121-506: Energy (from Ancient Greek ἐνέργεια ( enérgeia ) 'activity') is the quantitative property that is transferred to a body or to a physical system , recognizable in the performance of work and in the form of heat and light . Energy is a conserved quantity —the law of conservation of energy states that energy can be converted in form, but not created or destroyed; matter and energy may also be converted to one another. The unit of measurement for energy in
242-548: A basal metabolic rate of 80 watts. For example, if our bodies run (on average) at 80 watts, then a light bulb running at 100 watts is running at 1.25 human equivalents (100 ÷ 80) i.e. 1.25 H-e. For a difficult task of only a few seconds' duration, a person can put out thousands of watts, many times the 746 watts in one official horsepower. For tasks lasting a few minutes, a fit human can generate perhaps 1,000 watts. For an activity that must be sustained for an hour, output drops to around 300; for an activity kept up all day, 150 watts
363-462: A battery (from chemical energy to electric energy ), a dam (from gravitational potential energy to kinetic energy of moving water (and the blades of a turbine ) and ultimately to electric energy through an electric generator ), and a heat engine (from heat to work). Examples of energy transformation include generating electric energy from heat energy via a steam turbine, or lifting an object against gravity using electrical energy driving
484-543: A pitch accent . In Modern Greek, all vowels and consonants are short. Many vowels and diphthongs once pronounced distinctly are pronounced as /i/ ( iotacism ). Some of the stops and glides in diphthongs have become fricatives , and the pitch accent has changed to a stress accent . Many of the changes took place in the Koine Greek period. The writing system of Modern Greek, however, does not reflect all pronunciation changes. The examples below represent Attic Greek in
605-415: A system can be subdivided and classified into potential energy , kinetic energy , or combinations of the two in various ways. Kinetic energy is determined by the movement of an object – or the composite motion of the object's components – while potential energy reflects the potential of an object to have motion, generally being based upon the object's position within a field or what is stored within
726-427: A the acceleration of the object and the distance traveled by the accelerated object in time t , we find with v = a t {\displaystyle v=at} for the velocity v of the object The work done in accelerating a particle with mass m during the infinitesimal time interval dt is given by the dot product of force F and the infinitesimal displacement d x where we have assumed
847-466: A thermodynamic system , and rest energy associated with an object's rest mass . All living organisms constantly take in and release energy. The Earth's climate and ecosystems processes are driven primarily by radiant energy from the sun . The energy industry provides the energy required for human civilization to function, which it obtains from energy resources such as fossil fuels , nuclear fuel , and renewable energy . The total energy of
968-435: A Lagrangian; for example, dissipative systems with continuous symmetries need not have a corresponding conservation law. In the context of chemistry , energy is an attribute of a substance as a consequence of its atomic, molecular, or aggregate structure. Since a chemical transformation is accompanied by a change in one or more of these kinds of structure, it is usually accompanied by a decrease, and sometimes an increase, of
1089-474: A biological cell or organelle of a biological organism. Energy used in respiration is stored in substances such as carbohydrates (including sugars), lipids , and proteins stored by cells . In human terms, the human equivalent (H-e) (Human energy conversion) indicates, for a given amount of energy expenditure, the relative quantity of energy needed for human metabolism , using as a standard an average human energy expenditure of 12,500 kJ per day and
1210-410: A body's mass, inertia, and total energy. In fluid dynamics , the kinetic energy per unit volume at each point in an incompressible fluid flow field is called the dynamic pressure at that point. Dividing by V, the unit of volume: where q {\displaystyle q} is the dynamic pressure, and ρ is the density of the incompressible fluid. The speed, and thus the kinetic energy of
1331-515: A bound system is discrete (a set of permitted states, each characterized by an energy level ) which results in the concept of quanta . In the solution of the Schrödinger equation for any oscillator (vibrator) and for electromagnetic waves in a vacuum, the resulting energy states are related to the frequency by Planck's relation : E = h ν {\displaystyle E=h\nu } (where h {\displaystyle h}
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#17327689468351452-424: A century until this was generally accepted. The modern analog of this property, kinetic energy , differs from vis viva only by a factor of two. Writing in the early 18th century, Émilie du Châtelet proposed the concept of conservation of energy in the marginalia of her French language translation of Newton's Principia Mathematica , which represented the first formulation of a conserved measurable quantity that
1573-417: A core concept. Work , a function of energy, is force times distance. This says that the work ( W {\displaystyle W} ) is equal to the line integral of the force F along a path C ; for details see the mechanical work article. Work and thus energy is frame dependent . For example, consider a ball being hit by a bat. In the center-of-mass reference frame, the bat does no work on
1694-492: A crane motor. Lifting against gravity performs mechanical work on the object and stores gravitational potential energy in the object. If the object falls to the ground, gravity does mechanical work on the object which transforms the potential energy in the gravitational field to the kinetic energy released as heat on impact with the ground. The Sun transforms nuclear potential energy to other forms of energy; its total mass does not decrease due to that itself (since it still contains
1815-556: A few exceptions, like those generated by volcanic events for example. An example of a solar-mediated weather event is a hurricane, which occurs when large unstable areas of warm ocean, heated over months, suddenly give up some of their thermal energy to power a few days of violent air movement. In a slower process, radioactive decay of atoms in the core of the Earth releases heat. This thermal energy drives plate tectonics and may lift mountains, via orogenesis . This slow lifting represents
