Lever

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 less effort to be expended to move an object a greater distance. For instance, to use a lever to lift a certain unit of weight with an effort of half a unit, the distance from the fulcrum of the spot where force is applied must be twice the distance between the weight and the fulcrum. For example, to halve the effort of lifting 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 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.

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. The fulcrum is the center of the lever on which the bar (as in a seesaw) lays upon. This supports the effort arm and the load.

Examples:

1. Seesaw (also known as a teeter-totter)
2. Crowbar or claw hammer (removing nails)
3. Spud bar (moving heavy objects)
4. Pliers (double lever)
5. Scissors (double lever)
6. Wheel and axle because the wheel's motions follows the fulcrum, load arm, and effort arm principle
7. Trebuchet an upside down example of the above picture
8. Oars, when used for rowing, steering, or sculling
9. Can opener and bottle opener
10. Bicycle hand brakes
11. Hand trucks are L-shaped but works on the same principle on the wheel as a fulcrum
12. Hammer when pulling a nail with the hammer's claw
13. Tweezers that are shaped like scissors work as double levers
14. Shoehorn

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. Crowbar
5. Stapler
6. Diving board
7. Wrench
8. Dental Elevator
9. Can Opener

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. Slings, trebuchets, and fishing rods (also spoons, when used for flinging food. This uses your index finger as the fulcrum, your thumb as the effort, and the load is the food.)
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. shovel
7. broom
8. staple remover
9. hockey stick
10. The Human Mandible
11. Boat Paddle

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 denoted by the arrow with a hand symbol, and the "load" is the other arrow.) To remember what the different classes of levers look like, another mnemonic is "fre 123" In a 1st class lever the fulcrum is in the middle, 2nd class the resistance is in the middle, and 3rd class the effort is in the middle.

See also

• Engineering mechanics
• Engineering vehicles
• Linkage (mechanical)
• Simple machine

External links

• Lever and pendulum - the new effects by Veljko Milković
• DiracDelta.co.uk Levers and examples