Lever
Overview
Physics
Physics is a natural science that involves the study of matter and its motion through spacetime, along with related concepts such as energy and force. More broadly, it is the general analysis of nature, conducted in order to understand how the universe behaves.Physics is one of the oldest academic...
, a lever (from French
French language
French is a Romance language spoken as a first language in France, the Romandy region in Switzerland, Wallonia and Brussels in Belgium, Monaco, the regions of Quebec and Acadia in Canada, and by various communities elsewhere. Second-language speakers of French are distributed throughout many parts...
lever, "to raise", cf. a levant) is a rigid object that is used with an appropriate fulcrum or pivot point to either multiply the mechanical force (effort) that can be applied to another object or resistance force (load), or multiply the distance and speed at which the opposite end of the rigid object travels.
This leverage is also termed mechanical advantage
Mechanical advantage
Mechanical advantage is a measure of the force amplification achieved by using a tool, mechanical device or machine system. Ideally, the device preserves the input power and simply trades off forces against movement to obtain a desired amplification in the output force...
, and is one example of the principle of moments.
Unanswered Questions
Encyclopedia
In physics
, a lever (from French
lever, "to raise", cf. a levant) is a rigid object that is used with an appropriate fulcrum or pivot point to either multiply the mechanical force (effort) that can be applied to another object or resistance force (load), or multiply the distance and speed at which the opposite end of the rigid object travels.
This leverage is also termed mechanical advantage
, and is one example of the principle of moments. A lever is one of the six simple machine
s.
. "Give me a place to stand, and I shall move the Earth with a lever" is a remark of Archimedes who formally stated the correct mathematical principle of levers (quoted by Pappus of Alexandria).
It is assumed that in ancient Egypt, constructors used the lever to move and uplift obelisks weighting more than 100 tons.
Mathematically, this is expressed by , where is the force, is the perpendicular distance between the force and the fulcrum, and is the turning force known as the moment
or torque
.
These cases are described by the mnemonic "fre 123" where the fulcrum is in the middle for the 1st class lever, the resistance is in the middle for the 2nd class lever, and the effort is in the middle for the 3rd class lever.
is a movable bar that pivots on a fulcrum attached to the ground. The lever operates by applying forces at different distances from the fulcrum, or pivot.
As the lever rotates around the fulcrum, points farther from this pivot move faster than points closer to the pivot. The power
into and out of the lever must be the same, so a force applied to a point farther from the pivot must be less than the force applied to a point closer in.
If a and b are distances from the fulcrum to points A and B and let the force F_{A} applied to A is the input and the force F_{B} applied at B is the output, the ratio of the velocities of points A and B is given by a/b, so we have the ratio of the output force to the input force, or mechanical advantage, is given by
This is the law of the lever, which was proven by Archimedes
using geometric reasoning. It shows that if the distance a from the fulcrum to where the input force is applied (point A) is greater than the distance b from fulcrum to where the output force is applied (point B), then the lever amplifies the input force. On the other hand, if the distance a from the fulcrum to the input force is less than the distance b from the fulcrum to the output force, then the lever reduces the input force.
The use of velocity in the static analysis of a lever is an application of the principle of virtual work.
Physics
Physics is a natural science that involves the study of matter and its motion through spacetime, along with related concepts such as energy and force. More broadly, it is the general analysis of nature, conducted in order to understand how the universe behaves.Physics is one of the oldest academic...
, a lever (from French
French language
French is a Romance language spoken as a first language in France, the Romandy region in Switzerland, Wallonia and Brussels in Belgium, Monaco, the regions of Quebec and Acadia in Canada, and by various communities elsewhere. Second-language speakers of French are distributed throughout many parts...
lever, "to raise", cf. a levant) is a rigid object that is used with an appropriate fulcrum or pivot point to either multiply the mechanical force (effort) that can be applied to another object or resistance force (load), or multiply the distance and speed at which the opposite end of the rigid object travels.
