to trade force for distance.

Archimedes was the first to explain the principle of the lever, stating:

"(equal) weights at equal distances are in equilibrium, and equal weights at unequal distances are not in equilibrium but incline towards the weight which is at the greater distance."

The point where you apply the force is called the effort. The effect of applying this force is called the load. The load arm and the effort arm are the names given to the distances from the fulcrum to the load and effort, respectively. Using these definitions, the Law of the Lever is:

Load arm X load force = effort arm X effort force. When 2 things are balanced, when a 1 gram feather for instance is balanced by a one kilogram rock on a lever the feather would go up and the rock would go down, but if a 1 kilogram rock was balanced by a 1 kilogram rock, the lever would be in the middle.

The three classes of levers

There are three classes of levers which represent variations in the location of the fulcrum and the input and output forces.

First-class levers

A first-class lever is a lever in which the fulcrum is located between the input effort and the output load. In operation, a force is applied (by pulling or pushing) to a section of the bar, which causes the lever to swing about the fulcrum, overcoming the resistance force on the opposite side. The fulcrum may be at the center point of the lever as in a seesaw or at any point between the input and output. This supports the effort arm and the load.

Examples:

1. Seesaw (also known as a teeter-totter)
2. Triceps brachii muscle acting on the forearm
3. Bicycle hand brakes
4. Catapult
5. Crowbar (curved end)
6. Curb bit
7. Hammer Claw , when pulling a nail with the hammer's claw
8. Hand trucks are L-shaped but work on the same principle, with the axis as a fulcrum
9. Oars
10. Pliers (double lever)
11. Scissors (double lever)
12. Shoehorn
13. Spud bar (moving heavy objects)
14. Beam engine although here the aim is just to change the direction in which the applied force acts, since the fulcrum is normally in the centre of the beam (i.e. D1 = D2)
15. Wheel and axle because the wheel's motions follows the fulcrum, load arm, and effort arm principle