1936-525: A fifth major dialect group, or it is Mycenaean Greek overlaid by Doric, with a non-Greek native influence. Regarding the speech of the ancient Macedonians diverse theories have been put forward, but the epigraphic activity and the archaeological discoveries in the Greek region of Macedonia during the last decades has brought to light documents, among which the first texts written in Macedonian , such as
2057-455: A force of one newton through a distance of one metre. However energy can also be expressed in many other units not part of the SI, such as ergs , calories , British thermal units , kilowatt-hours and kilocalories , which require a conversion factor when expressed in SI units. The SI unit of power , defined as energy per unit of time, is the watt , which is a joule per second. Thus, one joule
2178-474: A given temperature T . This exponential dependence of a reaction rate on temperature is known as the Arrhenius equation . The activation energy necessary for a chemical reaction can be provided in the form of thermal energy. In biology , energy is an attribute of all biological systems, from the biosphere to the smallest living organism. Within an organism it is responsible for growth and development of
2299-477: A kind of gravitational potential energy storage of the thermal energy, which may later be transformed into active kinetic energy during landslides, after a triggering event. Earthquakes also release stored elastic potential energy in rocks, a store that has been produced ultimately from the same radioactive heat sources. Thus, according to present understanding, familiar events such as landslides and earthquakes release energy that has been stored as potential energy in
2420-550: A prefix /e-/, called the augment . This was probably originally a separate word, meaning something like "then", added because tenses in PIE had primarily aspectual meaning. The augment is added to the indicative of the aorist, imperfect, and pluperfect, but not to any of the other forms of the aorist (no other forms of the imperfect and pluperfect exist). The two kinds of augment in Greek are syllabic and quantitative. The syllabic augment
2541-402: A single object is frame-dependent (relative): it can take any non-negative value, by choosing a suitable inertial frame of reference . For example, a bullet passing an observer has kinetic energy in the reference frame of this observer. The same bullet is stationary to an observer moving with the same velocity as the bullet, and so has zero kinetic energy. By contrast, the total kinetic energy of
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#17327689468352662-542: A strong Northwest Greek influence, and can in some respects be considered a transitional dialect, as exemplified in the poems of the Boeotian poet Pindar who wrote in Doric with a small Aeolic admixture. Thessalian likewise had come under Northwest Greek influence, though to a lesser degree. Pamphylian Greek , spoken in a small area on the southwestern coast of Anatolia and little preserved in inscriptions, may be either
2783-449: A system of objects cannot be reduced to zero by a suitable choice of the inertial reference frame, unless all the objects have the same velocity. In any other case, the total kinetic energy has a non-zero minimum, as no inertial reference frame can be chosen in which all the objects are stationary. This minimum kinetic energy contributes to the system's invariant mass , which is independent of the reference frame. The total kinetic energy of
2904-425: A system. This property is responsible for the inertia and strength of gravitational interaction of the system ("mass manifestations"), and is also responsible for the potential ability of the system to perform work or heating ("energy manifestations"), subject to the limitations of other physical laws. In classical physics , energy is a scalar quantity, the canonical conjugate to time. In special relativity energy
3025-425: A tiny fraction of the original chemical energy is used for work : It would appear that living organisms are remarkably inefficient (in the physical sense) in their use of the energy they receive (chemical or radiant energy); most machines manage higher efficiencies. In growing organisms the energy that is converted to heat serves a vital purpose, as it allows the organism tissue to be highly ordered with regard to
3146-510: A vowel or /n s r/ ; final stops were lost, as in γάλα "milk", compared with γάλακτος "of milk" (genitive). Ancient Greek of the classical period also differed in both the inventory and distribution of original PIE phonemes due to numerous sound changes, notably the following: The pronunciation of Ancient Greek was very different from that of Modern Greek . Ancient Greek had long and short vowels ; many diphthongs ; double and single consonants; voiced, voiceless, and aspirated stops ; and
3267-458: Is about the maximum. The human equivalent assists understanding of energy flows in physical and biological systems by expressing energy units in human terms: it provides a "feel" for the use of a given amount of energy. Sunlight's radiant energy is also captured by plants as chemical potential energy in photosynthesis , when carbon dioxide and water (two low-energy compounds) are converted into carbohydrates, lipids, proteins and oxygen. Release of
3388-418: Is added to stems beginning with consonants, and simply prefixes e (stems beginning with r , however, add er ). The quantitative augment is added to stems beginning with vowels, and involves lengthening the vowel: Some verbs augment irregularly; the most common variation is e → ei . The irregularity can be explained diachronically by the loss of s between vowels, or that of the letter w , which affected
3509-433: Is also a scalar (although not a Lorentz scalar but a time component of the energy–momentum 4-vector ). In other words, energy is invariant with respect to rotations of space , but not invariant with respect to rotations of spacetime (= boosts ). Energy may be transformed between different forms at various efficiencies . Items that transform between these forms are called transducers . Examples of transducers include
3630-575: Is called the Lagrangian , after Joseph-Louis Lagrange . This formalism is as fundamental as the Hamiltonian, and both can be used to derive the equations of motion or be derived from them. It was invented in the context of classical mechanics , but is generally useful in modern physics. The Lagrangian is defined as the kinetic energy minus the potential energy. Usually, the Lagrange formalism