This leverage is also termed mechanical advantage
Mechanical advantage
Mechanical advantage is a measure of the force amplification achieved by using a tool, mechanical device or machine system. Ideally, the device preserves the input power and simply trades off forces against movement to obtain a desired amplification in the output force...
, and is one example of the principle of moments. A lever is one of the six simple machine
Simple machine
A simple machine is a mechanical device that changes the direction or magnitude of a force.In general, they can be defined as the simplest mechanisms that use mechanical advantage to multiply force. A simple machine uses a single applied force to do work against a single load force...
s.
Early use
The earliest remaining writings regarding levers date from the 3rd century BC and were provided by ArchimedesArchimedes
Archimedes of Syracuse was a Greek mathematician, physicist, engineer, inventor, and astronomer. Although few details of his life are known, he is regarded as one of the leading scientists in classical antiquity. Among his advances in physics are the foundations of hydrostatics, statics and an...
. "Give me a place to stand, and I shall move the Earth with a lever" is a remark of Archimedes who formally stated the correct mathematical principle of levers (quoted by Pappus of Alexandria).
It is assumed that in ancient Egypt, constructors used the lever to move and uplift obelisks weighting more than 100 tons.
Force and levers
A lever is a beam connected to ground by a hinge, or pivot, called a fulcrum. The ideal lever does not dissipate or store energy, which means there is no friction in the hinge or bending in the beam. In this case, the power into the lever equals the power out, and the ratio of output to input force is given by the ratio of the distances from the fulcrum to the points of application of these forces. This is known as the law of the lever.Mathematically, this is expressed by , where is the force, is the perpendicular distance between the force and the fulcrum, and is the turning force known as the moment
Moment (physics)
In physics, the term moment can refer to many different concepts:*Moment of force is the tendency of a force to twist or rotate an object; see the article torque for details. This is an important, basic concept in engineering and physics. A moment is valued mathematically as the product of the...
or torque
Torque
Torque, moment or moment of force , is the tendency of a force to rotate an object about an axis, fulcrum, or pivot. Just as a force is a push or a pull, a torque can be thought of as a twist....
.
Classes of levers
Levers are classified by the relative positions of the fulcrum and the input and output forces. It is common to call the input force the effort and the output force the load or the resistance. This allows the identification of three classes of levers by the relative locations of the fulcrum, the resistance and the effort:- Class 1: The effort is applied on one side of the fulcrum and the resistance on the other side, for example, a crowbarCrowbar (tool)A crowbar, a wrecking bar, pry bar, or prybar, or sometimes a prise bar or prisebar, and more informally a jimmy, jimmy bar, jemmy or gooseneck is a tool consisting of a metal bar with a single curved end and flattened points, often with a small fissure on one or both ends for removing nails...
or a pair of scissorsScissorsScissors are hand-operated cutting instruments. They consist of a pair of metal blades pivoted so that the sharpened edges slide against each other when the handles opposite to the pivot are closed. Scissors are used for cutting various thin materials, such as paper, cardboard, metal foil, thin...
or a seesawSeesawA seesaw is a long, narrow board pivoted in the middle so that, as one end goes up, the other goes down.-Mechanics:Mechanically a seesaw is a lever and fulcrum....
. - Class 2: The effort is applied on one side of the resistance and the fulcrum is located on the other side, for example, a wheelbarrowWheelbarrowA wheelbarrow is a small hand-propelled vehicle, usually with just one wheel, designed to be pushed and guided by a single person using two handles to the rear, or by a sail to push the ancient wheelbarrow by wind. The term "wheelbarrow" is made of two words: "wheel" and "barrow." "Barrow" is a...
or a nutcrackerNutcrackerA nutcracker is a mechanical device for cracking nuts. Usually they work on the principle of moments as described in Archimedes' analysis of the lever...
