Lever: Difference between revisions

Lever
Lever
	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.
Classification	Simple machine
Industry	Construction

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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 machines.

Early use

The earliest remaining writings regarding levers date from the 3rd century BC and were provided by Archimedes. "Give me a place to stand, and I shall move the Earth with a lever"^{[note 1]} is a remark of Archimedes who formally stated the correct mathematical principle of levers (quoted by Pappus of Alexandria).^[1]

It is assumed that in ancient Egypt, constructors used the lever to move and uplift obelisks weighting more than 100 tons.^[2]

Force and levers

The force applied (at end points of the lever) is proportional to the ratio of the length of the lever arm measured between the fulcrum (pivoting point) and application point of the force applied at each end of the lever.

Mathematically, this is expressed by $M=Fd$ , where $F$ is the force, $d$ is the perpendicular distance between the force and the fulcrum, and $M$ is the turning force known as the moment or torque.

Classes

There are three classes of levers representing variations in the relative locations of the fulcrum, the load and the force:^[3]

Class 1: The fulcrum is located between the applied force and the load, for example, a crowbar or a pair of scissors or a seesaw.
Class 2: The load is situated between the fulcrum and the force, for example, a wheelbarrow or a nutcracker.
Class 3: The force is applied between the fulcrum and the load, for example, a pair of tweezers or the human mandible.

In the real world

For the classical mechanics formulae 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. The classical formulae assume zero friction, which of course is never completely true, and depending on circumstances, may or may not be significant.

Mnemonics

To remember what the different classes of levers look like, a 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.

Notes

^ If this feat were attempted in a uniform gravitational field with an acceleration equivalent to that of the Earth, the corresponding distance to the fulcrum which a human of mass 70kg would be required to stand to balance a sphere of 1 Earth mass, with center of gravity 1m to the fulcrum, would be roughly equal to 8.5×10²²m. This distance might be exemplified in astronomical terms as the approximate distance to the Circinus galaxy (roughly 3.6 times the distance to the Andromeda Galaxy).

References

^ Mackay, Alan Lindsay (1991). "Archimedes ca 287–212 BC". A Dictionary of scientific quotations. London: Taylor and Francis. p. 11. ISBN 9780750301060.
^ Budge, E.A. Wallis (2003). Cleopatra's Needles and Other Egyptian Obelisks‎. Kessinger Publishing. p. 28. ISBN 9780766135246.
^ Davidovits, Paul (2008), Physics in Biology and Medicine, Third edition, Academic Press, p. 10, ISBN 978-0-12-369411-9, Chapter 1, p. 10

External links

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

[1] If this feat were attempted in a uniform gravitational field with an acceleration equivalent to that of the Earth, the corresponding distance to the fulcrum which a human of mass 70kg would be required to stand to balance a sphere of 1 Earth mass, with center of gravity 1m to the fulcrum, would be roughly equal to 8.5×10²²m. This distance might be exemplified in astronomical terms as the approximate distance to the Circinus galaxy (roughly 3.6 times the distance to the Andromeda Galaxy).

[2] Mackay, Alan Lindsay (1991). "Archimedes ca 287–212 BC". A Dictionary of scientific quotations. London: Taylor and Francis. p. 11. ISBN 9780750301060.

[3] Budge, E.A. Wallis (2003). Cleopatra's Needles and Other Egyptian Obelisks‎. Kessinger Publishing. p. 28. ISBN 9780766135246.

[4] Davidovits, Paul (2008), Physics in Biology and Medicine, Third edition, Academic Press, p. 10, ISBN 978-0-12-369411-9, Chapter 1, p. 10

[note 1]

[1]

[2]

[3]

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 ==Early use==
-The earliest remaining writings regarding levers date from the 3rd century BC and were provided by [[Archimedes]]. "''Give me a place to stand, and I shall move the earth with a lever''"{{#tag:ref|If this feat were attempted in a uniform gravitational field with an acceleration equivalent to that of the Earth, the corresponding distance to the fulcrum which a human of mass 70kg would be required to stand to balance a sphere of 1 Earth mass, with center of gravity 1m to the fulcrum, would be roughly equal to 8.5×10<sup>22</sup>m. This distance might be exemplified in astronomical terms as the approximate distance to the Circinus galaxy (roughly 3.6 times the distance to the Andromeda Galaxy).|group="note"}} is a remark of Archimedes who formally stated the correct mathematical principle of levers (quoted by Pappus of Alexandria).<ref>{{cite book|last=Mackay|first=Alan Lindsay|title=A Dictionary of scientific quotations|publisher=Taylor and Francis|location=London|year=1991|page=11|chapter=Archimedes ca 287–212 BC|isbn=9780750301060}}</ref>
+The earliest remaining writings regarding levers date from the 3rd century BC and were provided by [[Archimedes]]. "''Give me a place to stand, and I shall move the Earth with a lever''"{{#tag:ref|If this feat were attempted in a uniform gravitational field with an acceleration equivalent to that of the Earth, the corresponding distance to the fulcrum which a human of mass 70kg would be required to stand to balance a sphere of 1 Earth mass, with center of gravity 1m to the fulcrum, would be roughly equal to 8.5×10<sup>22</sup>m. This distance might be exemplified in astronomical terms as the approximate distance to the Circinus galaxy (roughly 3.6 times the distance to the Andromeda Galaxy).|group="note"}} is a remark of Archimedes who formally stated the correct mathematical principle of levers (quoted by Pappus of Alexandria).<ref>{{cite book|last=Mackay|first=Alan Lindsay|title=A Dictionary of scientific quotations|publisher=Taylor and Francis|location=London|year=1991|page=11|chapter=Archimedes ca 287–212 BC|isbn=9780750301060}}</ref>
 It is assumed that in ancient Egypt, constructors used the lever to move and uplift obelisks weighting more than 100 tons.<ref>{{cite book|last=Budge|first=E.A. Wallis|title=Cleopatra's Needles and Other Egyptian Obelisks‎|publisher=Kessinger Publishing|year=2003|page=28|isbn=9780766135246}}</ref>