lever

 

simple machine consisting of a bar supported at some stationary point along its length and used to overcome resistance at a second point by application of force at a third point. The stationary point of a lever is known as its fulcrum. The term lever is also applied to a projecting piece that is moved to operate or adjust inner machinery, such as a lever moved to the right or left to switch electric current on or off or to adjust the size of the opening of a shutter in a camera.

Principle of the Lever

It has been found by experiment that two equal forces acting in opposite directions, i.e., clockwise and counterclockwise, and applied to a uniform lever at equal distances from the fulcrum counteract each other and establish a state of equilibrium, or balance, in the lever. Experiment has also shown that two unequal forces when acting in opposite directions will bring about an equilibrium when the product of the magnitude of one force and its effort arm, or lever arm (the distance of its point of application from the fulcrum), is equal to the product of the magnitude of the other force and its effort arm. In physics the product of a force by its effort arm is called a moment of the force; the general conclusion known as the principle of moments states that equilibrium is established when the sum of the moments of the forces acting in a clockwise direction is equal to the sum of the moments of the forces acting in a counterclockwise direction. It is possible, as a result, to overcome a very large force at a short distance from the fulcrum with a very small force at a great distance from the fulcrum. Archimedes is supposed to have boasted, having the lever in mind, that given a place to stand he could move the world.

Classification and Application of Levers

In the use of a small force to overcome a large one the lever finds its many common applications. The lever is used for prying, as in the case of the crowbar, or for lifting. For example, the fulcrum is the point upon which a crowbar rests when used to lift or to pry loose some object; the effort is applied at the end farther from the fulcrum and is relatively small. The distance from the operator's hands to the fulcrum is known as the lever arm, or effort arm; the object being pried loose is the resisting force, or resistance; the object's distance from the fulcrum is the resistance arm. Levers in which the fulcrum is located between the effort and the resistance, as in the crowbar and the beam balance, are known as first-class levers. The fulcrum may also be located at one end of the lever, with the effort applied at the other end and the resistance in between; this type of lever, illustrated by the wheelbarrow and the nutcracker, is known as a second-class lever. The final possibility, known as a third-class lever, has the effort applied between the fulcrum and the resistance and is illustrated by various types of tongs.

Many other common tools, instruments, and appliances are applications of the principle of the lever. The human forearm is an application of the third-class lever, the elbow acting as the fulcrum, the weight held in the hand and being lifted as the resistance, and the pull of the muscles between the elbow and the hand as the effort. In a second-class lever, the effort arm is always longer than the resistance arm, so that a smaller effort moves a larger resistance, while in a third-class lever the reverse is always true, with the effort greater than the resistance. In a first-class lever, the effort may be either larger or smaller than the resistance, depending upon the location of the fulcrum.

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 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 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 of the spot where force is applied must be twice the distance between the weight and the fulcrum. For example, to halve 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. Levers are one of the six simple machines.

The three classes of levers

There are three classes of levers (first, second, and third-class) 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 in 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. 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 (ie D1 = D2)
2. Bicycle hand brakes
3. Can opener and bottle opener
4. Crowbar
5. Hammer, when pulling a nail with the hammer's claw
6. Hand trucks are L-shaped but works on the same principle on the wheel as a fulcrum
7. Oars, when used for moving or splashing water
8. Pliers (double lever)
9. Scissors (double lever)
10. Seesaw (also known as a teeter-totter)
11. Shoehorn
12. Spud bar (moving heavy objects)
13. Trebuchet, an upside down example of the above picture
14. Tweezers that are shaped like scissors work as double levers
15. Wheel and axle because the wheel's motions follows the fulcrum, load arm, and effort arm principle

Second-class levers

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. Crowbar
2. Dental elevator
3. Door
4. Nutcracker
5. Oars, when the boat is the resistance moving the same direction as the force and using water as the fulcrum
6. Paddle
7. Springboard (diving board)
8. Stapler
9. Wheelbarrow
10. Wrench

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 load. Thus it still has its uses in making certain tasks easier to do. Third class levers use the effort in between the output load on one side and the input on the opposite end.

Examples:

1. Arm
2. Baseball bat
3. Boat paddle
4. Broom
5. Door
6. Fishing rod
7. Hockey stick
8. Mandible
9. Mousetrap
10. Nail clippers, the main body handle exerts the incoming force
11. Shovel
12. Sling
13. Spoon, when used for flinging food, which uses the index finger as the fulcrum, the thumb as the effort, and the load is the food
14. Tools, such as a hoe or scythe
15. Tweezers

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 of it. Alternatively, the term 'Frogs lay eggs' can also be used in the similar manner. Some people remember the word 'elf', which sorts the classes from the third to first. Another way is "FREE Lever" Which means Fulcrum + Resistance + Effort Equals Lever.

See also

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

Resistance distance

Resistance distance is the distance from the resistance (on a lever) to the fulcrum.

External links

• DiracDelta.co.uk Levers and exampleszh-yue:槓桿

Donate to Wikimedia