''Vis viva'' (from the

Latin Latin ( or ) is a classical language belonging to the Italic languages, Italic branch of the Indo-European languages. Latin was originally spoken by the Latins (Italic tribe), Latins in Latium (now known as Lazio), the lower Tiber area aroun ...

for "living force") is a historical term used to describe a quantity similar to

kinetic energy In physics, the kinetic energy of an object is the form of energy that it possesses due to its motion. In classical mechanics, the kinetic energy of a non-rotating object of mass ''m'' traveling at a speed ''v'' is \fracmv^2.Resnick, Rober ...

in an early formulation of the principle of

conservation of energy The law of conservation of energy states that the total energy of an isolated system remains constant; it is said to be Conservation law, ''conserved'' over time. In the case of a Closed system#In thermodynamics, closed system, the principle s ...

Overview

Proposed by

Gottfried Leibniz Gottfried Wilhelm Leibniz (or Leibnitz; – 14 November 1716) was a German polymath active as a mathematician, philosopher, scientist and diplomat who is credited, alongside Isaac Newton, Sir Isaac Newton, with the creation of calculus in ad ...

over the period 1676–1689, the theory was controversial as it seemed to oppose the theory of conservation of quantity of motion advocated by

René Descartes René Descartes ( , ; ; 31 March 1596 – 11 February 1650) was a French philosopher, scientist, and mathematician, widely considered a seminal figure in the emergence of modern philosophy and Modern science, science. Mathematics was paramou ...

. Descartes' quantity of motion was different from

momentum In Newtonian mechanics, momentum (: momenta or momentums; more specifically linear momentum or translational momentum) is the product of the mass and velocity of an object. It is a vector quantity, possessing a magnitude and a direction. ...

, but Newton defined the quantity of motion as the conjunction of the quantity of matter and velocity in Definition II of his '' Principia''. In Definition III, he defined the force that resists a change in motion as the ''vis inertia'' of Descartes.

Newton's third law of motion Newton's laws of motion are three physical laws that describe the relationship between the motion of an object and the forces acting on it. These laws, which provide the basis for Newtonian mechanics, can be paraphrased as follows: # A body r ...

(for every action there is an equal and opposite reaction) is also equivalent to the principle of

conservation of momentum In Newtonian mechanics, momentum (: momenta or momentums; more specifically linear momentum or translational momentum) is the product of the mass and velocity of an object. It is a vector quantity, possessing a magnitude and a direction. ...

. Leibniz accepted the principle of conservation of momentum, but rejected the Cartesian version of it. 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 of

energy Energy () is the physical quantity, quantitative physical property, property that is transferred to a physical body, body or to a physical system, recognizable in the performance of Work (thermodynamics), work and in the form of heat and l ...

, though the term still survives in the context of

celestial mechanics Celestial mechanics is the branch of astronomy that deals with the motions of objects in outer space. Historically, celestial mechanics applies principles of physics (classical mechanics) to astronomical objects, such as stars and planets, to ...

through the ''vis viva'' equation. The English equivalent "living force" was also used, for example by George William Hill. The term is due to the German philosopher

Gottfried Wilhelm Leibniz Gottfried Wilhelm Leibniz (or Leibnitz; – 14 November 1716) was a German polymath active as a mathematician, philosopher, scientist and diplomat who is credited, alongside Sir Isaac Newton, with the creation of calculus in addition to ...

, who was the first to attempt a mathematical formulation from 1676 to 1689. Leibniz noticed that in many mechanical systems (of several

mass Mass is an Intrinsic and extrinsic properties, intrinsic property of a physical body, body. It was traditionally believed to be related to the physical quantity, quantity of matter in a body, until the discovery of the atom and particle physi ...

es, ''m_i'' each with

velocity Velocity is a measurement of speed in a certain direction of motion. It is a fundamental concept in kinematics, the branch of classical mechanics that describes the motion of physical objects. Velocity is a vector (geometry), vector Physical q ...

''v_i'') the quantity was conserved. He called this quantity the ''vis viva'' or "living force" of the system. The principle represented an accurate statement of the conservation of

in elastic collisions that was independent of the

. However, many

physicist A physicist is a scientist who specializes in the field of physics, which encompasses the interactions of matter and energy at all length and time scales in the physical universe. Physicists generally are interested in the root or ultimate cau ...

s at the time were unaware of this fact and, instead, were influenced by the prestige of Sir

Isaac Newton Sir Isaac Newton () was an English polymath active as a mathematician, physicist, astronomer, alchemist, theologian, and author. Newton was a key figure in the Scientific Revolution and the Age of Enlightenment, Enlightenment that followed ...