3751-448: Is considered by some linguists to have been closely related to Greek . Among Indo-European branches with living descendants, Greek is often argued to have the closest genetic ties with Armenian (see also Graeco-Armenian ) and Indo-Iranian languages (see Graeco-Aryan ). Ancient Greek differs from Proto-Indo-European (PIE) and other Indo-European languages in certain ways. In phonotactics , ancient Greek words could end only in
Energy - Misplaced Pages Continue
3872-473: Is defined in terms of the energy operator (Hamiltonian) as a time derivative of the wave function . The Schrödinger equation equates the energy operator to the full energy of a particle or a system. Its results can be considered as a definition of measurement of energy in quantum mechanics. The Schrödinger equation describes the space- and time-dependence of a slowly changing (non-relativistic) wave function of quantum systems. The solution of this equation for
3993-418: Is directly proportional to the mass of the body: E 0 = m 0 c 2 , {\displaystyle E_{0}=m_{0}c^{2},} where For example, consider electron – positron annihilation, in which the rest energy of these two individual particles (equivalent to their rest mass) is converted to the radiant energy of the photons produced in the process. In this system
4114-421: Is dissipated in various forms of energy, such as heat, sound and binding energy (breaking bound structures). Flywheels have been developed as a method of energy storage . This illustrates that kinetic energy is also stored in rotational motion. Several mathematical descriptions of kinetic energy exist that describe it in the appropriate physical situation. For objects and processes in common human experience,
4235-460: Is done by the object when decelerating from its current speed to a state of rest . The SI unit of kinetic energy is the joule , while the English unit of kinetic energy is the foot-pound . In relativistic mechanics , 1 2 m v 2 {\textstyle {\frac {1}{2}}mv^{2}} is a good approximation of kinetic energy only when v is much less than
4356-516: Is either from gravitational collapse of matter (usually molecular hydrogen) into various classes of astronomical objects (stars, black holes, etc.), or from nuclear fusion (of lighter elements, primarily hydrogen). The nuclear fusion of hydrogen in the Sun also releases another store of potential energy which was created at the time of the Big Bang . At that time, according to theory, space expanded and
4477-446: Is equal to where: The kinetic energy of any entity depends on the reference frame in which it is measured. However, the total energy of an isolated system, i.e. one in which energy can neither enter nor leave, does not change over time in the reference frame in which it is measured. Thus, the chemical energy converted to kinetic energy by a rocket engine is divided differently between the rocket ship and its exhaust stream depending upon
4598-419: Is equal to 1/2 the product of the mass and the square of the speed. In formula form: where m {\displaystyle m} is the mass and v {\displaystyle v} is the speed (magnitude of the velocity) of the body. In SI units, mass is measured in kilograms , speed in metres per second , and the resulting kinetic energy is in joules . For example, one would calculate
4719-510: Is extremely large relative to ordinary human scales, the conversion of an everyday amount of rest mass (for example, 1 kg) from rest energy to other forms of energy (such as kinetic energy, thermal energy, or the radiant energy carried by light and other radiation) can liberate tremendous amounts of energy (~ 9 × 10 16 {\displaystyle 9\times 10^{16}} joules = 21 megatons of TNT), as can be seen in nuclear reactors and nuclear weapons. Conversely,
4840-602: Is given the credit for coining the term "kinetic energy" c. 1849–1851. William Rankine , who had introduced the term "potential energy" in 1853, and the phrase "actual energy" to complement it, later cites William Thomson and Peter Tait as substituting the word "kinetic" for "actual". Energy occurs in many forms, including chemical energy , thermal energy , electromagnetic radiation , gravitational energy , electric energy , elastic energy , nuclear energy , and rest energy . These can be categorized in two main classes: potential energy and kinetic energy. Kinetic energy
4961-623: Is mathematically more convenient than the Hamiltonian for non-conservative systems (such as systems with friction). Noether's theorem (1918) states that any differentiable symmetry of the action of a physical system has a corresponding conservation law. Noether's theorem has become a fundamental tool of modern theoretical physics and the calculus of variations. A generalisation of the seminal formulations on constants of motion in Lagrangian and Hamiltonian mechanics (1788 and 1833, respectively), it does not apply to systems that cannot be modeled with
Energy - Misplaced Pages Continue
5082-402: Is no friction or other losses, the conversion of energy between these processes would be perfect, and the pendulum would continue swinging forever. Energy is also transferred from potential energy ( E p {\displaystyle E_{p}} ) to kinetic energy ( E k {\displaystyle E_{k}} ) and then back to potential energy constantly. This
5203-436: Is one watt-second, and 3600 joules equal one watt-hour. The CGS energy unit is the erg and the imperial and US customary unit is the foot pound . Other energy units such as the electronvolt , food calorie or thermodynamic kcal (based on the temperature change of water in a heating process), and BTU are used in specific areas of science and commerce. In 1843, French physicist James Prescott Joule , namesake of
5324-415: Is referred to as conservation of energy. In this isolated system , energy cannot be created or destroyed; therefore, the initial energy and the final energy will be equal to each other. This can be demonstrated by the following: The equation can then be simplified further since E p = m g h {\displaystyle E_{p}=mgh} (mass times acceleration due to gravity times
5445-418: Is simply the sum of the kinetic energies of its moving parts, and is thus given by: where: (In this equation the moment of inertia must be taken about an axis through the center of mass and the rotation measured by ω must be around that axis; more general equations exist for systems where the object is subject to wobble due to its eccentric shape). A system of bodies may have internal kinetic energy due to
5566-696: Is the Planck constant and ν {\displaystyle \nu } the frequency). In the case of an electromagnetic wave these energy states are called quanta of light or photons . When calculating kinetic energy ( work to accelerate a massive body from zero speed to some finite speed) relativistically – using Lorentz transformations instead of Newtonian mechanics – Einstein discovered an unexpected by-product of these calculations to be an energy term which does not vanish at zero speed. He called it rest energy : energy which every massive body must possess even when being at rest. The amount of energy