. - Class 3: The resistance is on one side of the effort and the fulcrum is located on the other side, for example, a pair of tweezersTweezersTweezers are tools used for picking up and manipulating objects too small to be easily handled with the human hands. They are probably derived from tongs, pincers, or scissors-like pliers used to grab or hold hot objects since the dawn of recorded history...
or the human mandible.
These cases are described by the mnemonic "fre 123" where the fulcrum is in the middle for the 1st class lever, the resistance is in the middle for the 2nd class lever, and the effort is in the middle for the 3rd class lever.
Law of the lever
The leverLever
In physics, a lever is a rigid object that is used with an appropriate fulcrum or pivot point to either multiply the mechanical force that can be applied to another object or resistance force , or multiply the distance and speed at which the opposite end of the rigid object travels.This leverage...
is a movable bar that pivots on a fulcrum attached to the ground. The lever operates by applying forces at different distances from the fulcrum, or pivot.
As the lever rotates around the fulcrum, points farther from this pivot move faster than points closer to the pivot. The power
Power (physics)
In physics, power is the rate at which energy is transferred, used, or transformed. For example, the rate at which a light bulb transforms electrical energy into heat and light is measured in watts—the more wattage, the more power, or equivalently the more electrical energy is used per unit...
into and out of the lever must be the same, so a force applied to a point farther from the pivot must be less than the force applied to a point closer in.
If a and b are distances from the fulcrum to points A and B and let the force F_{A} applied to A is the input and the force F_{B} applied at B is the output, the ratio of the velocities of points A and B is given by a/b, so we have the ratio of the output force to the input force, or mechanical advantage, is given by
This is the law of the lever, which was proven by Archimedes
Archimedes
Archimedes of Syracuse was a Greek mathematician, physicist, engineer, inventor, and astronomer. Although few details of his life are known, he is regarded as one of the leading scientists in classical antiquity. Among his advances in physics are the foundations of hydrostatics, statics and an...
using geometric reasoning. It shows that if the distance a from the fulcrum to where the input force is applied (point A) is greater than the distance b from fulcrum to where the output force is applied (point B), then the lever amplifies the input force. On the other hand, if the distance a from the fulcrum to the input force is less than the distance b from the fulcrum to the output force, then the lever reduces the input force.
The use of velocity in the static analysis of a lever is an application of the principle of virtual work.
See also
- Engineering mechanics
- Mechanical advantageMechanical advantageMechanical advantage is a measure of the force amplification achieved by using a tool, mechanical device or machine system. Ideally, the device preserves the input power and simply trades off forces against movement to obtain a desired amplification in the output force...
- Virtual workVirtual workVirtual work arises in the application of the principle of least action to the study of forces and movement of a mechanical system. Historically, virtual work and the associated calculus of variations were formulated to analyze systems of rigid bodies, but they have also been developed for the...
- Mechanism (engineering)Mechanism (engineering)A mechanism is a device designed to transform input forces and movement into a desired set of output forces and movement. Mechanisms generally consist of moving components such as gears and gear trains, belt and chain drives, cam and follower mechanisms, and linkages as well as friction devices...
- Linkage (mechanical)Linkage (mechanical)A mechanical linkage is an assembly of bodies connected together to manage forces and movement. The movement of a body, or link, is studied using geometry so the link is considered to be rigid. The connections between links are modeled as providing ideal movement, pure rotation or sliding for...
- Heavy equipment
External links
- Lever at Diracdelta science and engineering encyclopedia
- A Simple Lever by Stephen WolframStephen WolframStephen Wolfram is a British scientist and the chief designer of the Mathematica software application and the Wolfram Alpha computational knowledge engine.- Biography :...
, Wolfram Demonstrations ProjectWolfram Demonstrations ProjectThe Wolfram Demonstrations Project is hosted by Wolfram Research, whose stated goal is to bring computational exploration to the widest possible audience. It consists of an organized, open-source collection of small interactive programs called Demonstrations, which are meant to visually and...
. - Levers: Simple Machines at EnchantedLearning.com