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.
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.
Simple machine used to amplify physical force. All early people used the lever in some form, for moving heavy stones or as digging sticks for land cultivation. Balance beams for weighing were probably used in Egypt circa 5000 BC; they consist of a bar pivoted at its center with weights on one end balancing the object on the other. As early as 1500 BC people were raising water and lifting soldiers over battlements using the swape or shadoof, a long lever pivoted near one end with a platform or container hanging from the short arm and counterweights attached to the long arm.
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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.
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:
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.
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:
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.