5687-445: Is the main input to Earth's energy budget which accounts for its temperature and climate stability. Sunlight may be stored as gravitational potential energy after it strikes the Earth, as (for example when) water evaporates from oceans and is deposited upon mountains (where, after being released at a hydroelectric dam, it can be used to drive turbines or generators to produce electricity). Sunlight also drives most weather phenomena, save
5808-550: Is the movement energy of an object. Kinetic energy can be transferred between objects and transformed into other kinds of energy. Kinetic energy may be best understood by examples that demonstrate how it is transformed to and from other forms of energy. For example, a cyclist uses chemical energy provided by food to accelerate a bicycle to a chosen speed. On a level surface, this speed can be maintained without further work, except to overcome air resistance and friction . The chemical energy has been converted into kinetic energy,
5929-424: Is transformed to what other kind) is often determined by entropy (equal energy spread among all available degrees of freedom ) considerations. In practice all energy transformations are permitted on a small scale, but certain larger transformations are not permitted because it is statistically unlikely that energy or matter will randomly move into more concentrated forms or smaller spaces. Energy transformations in
6050-433: Is trapped in a system with zero momentum, where it can be weighed. It is also equivalent to mass, and this mass is always associated with it. Mass is also equivalent to a certain amount of energy, and likewise always appears associated with it, as described in mass–energy equivalence . The formula E = mc ², derived by Albert Einstein (1905) quantifies the relationship between relativistic mass and energy within
6171-679: The Archaic or Epic period ( c. 800–500 BC ), and the Classical period ( c. 500–300 BC ). Ancient Greek was the language of Homer and of fifth-century Athenian historians, playwrights, and philosophers . It has contributed many words to English vocabulary and has been a standard subject of study in educational institutions of the Western world since the Renaissance . This article primarily contains information about
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#17327689468356292-606: The Epic and Classical periods of the language, which are the best-attested periods and considered most typical of Ancient Greek. From the Hellenistic period ( c. 300 BC ), Ancient Greek was followed by Koine Greek , which is regarded as a separate historical stage, though its earliest form closely resembles Attic Greek , and its latest form approaches Medieval Greek . There were several regional dialects of Ancient Greek; Attic Greek developed into Koine. Ancient Greek
6413-493: The International System of Units (SI) is the joule (J). Forms of energy include the kinetic energy of a moving object, the potential energy stored by an object (for instance due to its position in a field ), the elastic energy stored in a solid object, chemical energy associated with chemical reactions , the radiant energy carried by electromagnetic radiation , the internal energy contained within
6534-501: The Pella curse tablet , as Hatzopoulos and other scholars note. Based on the conclusions drawn by several studies and findings such as Pella curse tablet , Emilio Crespo and other scholars suggest that ancient Macedonian was a Northwest Doric dialect , which shares isoglosses with its neighboring Thessalian dialects spoken in northeastern Thessaly . Some have also suggested an Aeolic Greek classification. The Lesbian dialect
6655-603: The epic poems , the Iliad and the Odyssey , and in later poems by other authors. Homeric Greek had significant differences in grammar and pronunciation from Classical Attic and other Classical-era dialects. The origins, early form and development of the Hellenic language family are not well understood because of a lack of contemporaneous evidence. Several theories exist about what Hellenic dialect groups may have existed between
6776-487: The gravitational collapse of supernovae to "store" energy in the creation of heavy isotopes (such as uranium and thorium ), and nuclear decay , a process in which energy is released that was originally stored in these heavy elements, before they were incorporated into the Solar System and the Earth. This energy is triggered and released in nuclear fission bombs or in civil nuclear power generation. Similarly, in
6897-558: The living force or vis viva . Willem 's Gravesande of the Netherlands provided experimental evidence of this relationship in 1722. By dropping weights from different heights into a block of clay, Gravesande determined that their penetration depth was proportional to the square of their impact speed. Émilie du Châtelet recognized the implications of the experiment and published an explanation. The terms kinetic energy and work in their present scientific meanings date back to
7018-416: The matter and antimatter (electrons and positrons) are destroyed and changed to non-matter (the photons). However, the total mass and total energy do not change during this interaction. The photons each have no rest mass but nonetheless have radiant energy which exhibits the same inertia as did the two original particles. This is a reversible process – the inverse process is called pair creation – in which
7139-524: The nuclear force or the weak force , among other examples. The word energy derives from the Ancient Greek : ἐνέργεια , romanized : energeia , lit. 'activity, operation', which possibly appears for the first time in the work of Aristotle in the 4th century BC. In contrast to the modern definition, energeia was a qualitative philosophical concept, broad enough to include ideas such as happiness and pleasure. In
7260-501: The present , future , and imperfect are imperfective in aspect; the aorist , present perfect , pluperfect and future perfect are perfective in aspect. Most tenses display all four moods and three voices, although there is no future subjunctive or imperative. Also, there is no imperfect subjunctive, optative or imperative. The infinitives and participles correspond to the finite combinations of tense, aspect, and voice. The indicative of past tenses adds (conceptually, at least)
7381-428: The speed of light . The adjective kinetic has its roots in the Greek word κίνησις kinesis , meaning "motion". The dichotomy between kinetic energy and potential energy can be traced back to Aristotle 's concepts of actuality and potentiality . The principle of classical mechanics that E ∝ mv is conserved was first developed by Gottfried Leibniz and Johann Bernoulli , who described kinetic energy as
