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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.

Theory of operation

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 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."

Archimedes once famously remarked: "Πα βω και χαριστιωνι ταν γαν κινησω πασαν." ("Give me a place to stand and with a lever I will move the whole world.")

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. 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.

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

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 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 of it)
6. Hammer Claw , when pulling a nail with the hammer's claw
7. Hand trucks are L-shaped but work on the same principle, with the axis as a fulcrum
8. Oars
9. Pliers (double lever)
10. Scissors (double lever)
11. Shoehorn
12. Spud bar (moving heavy objects)
13. 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)
14. Wheel and axle because the wheel's motions follows the fulcrum, load arm, and effort arm principle.

Second-class levers

Second class lever

In a second class lever the input effort is located at one 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. Dental elevator
2. Nutcracker
3. Paddle
4. Curb bit
5. Wheelbarrow
6. Wrench
7. Bottle opener
8. Diving Board (spring board)
9. Crowbar (flat end)
10. Push-up
11. Doorknob(could be a wheel and axle also)

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.

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. Biceps brachii muscle acting on the forearm
3. Boat paddle
4. Broom
5. Electric Gates
6. Fishing rod
7. Hockey stick
8. Mandible
9. Mousetrap
10. Nail clippers, the main body handle exerts the incoming force
11. Shovel (the action of picking or lifting up sand or dirt)
12. Stapler
13. Tongs
14. Tweezers
15. Hammer

See also

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

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, The Wolfram Demonstrations Project.
• Levers: Simple Machines at EnchantedLearning.com

Wikipedia content modification information:

• This page was last modified on 20 November 2008, at 09:22.

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