Energy – The Physics Hypertextbook (2023)



A system possesses energy if it has the ability to do work.

Energy is transferred or transformed whenever work is done..

(Video) Modern Physics Lesson 1

Energy is…

  • a scalar quantity
  • abstract and cannot always be perceived
  • given meaning through calculation
  • a central concept in science

Energy can exist in many different forms. All forms of energy are either kinetic or potential. The energy associated with motion is called kineticenergy. The energy associated with position is called potentialenergy. Potential energy is not "stored energy". Energy can be stored in motion just as well as it can be stored in position. Is kinetic energy "used up energy"?

kinetic energy

  • kinetic energy — motion
    • mechanical energy — motion of macroscopic systems
      • machines
      • wind energy
      • wave energy
      • sound (sonic, acoustic) energy
    • thermal energy — motion of particles of matter
      • geothermal energy
    • electric energy — motion of charges
      • household current
      • lightning
    • electromagnetic radiation — disturbance of electric and magnetic fields (classical physics) or the motion of photons (quantum physics)
      • radio, microwaves, infrared, light, ultraviolet, x-rays, gamma rays
      • solar energy
Types of kinetic energy (classified by type of object)
typemotionexamples and subtypes
motion of macroscopic objectsmachines, muscles, projectiles, wind, flowing water, ocean waves, sound, …
random motion of microscopic particles of matter (molecules, atoms, ions)heat, fire, geothermal, …
bulk flow of charges (electrons, protons, ions)household current, AC and DC circuits, lightning, …
disturbance propagating through electric and magnetic fields (classical physics) or the motion of photons (modern physics)radio waves, microwaves, infrared, light, ultraviolet, x-rays, gamma rays

potential energy

  • potential energy — position or arrangement
    • gravitational potential energy
      • roller coaster
      • waterwheel
      • hydroelectric power
    • electromagnetic potential energy
      • electric potential energy
      • magnetic potential energy
      • chemical potential energy
      • elastic potential energy
    • strong nuclear potential energy
      • nuclear power
      • nuclear weapons
    • weak nuclear potential energy
      • radioactive decay
Types of potential energy (classifiedbytypeoffield)
force fieldquantity infieldexamples and subtypes
gravita­tionalmassroller coaster, waterwheel,
hydroelectric reservoir, …
electro­magneticchargeelectric, magnetic,
chemical, elastic, …
strong nuclearcolornuclear reactors,
nuclear weapons, …
weak nuclearflavorradioactive decay,
the first step in solar fusion, …



(Video) i made one drop of water 1,000,000x hotter than the sun and this happened

English brewer and scientist James Joule (1818–1889) who determined the mechanical equivalent of heat.


Approximate energy of selected events (smallesttolargest)
energy(J)typedevice, event, phenomenon, process
650×10−9kineticfalling snowflake
85×10−6kineticfalling raindrop
3–12gravitationalan apple in a tree
51kineticmost energetic cosmic ray
60×103heatmaking a cup of coffee or tea
270×103chemicalan apple in the digestive tract
390×103kineticcar driving at freeway speed
1.4×106electricaltelevision running for four hours
2×106chemicalstick of dynamite
3.8×109chemicalfood for one person for one year
4.184×109chemicalton of TNT, by definition
63×1012nuclearHiroshima atomic bomb (Little Boy, 1945)
1.8×1015kineticChelyabinsk meteor impact (2013)
42×1015kineticTunguska meteor impact (1908)
240×1015nuclearLargest nuclear bomb tested (Tsar Bomba, 1961)
21×1018electricalone year of operation of Google (2017)
37×1018electricalone year of Bitcoin mining (2017)


For those who want some proof that physicists are human, the proof is is the idiocy of all the different units which they use for measuring energy.