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#17327689468357502-1031: The 5th century BC. Ancient pronunciation cannot be reconstructed with certainty, but Greek from the period is well documented, and there is little disagreement among linguists as to the general nature of the sounds that the letters represent. /oː/ raised to [uː] , probably by the 4th century BC. Greek, like all of the older Indo-European languages , is highly inflected. It is highly archaic in its preservation of Proto-Indo-European forms. In ancient Greek, nouns (including proper nouns) have five cases ( nominative , genitive , dative , accusative , and vocative ), three genders ( masculine , feminine , and neuter ), and three numbers (singular, dual , and plural ). Verbs have four moods ( indicative , imperative , subjunctive , and optative ) and three voices (active, middle, and passive ), as well as three persons (first, second, and third) and various other forms. Verbs are conjugated through seven combinations of tenses and aspect (generally simply called "tenses"):
7623-495: The Archaic period of ancient Greek (see Homeric Greek for more details): Μῆνιν ἄειδε, θεά, Πηληϊάδεω Ἀχιλῆος οὐλομένην, ἣ μυρί' Ἀχαιοῖς ἄλγε' ἔθηκε, πολλὰς δ' ἰφθίμους ψυχὰς Ἄϊδι προΐαψεν ἡρώων, αὐτοὺς δὲ ἑλώρια τεῦχε κύνεσσιν οἰωνοῖσί τε πᾶσι· Διὸς δ' ἐτελείετο βουλή· ἐξ οὗ δὴ τὰ πρῶτα διαστήτην ἐρίσαντε Ἀτρεΐδης τε ἄναξ ἀνδρῶν καὶ δῖος Ἀχιλλεύς. The beginning of Apology by Plato exemplifies Attic Greek from
7744-636: The Classical period of ancient Greek. (The second line is the IPA , the third is transliterated into the Latin alphabet using a modern version of the Erasmian scheme .) Ὅτι [hóti Hóti μὲν men mèn ὑμεῖς, hyːmêːs hūmeîs, 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 ,
7865-545: The Dorians. The Greeks of this period believed there were three major divisions of all Greek people – Dorians, Aeolians, and Ionians (including Athenians), each with their own defining and distinctive dialects. Allowing for their oversight of Arcadian, an obscure mountain dialect, and Cypriot, far from the center of Greek scholarship, this division of people and language is quite similar to the results of modern archaeological-linguistic investigation. One standard formulation for
7986-571: The Earth's gravitational field or elastic strain (mechanical potential energy) in rocks. Prior to this, they represent release of energy that has been stored in heavy atoms since the collapse of long-destroyed supernova stars (which created these atoms). In cosmology and astronomy the phenomena of stars , nova , supernova , quasars and gamma-ray bursts are the universe's highest-output energy transformations of matter. All stellar phenomena (including solar activity) are driven by various kinds of energy transformations. Energy in such transformations
8107-550: The aorist. Following Homer 's practice, the augment is sometimes not made in poetry , especially epic poetry. The augment sometimes substitutes for reduplication; see below. Almost all forms of the perfect, pluperfect, and future perfect reduplicate the initial syllable of the verb stem. (A few irregular forms of perfect do not reduplicate, whereas a handful of irregular aorists reduplicate.) The three types of reduplication are: Irregular duplication can be understood diachronically. For example, lambanō (root lab ) has
8228-419: The augment when it was word-initial. In verbs with a preposition as a prefix, the augment is placed not at the start of the word, but between the preposition and the original verb. For example, προσ(-)βάλλω (I attack) goes to προσ έ βαλoν in the aorist. However compound verbs consisting of a prefix that is not a preposition retain the augment at the start of the word: αὐτο(-)μολῶ goes to ηὐ τομόλησα in
8349-509: The ball. But, in the reference frame of the person swinging the bat, considerable work is done on the ball. The total energy of a system is sometimes called the Hamiltonian , after William Rowan Hamilton . The classical equations of motion can be written in terms of the Hamiltonian, even for highly complex or abstract systems. These classical equations have direct analogs in nonrelativistic quantum mechanics. Another energy-related concept
8470-447: The case of a chemical explosion , chemical potential energy is transformed to kinetic and thermal energy in a very short time. Yet another example is that of a pendulum . At its highest points the kinetic energy is zero and the gravitational potential energy is at its maximum. At its lowest point the kinetic energy is at its maximum and is equal to the decrease in potential energy . If one (unrealistically) assumes that there
8591-965: The case of animals. The daily 1500–2000 Calories (6–8 MJ) recommended for a human adult are taken as food molecules, mostly carbohydrates and fats, of which glucose (C 6 H 12 O 6 ) and stearin (C 57 H 110 O 6 ) are convenient examples. The food molecules are oxidized to carbon dioxide and water in the mitochondria C 6 H 12 O 6 + 6 O 2 ⟶ 6 CO 2 + 6 H 2 O {\displaystyle {\ce {C6H12O6 + 6O2 -> 6CO2 + 6H2O}}} C 57 H 110 O 6 + ( 81 1 2 ) O 2 ⟶ 57 CO 2 + 55 H 2 O {\displaystyle {\ce {C57H110O6 + (81 1/2) O2 -> 57CO2 + 55H2O}}} and some of
8712-480: The chosen reference frame. This is called the Oberth effect . But the total energy of the system, including kinetic energy, fuel chemical energy, heat, etc., is conserved over time, regardless of the choice of reference frame. Different observers moving with different reference frames would however disagree on the value of this conserved energy. The kinetic energy of such systems depends on the choice of reference frame:
8833-498: The complete conversion of matter (such as atoms) to non-matter (such as photons) is forbidden by conservation laws . Ancient Greek language Ancient Greek ( Ἑλληνῐκή , Hellēnikḗ ; [hellɛːnikɛ́ː] ) includes the forms of the Greek language used in ancient Greece and the ancient world from around 1500 BC to 300 BC. It is often roughly divided into the following periods: Mycenaean Greek ( c. 1400–1200 BC ), Dark Ages ( c. 1200–800 BC ),
8954-451: The complex organisms can occupy ecological niches that are not available to their simpler brethren. The conversion of a portion of the chemical energy to heat at each step in a metabolic pathway is the physical reason behind the pyramid of biomass observed in ecology . As an example, to take just the first step in the food chain : of the estimated 124.7 Pg/a of carbon that is fixed by photosynthesis , 64.3 Pg/a (52%) are used for