England England is a Countries of the United Kingdom, country that is part of the United Kingdom. It is located on the island of Great Britain, of which it covers about 62%, and List of islands of England, more than 100 smaller adjacent islands. It ...

and of

France France, officially the French Republic, is a country located primarily in Western Europe. Overseas France, Its overseas regions and territories include French Guiana in South America, Saint Pierre and Miquelon in the Atlantic Ocean#North Atlan ...

, both of whom advanced the

as a guiding principle. Thus the

: was held by the rival camp to be the conserved ''vis viva''. It was largely

engineer Engineers, as practitioners of engineering, are professionals who Invention, invent, design, build, maintain and test machines, complex systems, structures, gadgets and materials. They aim to fulfill functional objectives and requirements while ...

s such as

John Smeaton John Smeaton (8 June 1724 – 28 October 1792) was an English civil engineer responsible for the design of bridges, canals, harbours and lighthouses. He was also a capable mechanical engineer and an eminent scholar, who introduced various ...

, Peter Ewart, Karl Holtzmann, Gustave-Adolphe Hirn and Marc 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 some

chemist A chemist (from Greek ''chēm(ía)'' alchemy; replacing ''chymist'' from Medieval Latin ''alchemist'') is a graduated scientist trained in the study of chemistry, or an officially enrolled student in the field. Chemists study the composition of ...

s such as William Hyde Wollaston. The French mathematician

Émilie du Châtelet Gabrielle Émilie Le Tonnelier de Breteuil, Marquise du Châtelet (; 17 December 1706 – 10 September 1749) was a French mathematician and physicist. Her most recognized achievement is her philosophical magnum opus, ''Institutions de Physique'' ...

, 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. 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 The second law of thermodynamics is a physical law based on Universal (metaphysics), universal empirical observation concerning heat and Energy transformation, energy interconversions. A simple statement of the law is that heat always flows spont ...

, 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 In thermodynamics, heat is energy in transfer between a thermodynamic system and its surroundings by such mechanisms as thermal conduction, electromagnetic radiation, and friction, which are microscopic in nature, involving sub-atomic, ato ...

inevitably generated by motion was another form of ''vis viva''. In 1783,

Antoine Lavoisier Antoine-Laurent de Lavoisier ( ; ; 26 August 17438 May 1794), When reduced without charcoal, it gave off an air which supported respiration and combustion in an enhanced way. He concluded that this was just a pure form of common air and that i ...

and

Pierre-Simon Laplace Pierre-Simon, Marquis de Laplace (; ; 23 March 1749 – 5 March 1827) was a French polymath, a scholar whose work has been instrumental in the fields of physics, astronomy, mathematics, engineering, statistics, and philosophy. He summariz ...

reviewed the two competing theories of ''vis viva'' and caloric theory.

Count Rumford Colonel (United Kingdom), Colonel Sir Benjamin Thompson, Count Rumford, Fellow of the Royal Society, FRS (26 March 175321 August 1814), was an American-born British military officer, scientist and inventor. Born in Woburn, Massachusetts, he sup ...

's 1798 observations of heat generation during the boring of

cannon A cannon is a large-caliber gun classified as a type of artillery, which usually launches a projectile using explosive chemical propellant. Gunpowder ("black powder") was the primary propellant before the invention of smokeless powder during th ...

s added more weight to the view that mechanical motion could be converted into heat. ''Vis viva'' began to be known as ''energy'' after Thomas Young first used the term in 1807. The recalibration of ''vis viva'' to include the coefficient of a half, namely: was largely the result of the work of

Gaspard-Gustave Coriolis Gaspard-Gustave de Coriolis (; 21 May 1792 – 19 September 1843) was a French mathematician, mechanical engineer and scientist. He is best known for his work on the supplementary forces that are detected in a rotating frame of reference, le ...

and Jean-Victor Poncelet over the period 1819–1839, although the present-day definition can occasionally be found earlier (e.g., in

Daniel Bernoulli Daniel Bernoulli ( ; ; – 27 March 1782) was a Swiss people, Swiss-France, French mathematician and physicist and was one of the many prominent mathematicians in the Bernoulli family from Basel. He is particularly remembered for his applicati ...

's texts). The former called it the ''quantité de travail'' (quantity of work) and the latter, ''travail mécanique'' (mechanical work) and both championed its use in engineering calculation.

Notes

References

* George E. Smith
"The Vis Viva Dispute: A Controversy at the Dawn of Dynamics"
''Physics Today'' 59 (October 2006) Issue 10 pp 31–36

(see als
erratum

Overview

See also

Notes

References

Further reading