Levers can be used to exert a large force over a small distance at one end by exerting only a small force over a greater distance at the other.

In physics, a lever (from French lever, "to raise", c.f. a 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 leverage is also termed mechanical advantage, and is one example of the principle of moments. A lever is one of the six simple machines. Archimedes once said, "Give me a lever long enough and a fulcrum on which to place it, and I shall move the world." First class levers are similar but not the same as second or third class levers, in which the fulcrum, resistance, and effort are in different locations.

[edit] Theory of levers

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

The principle of leverage can be derived using Newton's laws of motion, and modern statics. It is important to note the 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:

.

If, for example, a 1 gram feather were balanced by a one kilogram rock, the feather would be 1000 times further from the fulcrum than the rock; if a 1 kilogram rock were balanced by another 1 kilogram rock, the fulcrum would be in the middle.

[edit] 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.

[edit] First-class levers

First class lever

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 maneets arm.

Examples:

1. Seesaw
2. Trebuchet
3. Crowbar (curved end of it)
4. Hammer Claw, when pulling a nail with the hammer's claw
5. Hand trucks are L-shaped but work on the same principle, with the axis as a fulcrum
6. Pliers (double lever)
7. Scissors (double lever)
8. Shoehorn (used for putting feet into shoes)
9. Spud bar (moving heavy objects)
10. 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 center of the beam (i.e. D1 = D2)
11. Wheel and axle because the wheel's motions follows the fulcrum, load arm, and effort arm principle.
12. Chopsticks with hand the middle finger acts as a pivot. The whole system is a double lever. (Could also be seen as a third class lever, since the effort is between the fulcrum and the load)

[edit] Second-class levers

Second class lever

In a second class lever the input effort is located at the end of the bar and the fulcrum is located at the other end of the bar, opposite to the input, with the output load at a point between these two forces. Examples:

1. Bottle opener
2. Crowbar (flat end)
3. Curb bit
4. Dental elevator
5. Doorknob (could be a wheel and axle also)
6. Nail clippers, the main body handle exerts the incoming force
7. Nutcracker
8. Oar: the water is the fulcrum; the boat is the load and the effort is at the inboard end^[1]
9. Press-up
10. Spring board
11. Torsion spring, the main body handle exerts the incoming force
12. Wheelbarrow
13. Wrench

[edit] Third-class levers

Third class lever. For the lever in this diagram to work correctly, one must assume that the fulcrum is attached to the bar or acting in opposition to the other two forces.

For this class of levers, the input effort is higher than the output load, which is different from second-class levers and some first-class levers. However, the distance moved by the resistance (load) is greater than the distance moved by the effort. Since this motion occurs in the same length of time, the resistance necessarily moves faster than the effort. Thus, a third-class lever still has its uses in making certain tasks easier to do. In third class levers, effort is applied between the output load on one end and the fulcrum on the opposite end.

Examples:

1. Baseball bat
2. Boat paddle^[2]
3. Broom
4. Electric gates
5. Fishing rod
6. Hammer
7. Hockey stick
8. Human arm
9. Mandible
10. Mousetrap (Spring-loaded bar type)
11. Shovel (the action of picking or lifting up sand or dirt)
12. Stapler
13. Tennis racket
14. Tongs
15. Tweezers
16. Chopsticks with hand (could also be seen as a first class lever, see above)

[edit] In the real world

For the classical mechanics formulas to work, or to be a good approximation of real world applications, the lever must be made from a combination of rigid bodies, i.e. a beam and a rigid fulcrum. Any bending or other deformation must be negligible.

[edit] See also

• Engineering mechanics
• Heavy equipment
• Linkage (mechanical)
• Switch
• Archimedes
• Simple machine

[edit] References

[edit] External links

Wikimedia Commons has media related to: Levers

Look up lever in Wiktionary, the free dictionary.

• Lever at Diracdelta science and engineering encyclopedia
• A Simple Lever by Stephen Wolfram, Wolfram Demonstrations Project.
• Levers: Simple Machines at EnchantedLearning.com