Vis viva (from theLatin for "living force") is a historical term used to describe a quantity similar tokinetic energy in an early formulation of the principle ofconservation of energy.
Proposed byGottfried Leibniz over the period 1676–1689, the theory was controversial as it seemed to oppose the theory of conservation of quantity of motion advocated byRené Descartes.[1] Descartes' quantity of motion was different frommomentum, but Newton defined the quantity of motion as the conjunction of the quantity of matter and velocity in Definition II of hisPrincipia. In Definition III, he defined the force that resists a change in motion as thevis inertia of Descartes.Newton’s Third Law of Motion (for every action there is an equal and opposite reaction) is also equivalent to the principle ofconservation of momentum. Leibniz accepted the principle of conservation of momentum, but rejected the Cartesian version of it.[2] The difference between these ideas was whether the quantity of motion was simply related to a body's resistance to a change in velocity (vis inertia) or whether a body's amount of force due to its motion (vis viva) was related to the square of its velocity.
The theory was eventually absorbed into the modern theory ofenergy, though the term still survives in the context ofcelestial mechanics through thevis viva equation. The English equivalent "living force" was also used, for example byGeorge William Hill.[3]
The term is due to theGerman philosopherGottfried Wilhelm Leibniz, who was the first to attempt a mathematical formulation from 1676 to 1689. Leibniz noticed that in many mechanical systems (of severalmasses,mi each withvelocityvi) the quantity[4]
was conserved. He called this quantity thevis viva or "living force" of the system.[4] The principle represented an accurate statement of the conservation ofkinetic energy inelastic collisions that was independent of theconservation of momentum.
However, manyphysicists at the time were unaware of this fact and, instead, were influenced by the prestige of SirIsaac Newton inEngland and ofRené Descartes inFrance, both of whom advanced theconservation of momentum as a guiding principle. Thus themomentum:[4]
was held by the rival camp to be the conservedvis viva. It was largelyengineers such asJohn Smeaton,Peter Ewart,Karl Holtzmann,Gustave-Adolphe Hirn andMarc Seguin 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 somechemists such asWilliam Hyde Wollaston.
The French mathematicianÉmilie du Châtelet, who had a sound grasp of Newtonian mechanics, developed Leibniz's concept and, combining it with the observations ofWillem 's Gravesande, showed thatvis viva was dependent on the square of the velocities.[5]
Members of the academic establishment such asJohn Playfair were quick to point out that kinetic energy is clearly not conserved. This is obvious to a modern analysis based on thesecond 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 theheat inevitably generated by motion was another form ofvis viva. In 1783,Antoine Lavoisier andPierre-Simon Laplace reviewed the two competing theories ofvis viva andcaloric theory.[1]Count Rumford's 1798 observations of heat generation during theboring ofcannons added more weight to the view that mechanical motion could be converted into heat.Vis viva began to be known asenergy afterThomas Young first used the term in 1807.
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The recalibration ofvis viva to include the coefficient of a half, namely:
was largely the result of the work ofGaspard-Gustave Coriolis andJean-Victor Poncelet over the period 1819–1839,[7] although the present-day definition can occasionally be found earlier (e.g., inDaniel Bernoulli's texts). The former called it thequantité de travail (quantity of work) and the latter,travail mécanique (mechanical work) and both championed its use in engineering calculation.
