Mirror of English Wikipedia, the free encyclopedia

The principle of the lever tells us that the above is in static equilibrium, with all forces balancing, if F₁D₁ = F₂D₂.

In physics, a lever (from Old French levier, the agent noun to lever "to raise", c. f. levant) is a rigid object that is used with an appropriate fulcrum or pivot point to multiply the mechanical force that can be applied to another object. This is also termed mechanical advantage, and is one example of the principle of moments. The principle of leverage can also be derived using Newton's laws of motion and modern statics. It is important to notice that the amount of work done is given by force times distance. The lever allows to do less effort but for a greater distance. For instance to lift a certain unit of weight with a lever with an effort of half a unit we need a distance from the fulcrum in the effort's side to be twice the distance of the weight's side. It also means that to lift the weight 1 meter we need to push the lever for 2 meter. 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 effort for distance. Levers are one of the six simple machines.

Early studies

The earliest remaining writings regarding levers date from the 3rd century BCE and were provided by Archimedes. Give me the place to stand, and I shall move the earth is a remark of Archimedes who formally stated the correct mathematical principle of levers (quoted by Pappus of Alexandria).

In ancient Egypt, builders used the lever to move and uplift obelisks weighing more than 100 tons.

Force and levers

The force applied (at end points of the lever) is proportional to the ratio of the length of the lever arm measured between the fulcrum and application point of the force applied at each end of the lever. F= M*A

The three classes of levers

There are three classes of levers representing 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 in between the input force and the output force. 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.

Examples:

1. Seesaw (also known as a teeter-totter)
2. Crowbar (removing nails)
3. Pliers (double lever)
4. Scissors (double lever)
5. Wheel and axle because the wheel's motions follows the fulcrum, load arm, and effort arm principle
6. Trebuchet an upside down example of the above picture

Second-class levers

In a second-class lever the input is located to the far side of the bar, the output is located in the middle of the bar, and the fulcrum is located on the side of the bar opposite to the input. Examples:

1. Wheelbarrow
2. Nutcracker
3. Door
4. Oars, when used for rowing, steering, or sculling

Third-class levers

It is to be noted that for this class of levers, the input effort is higher than the output load, which is different from the first-class and second-class levers. However, also notice that the input effort moves through a shorter distance than the output load. Thus it still has its uses in making certain tasks easier to do.

Examples:

1. Human arm
2. Tweezers
3. Catapult and fishing rod (catapults that act as a see-saw, catapulting their load when something of great mass lands on the board on the opposite side of the fulcrum are first-class levers. Third-class catapults would be similar to the following: take a bobby-pin and bend it so that it looks like the upper-case letter "L." Then, take one arm and staple it to a wooden board. Then bend the free arm towards the stapled arm, and if released, this can be used to send things flying! You have just made yourself a third-class catapult.)
4. Any number of tools, such as a hoe or scythe
5. The main body of a pair of nail clippers, in which the handle exerts the incoming force
6. A baseball bat
7. A shovel
8. A broom

Mnemonic

A mnemonic for remembering the three classes of levers is the word flex, where the letters f-l-e represent the fulcrum, the load, and the effort as being between the other two, in the first-class lever, the second-class lever, and the third-class lever respectively. (To relate the mnemonic to the above diagrams, note that: the "fulcrum" is represented by the triangle, the "effort" is labelled "INPUT", and the "load" is labelled "OUTPUT".)

See also

• Engineering mechanics
• Linkage (mechanical)
• Simple machine