9075-553: The concept of special relativity. In different theoretical frameworks, similar formulas were derived by J.J. Thomson (1881), Henri Poincaré (1900), Friedrich Hasenöhrl (1904) and others (see Mass–energy equivalence#History for further information). Part of the rest energy (equivalent to rest mass) of matter may be converted to other forms of energy (still exhibiting mass), but neither energy nor mass can be destroyed; rather, both remain constant during any process. However, since c 2 {\displaystyle c^{2}}
9196-615: The dialect of Sparta ), and Northern Peloponnesus Doric (including Corinthian ). All the groups were represented by colonies beyond Greece proper as well, and these colonies generally developed local characteristics, often under the influence of settlers or neighbors speaking different Greek dialects. After the conquests of Alexander the Great in the late 4th century BC, a new international dialect known as Koine or Common Greek developed, largely based on Attic Greek , but with influence from other dialects. This dialect slowly replaced most of
9317-530: The dialects is: West vs. non-West Greek is the strongest-marked and earliest division, with non-West in subsets of Ionic-Attic (or Attic-Ionic) and Aeolic vs. Arcadocypriot, or Aeolic and Arcado-Cypriot vs. Ionic-Attic. Often non-West is called 'East Greek'. Arcadocypriot apparently descended more closely from the Mycenaean Greek of the Bronze Age. Boeotian Greek had come under
9438-510: The divergence of early Greek-like speech from the common Proto-Indo-European language and the Classical period. They have the same general outline but differ in some of the detail. The only attested dialect from this period is Mycenaean Greek , but its relationship to the historical dialects and the historical circumstances of the times imply that the overall groups already existed in some form. Scholars assume that major Ancient Greek period dialect groups developed not later than 1120 BC, at
9559-428: The early 19th century, and applies to any isolated system . It was argued for some years whether heat was a physical substance, dubbed the caloric , or merely a physical quantity, such as momentum . In 1845 James Prescott Joule discovered the link between mechanical work and the generation of heat. These developments led to the theory of conservation of energy, formalized largely by William Thomson ( Lord Kelvin ) as
9680-473: The energy is used to convert ADP into ATP : The rest of the chemical energy of the carbohydrate or fat are converted into heat: the ATP is used as a sort of "energy currency", and some of the chemical energy it contains is used for other metabolism when ATP reacts with OH groups and eventually splits into ADP and phosphate (at each stage of a metabolic pathway , some chemical energy is converted into heat). Only
9801-458: The energy of motion, but the process is not completely efficient and produces heat within the cyclist. The kinetic energy in the moving cyclist and the bicycle can be converted to other forms. For example, the cyclist could encounter a hill just high enough to coast up, so that the bicycle comes to a complete halt at the top. The kinetic energy has now largely been converted to gravitational potential energy that can be released by freewheeling down
9922-457: The energy stored during photosynthesis as heat or light may be triggered suddenly by a spark in a forest fire, or it may be made available more slowly for animal or human metabolism when organic molecules are ingested and catabolism is triggered by enzyme action. All living creatures rely on an external source of energy to be able to grow and reproduce – radiant energy from the Sun in the case of green plants and chemical energy (in some form) in
10043-437: The fact that the laws of physics do not change over time. Thus, since 1918, theorists have understood that the law of conservation of energy is the direct mathematical consequence of the translational symmetry of the quantity conjugate to energy, namely time. In the International System of Units (SI), the unit of energy is the joule . It is a derived unit that is equal to the energy expended, or work done, in applying
10164-435: The field itself. While these two categories are sufficient to describe all forms of energy, it is often convenient to refer to particular combinations of potential and kinetic energy as its own form. For example, the sum of translational and rotational kinetic and potential energy within a system is referred to as mechanical energy , whereas nuclear energy refers to the combined potentials within an atomic nucleus from either
10285-413: The field of thermodynamics . Thermodynamics aided the rapid development of explanations of chemical processes by Rudolf Clausius , Josiah Willard Gibbs , and Walther Nernst . It also led to a mathematical formulation of the concept of entropy by Clausius and to the introduction of laws of radiant energy by Jožef Stefan . According to Noether's theorem , the conservation of energy is a consequence of
10406-432: The formula 1 / 2 mv given by classical mechanics is suitable. However, if the speed of the object is comparable to the speed of light, relativistic effects become significant and the relativistic formula is used. If the object is on the atomic or sub-atomic scale , quantum mechanical effects are significant, and a quantum mechanical model must be employed. Treatments of kinetic energy depend upon
10527-399: The game of billiards , the player imposes kinetic energy on the cue ball by striking it with the cue stick. If the cue ball collides with another ball, it slows down dramatically, and the ball it hit accelerates as the kinetic energy is passed on to it. Collisions in billiards are effectively elastic collisions , in which kinetic energy is preserved. In inelastic collisions , kinetic energy
10648-413: The height) and E k = 1 2 m v 2 {\textstyle E_{k}={\frac {1}{2}}mv^{2}} (half mass times velocity squared). Then the total amount of energy can be found by adding E p + E k = E total {\displaystyle E_{p}+E_{k}=E_{\text{total}}} . Energy gives rise to weight when it
10769-439: The hill than without the generator because some of the energy has been diverted into electrical energy. Another possibility would be for the cyclist to apply the brakes, in which case the kinetic energy would be dissipated through friction as heat . Like any physical quantity that is a function of velocity, the kinetic energy of an object depends on the relationship between the object and the observer's frame of reference . Thus,
10890-467: The kinetic energy of a non-rotating object of mass m traveling at a speed v is 1 2 m v 2 {\textstyle {\frac {1}{2}}mv^{2}} . The kinetic energy of an object is equal to the work , force ( F ) times displacement ( s ), needed to achieve its stated velocity . Having gained this energy during its acceleration , the mass maintains this kinetic energy unless its speed changes. The same amount of work
