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| In the history of [[science]], '''''vis viva''''' (from the [[Latin]] for ''living force'') is an [[obsolete scientific theory]] that served as an elementary and limited early formulation of the principle of [[conservation of energy]]. It was the first [known] description of what we now call [[kinetic energy]] or of energy related to sensible motions.
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| Proposed by [[Gottfried Leibniz]] over the period 1676–1689, the theory was controversial as it seemed to oppose the theory of [[conservation of momentum]] advocated by Sir [[Isaac Newton]] and [[René Descartes]]. The two theories are now understood to be complementary.
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| The theory was eventually absorbed into the modern theory of [[energy]] though the term still survives in the context of [[celestial mechanics]] through the [[Vis-viva equation|''vis viva'' equation]].
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| ==History==
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| Although [[ancient]] [[philosopher]]s as far back as [[Thales|Thales of Miletus]] had inklings of the law of conservation of energy{{Citation needed|date=January 2011}}, it was the [[Germany|German]] [[Gottfried Wilhelm Leibniz]] during 1676–1689 who first attempted a mathematical formulation. Leibniz noticed that in many mechanical systems (of several [[mass]]es, ''m<sub>i</sub>'' each with [[velocity]] ''v<sub>i</sub>'') the quantity:
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| :<math>\sum_{i} m_i v_i^2</math>
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| was conserved. He called this quantity the ''vis viva'' or ''living force'' of the system. The principle, it is now realised, represents an accurate statement of the conservation of [[kinetic energy]] in [[elastic collision]]s, and is a consequence of the [[conservation of momentum]]. However, many [[physicist]]s at the time were unaware of this connection and, instead, were influenced by the prestige of Sir [[Isaac Newton]] in [[England]] and of [[René Descartes]] in [[France]], both of whom had set great store by the [[conservation of momentum]] as a guiding principle. Thus the [[momentum]]:
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| :<math>\,\!\sum_{i} m_i \mathbf{v}_i</math>
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| was held by the rival camp to be the conserved ''vis viva''. It was largely [[engineer]]s such as [[John Smeaton]], [[Peter Ewart]], [[Karl Holtzmann]], [[Gustave-Adolphe Hirn]] and [[Marc Séguin]] who objected that conservation of momentum alone was not adequate for practical calculation and who made use of Leibniz's principle. The principle was also championed by some [[chemist]]s such as [[William Hyde Wollaston]].
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| The French mathematician [[Émilie du Châtelet]], who had a sound grasp of Newtonian mechanics, developed Leibniz's concept and, combining it with the observations of [[Willem 's Gravesande]], showed that ''vis viva'' was dependent on the square of the velocities.
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| Members of the academic establishment such as [[John Playfair]] were quick to point out that kinetic energy is clearly not conserved. This is obvious to a modern analysis based on the [[second law of thermodynamics]] but in the 18th and 19th centuries, the fate of the lost energy was still unknown. Gradually it came to be suspected that the [[heat]] inevitably generated by motion was another form of ''vis viva''. In 1783, [[Antoine Lavoisier]] and [[Pierre-Simon Laplace]] reviewed the two competing theories of ''vis viva'' and [[caloric theory]].{{ref|LL}} [[Benjamin Thompson|Count Rumford]]'s 1798 observations of heat generation during the [[Boring (manufacturing)|boring]] of [[cannon]]s added more weight to the view that mechanical motion could be converted into heat. ''Vis viva'' now started to be known as ''energy'', after the term was first used in that sense by [[Thomas Young (scientist)|Thomas Young]] in 1807.
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| [[File:Bernoulli-vis-viva-with-0.5-multiplier-1736 (1741).gif|thumb|An excerpt from [[Daniel Bernoulli|D.Bernoulli's]] article, published in 1741,<ref>{{cite journal|author=Bernoulli D.|title=De legibus quibusdam mechanicis…|url=http://gidropraktikum.narod.ru/jet.htm|journal=Commentarii Academiae scientiarum imperialis Petropolitanae|year=1741 (1736)|volume=8|pages=99–127}}</ref> with the definition of vis viva with 1/2 multiplier.]]
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| The recalibration of ''vis viva'' to include the coefficient of a half, namely:
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| :<math>\frac {1} {2}\sum_{i} m_i v_i^2</math>
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| was largely the result of the work of [[Gaspard-Gustave Coriolis]] and [[Jean-Victor Poncelet]] over the period 1819–1839, although present-day definition can occasionally be found earlier (e.g., in [[Daniel Bernoulli]] texts).
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| The former called the ''quantité de travail'' (quantity of work) and the latter, ''travail mécanique'' (mechanical work) and both championed its use in engineering calculation.
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| ==See also==
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| *[[Conservation of energy#History|Conservation of energy: Historical development]]
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| *[[Vis-viva equation]]
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| ==References==
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| <references />
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| * George E. Smith, [http://ptonline.aip.org/getpdf/servlet/GetPDFServlet?filetype=pdf&id=PHTOAD000059000010000031000001&idtype=cvips "The Vis Viva Dispute: A Controversy at the Dawn of Dynamics"], ''Physics Today'' '''59''' (October 2006) Issue 10 pp 31–36. [http://ptonline.aip.org/getpdf/servlet/GetPDFServlet?filetype=pdf&id=PHTOAD000059000010000031000001&idtype=cvips ] (see also [http://www.physicstoday.org/vol-59/iss-12/p16.html erratum])
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| {{Gottfried Wilhelm Leibniz}}
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| {{DEFAULTSORT:Vis Viva}}
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| [[Category:Natural philosophy]]
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| [[Category:Obsolete scientific theories]]
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| [[Category:Mechanics]]
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| [[Category:Thermodynamics]]
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| [[Category:Gottfried Leibniz]]
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| [[Category:History of thermodynamics]]
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Hello and welcome. My title is Figures Wunder. To do aerobics is a factor that I'm totally addicted to. North Dakota is her birth place but she will have to move one working day or another. I am a meter reader but I strategy on changing it.
Feel free to surf to my webpage ... bit.ly