11011-428: The kinetic energy of an 80 kg mass (about 180 lbs) traveling at 18 metres per second (about 40 mph, or 65 km/h) as When a person throws a ball, the person does work on it to give it speed as it leaves the hand. The moving ball can then hit something and push it, doing work on what it hits. The kinetic energy of a moving object is equal to the work required to bring it from rest to that speed, or
11132-445: The kinetic energy of an object is not invariant . Spacecraft use chemical energy to launch and gain considerable kinetic energy to reach orbital velocity . In an entirely circular orbit, this kinetic energy remains constant because there is almost no friction in near-earth space. However, it becomes apparent at re-entry when some of the kinetic energy is converted to heat. If the orbit is elliptical or hyperbolic , then throughout
11253-459: The late 17th century, Gottfried Leibniz proposed the idea of the Latin : vis viva , or living force, which defined as the product of the mass of an object and its velocity squared; he believed that total vis viva was conserved. To account for slowing due to friction, Leibniz theorized that thermal energy consisted of the motions of the constituent parts of matter, although it would be more than
11374-424: The mass equivalent of an everyday amount energy is minuscule, which is why a loss of energy (loss of mass) from most systems is difficult to measure on a weighing scale, unless the energy loss is very large. Examples of large transformations between rest energy (of matter) and other forms of energy (e.g., kinetic energy into particles with rest mass) are found in nuclear physics and particle physics . Often, however,
11495-472: The metabolism of green plants, i.e. reconverted into carbon dioxide and heat. In geology , continental drift , mountain ranges , volcanoes , and earthquakes are phenomena that can be explained in terms of energy transformations in the Earth's interior, while meteorological phenomena like wind, rain, hail , snow, lightning, tornadoes and hurricanes are all a result of energy transformations in our atmosphere brought about by solar energy . Sunlight
11616-496: The mid-19th century. Early understandings of these ideas can be attributed to Thomas Young , who in his 1802 lecture to the Royal Society, was the first to use the term energy to refer to kinetic energy in its modern sense, instead of vis viva . Gaspard-Gustave Coriolis published in 1829 the paper titled Du Calcul de l'Effet des Machines outlining the mathematics of kinetic energy. William Thomson , later Lord Kelvin,
11737-453: The molecular or atomic level, which may be regarded as kinetic energy, due to molecular translation, rotation, and vibration, electron translation and spin, and nuclear spin. These all contribute to the body's mass, as provided by the special theory of relativity. When discussing movements of a macroscopic body, the kinetic energy referred to is usually that of the macroscopic movement only. However, all internal energies of all types contribute to
11858-426: The molecules it is built from. The second law of thermodynamics states that energy (and matter) tends to become more evenly spread out across the universe: to concentrate energy (or matter) in one specific place, it is necessary to spread out a greater amount of energy (as heat) across the remainder of the universe ("the surroundings"). Simpler organisms can achieve higher energy efficiencies than more complex ones, but
11979-508: The older dialects, although the Doric dialect has survived in the Tsakonian language , which is spoken in the region of modern Sparta. Doric has also passed down its aorist terminations into most verbs of Demotic Greek . By about the 6th century AD, the Koine had slowly metamorphosed into Medieval Greek . Phrygian is an extinct Indo-European language of West and Central Anatolia , which
12100-411: The orbit kinetic and potential energy are exchanged; kinetic energy is greatest and potential energy lowest at closest approach to the earth or other massive body, while potential energy is greatest and kinetic energy the lowest at maximum distance. Disregarding loss or gain however, the sum of the kinetic and potential energy remains constant. Kinetic energy can be passed from one object to another. In
12221-412: The other side of the hill. Since the bicycle lost some of its energy to friction, it never regains all of its speed without additional pedaling. The energy is not destroyed; it has only been converted to another form by friction. Alternatively, the cyclist could connect a dynamo to one of the wheels and generate some electrical energy on the descent. The bicycle would be traveling slower at the bottom of
12342-487: The perfect stem eilēpha (not * lelēpha ) because it was originally slambanō , with perfect seslēpha , becoming eilēpha through compensatory lengthening. Reduplication is also visible in the present tense stems of certain verbs. These stems add a syllable consisting of the root's initial consonant followed by i . A nasal stop appears after the reduplication in some verbs. The earliest extant examples of ancient Greek writing ( c. 1450 BC ) are in
12463-409: The reference frame that gives the minimum value of that energy is the center of momentum frame, i.e. the reference frame in which the total momentum of the system is zero. This minimum kinetic energy contributes to the invariant mass of the system as a whole. The work W done by a force F on an object over a distance s parallel to F equals Using Newton's Second Law with m the mass and
12584-408: The relationship p = m v and the validity of Newton's Second Law . (However, also see the special relativistic derivation below .) Applying the product rule we see that: Therefore, (assuming constant mass so that dm = 0), we have, Since this is a total differential (that is, it only depends on the final state, not how the particle got there), we can integrate it and call
12705-526: The relative motion of the bodies in the system. For example, in the Solar System the planets and planetoids are orbiting the Sun. In a tank of gas, the molecules are moving in all directions. The kinetic energy of the system is the sum of the kinetic energies of the bodies it contains. A macroscopic body that is stationary (i.e. a reference frame has been chosen to correspond to the body's center of momentum ) may have various kinds of internal energy at
12826-434: The relative velocity of objects compared to the fixed speed of light . Speeds experienced directly by humans are non-relativisitic ; higher speeds require the theory of relativity . In classical mechanics , the kinetic energy of a point object (an object so small that its mass can be assumed to exist at one point), or a non-rotating rigid body depends on the mass of the body as well as its speed . The kinetic energy
12947-404: The rest mass of particles is created from the radiant energy of two (or more) annihilating photons. In general relativity, the stress–energy tensor serves as the source term for the gravitational field, in rough analogy to the way mass serves as the source term in the non-relativistic Newtonian approximation. Energy and mass are manifestations of one and the same underlying physical property of
13068-523: The result kinetic energy: This equation states that the kinetic energy ( E k ) is equal to the integral of the dot product of the momentum ( p ) of a body and the infinitesimal change of the velocity ( v ) of the body. It is assumed that the body starts with no kinetic energy when it is at rest (motionless). If a rigid body Q is rotating about any line through the center of mass then it has rotational kinetic energy ( E r {\displaystyle E_{\text{r}}\,} ) which
13189-474: The same total energy even in different forms) but its mass does decrease when the energy escapes out to its surroundings, largely as radiant energy . There are strict limits to how efficiently heat can be converted into work in a cyclic process, e.g. in a heat engine, as described by Carnot's theorem and the second law of thermodynamics . However, some energy transformations can be quite efficient. The direction of transformations in energy (what kind of energy
13310-466: The situation is the reverse. Chemical reactions are usually not possible unless the reactants surmount an energy barrier known as the activation energy . The speed of a chemical reaction (at a given temperature T ) is related to the activation energy E by the Boltzmann's population factor e; that is, the probability of a molecule to have energy greater than or equal to E at
13431-517: The syllabic script Linear B . Beginning in the 8th century BC, however, the Greek alphabet became standard, albeit with some variation among dialects. Early texts are written in boustrophedon style, but left-to-right became standard during the classic period. Modern editions of ancient Greek texts are usually written with accents and breathing marks , interword spacing , modern punctuation , and sometimes mixed case , but these were all introduced later. The beginning of Homer 's Iliad exemplifies
13552-467: The time of the Dorian invasions —and that their first appearances as precise alphabetic writing began in the 8th century BC. The invasion would not be "Dorian" unless the invaders had some cultural relationship to the historical Dorians . The invasion is known to have displaced population to the later Attic-Ionic regions, who regarded themselves as descendants of the population displaced by or contending with
13673-420: The total energy of the substances involved. Some energy may be transferred between the surroundings and the reactants in the form of heat or light; thus the products of a reaction have sometimes more but usually less energy than the reactants. A reaction is said to be exothermic or exergonic if the final state is lower on the energy scale than the initial state; in the less common case of endothermic reactions
13794-406: The unit of measure, discovered that the gravitational potential energy lost by a descending weight attached via a string was equal to the internal energy gained by the water through friction with the paddle. In classical mechanics, energy is a conceptually and mathematically useful property, as it is a conserved quantity . Several formulations of mechanics have been developed using energy as
13915-421: The universe cooled too rapidly for hydrogen to completely fuse into heavier elements. This meant that hydrogen represents a store of potential energy that can be released by fusion. Such a fusion process is triggered by heat and pressure generated from gravitational collapse of hydrogen clouds when they produce stars, and some of the fusion energy is then transformed into sunlight. In quantum mechanics , energy
14036-401: The universe over time are characterized by various kinds of potential energy, that has been available since the Big Bang , being "released" (transformed to more active types of energy such as kinetic or radiant energy) when a triggering mechanism is available. Familiar examples of such processes include nucleosynthesis , a process ultimately using the gravitational potential energy released from
14157-434: The work the object can do while being brought to rest: net force × displacement = kinetic energy , i.e., Since the kinetic energy increases with the square of the speed, an object doubling its speed has four times as much kinetic energy. For example, a car traveling twice as fast as another requires four times as much distance to stop, assuming a constant braking force. As a consequence of this quadrupling, it takes four times
14278-435: The work to double the speed. The kinetic energy of an object is related to its momentum by the equation: where: For the translational kinetic energy, that is the kinetic energy associated with rectilinear motion , of a rigid body with constant mass m {\displaystyle m} , whose center of mass is moving in a straight line with speed v {\displaystyle v} , as seen above
14399-480: Was Aeolic. For example, fragments of the works of the poet Sappho from the island of Lesbos are in Aeolian. Most of the dialect sub-groups listed above had further subdivisions, generally equivalent to a city-state and its surrounding territory, or to an island. Doric notably had several intermediate divisions as well, into Island Doric (including Cretan Doric ), Southern Peloponnesus Doric (including Laconian ,
14520-452: Was a pluricentric language , divided into many dialects. The main dialect groups are Attic and Ionic , Aeolic , Arcadocypriot , and Doric , many of them with several subdivisions. Some dialects are found in standardized literary forms in literature , while others are attested only in inscriptions. There are also several historical forms. Homeric Greek is a literary form of Archaic Greek (derived primarily from Ionic and Aeolic) used in
14641-408: Was distinct from momentum , and which would later be called "energy". In 1807, Thomas Young was possibly the first to use the term "energy" instead of vis viva , in its modern sense. Gustave-Gaspard Coriolis described " kinetic energy " in 1829 in its modern sense, and in 1853, William Rankine coined the term " potential energy ". The law of conservation of energy was also first postulated in
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