(Video) Atomic Orbitals, Visualized Dynamically

Richard Feynman, 1965 (paid link)

Energy units discussed in this book*The kilocalorie is also known as the kilogramcalorie, dieteticcalorie, foodcalorie, and Calorie (with an uppercase "C"). Btu is the abbreviation for "British thermal unit". Quad is the shortened form of "quadrillion Btu". §Exact by definition.
in this
foot pound1.355818J"
watt second1Jpower
watt hour3.6kJ3,600Ws"
kilowatt hour3.6MJ1,000Wh"
therm­ochemical calorie4.184J§heat
Inter­national Table calorie4.1868J§"
kilocalorie*1,000 calorie"
thermo­chemical Btu1.054350kJ"
therm105.4350MJ100,000 Btu"
Inter­national Table Btu1.05505585262kJ§"
cubic meter natural gas37~39MJchemical
ton of oil equivalent41~45GJ"
ton of coal equivalent~29.3GJ"
ton of TNT4.184GJ§"

Atomic and nuclear units

Energy equivalents from atomic and nuclearphysicsNote:All values are exact by definition or calculation except for the atomic mass unit which is accurate to the number of digits displayed.Symbols:c=speed of light in avacuum,k=Boltzmannconstant,e=elementarycharge,mu=atomicmassunit,h=Planckconstant,R=Rydbergconstant
unit (symbol)joule equivalent
atomic mass unit(u)muc2=1.492418086×10−10J
electronvolt (eV)e=1.602176634×10−19J
hartree (Eh)2Rhc=4.35974381×10−18J
inverse meter(m−1)hc=1.986445857×10−25J
inverse second(s−1)h=6.62607015×10−34J
kelvin (K)k=1.380649×10−23J
kilogram (kg)c2=89,875,517,873,681,764J


Another scheme

(Video) Matt Cinker and Miles Miller Senario

  • solar
    • sunshine
    • wind
    • ocean currents
    • ocean thermal temperature gradients
    • biomass
      • food
      • wood/charcoal
      • dung
    • fossil fuels
      • coal
      • petroleum
      • natural gas
  • everything else
    • geothermal
    • tidal
    • nuclear

Historical Notes

  • Aristotle of Stagira (384–322 BCE) Greece: first use of the word energeia (ενεργεια) in the Nicomachean Ethics. Its contemporary meaning has diverged significantly from Aristotle's original meaning. Aristotle's sense of the word is often translated as "activity" or "being at work". Energeia literally means "in work" or "to contain work", en+ergon (εν+εργον). In the Nicomachean Ethics, energeia was contrasted with hexis (εξις), which meant to "possess" or "to be in the state of". Energeia meant doing. Hexis meant possessing. Aristotle argues that virtue stems from actions and not merely from existence. These are terms of ethical philosophy, not science.
Τοῖς μὲν οὖν λέγουσι τὴν ἀρετὴν ἢ ἀρετήν τινα συνῳδός ἐστιν ὁ λόγος· ταύτης γάρ ἐστιν ἡ κατ᾽ αὐτὴν ἐνέργεια. διαφέρει δὲ ἴσως οὐ μικρὸν ἐν κτήσει ἢ χρήσει τὸ ἄριστον ὑπολαμβάνειν, καὶ ἐν ἕξει ἢ ἐνεργείᾳ. τὴν μὲν γὰρ ἕξιν ἐνδέχεται μηδὲν ἀγαθὸν ἀποτελεῖν ὑπάρχουσαν, οἷον τῷ καθεύδοντι ἢ καὶ ἄλλως πως ἐξηργηκότι, τὴν δ᾽ ἐνέργειαν οὐχ οἷόν τε· πράξει γὰρ ἐξ ἀνάγκης, καὶ εὖ πράξει. ὥσπερ δ᾽ Ὀλυμπίασιν οὐχ οἱ κάλλιστοι καὶ ἰσχυρότατοι στεφανοῦνται ἀλλ᾽ οἱ ἀγωνιζόμενοι (τούτων γάρ τινες νικῶσιν), οὕτω καὶ τῶν ἐν τῷ βίῳ καλῶν κἀγαθῶν οἱ πράττοντες ὀρθῶς ἐπήβολοι γίνονται.With those who identify happiness with virtue or some one virtue our account is in harmony; for to virtue belongs virtuous activity. But it makes, perhaps, no small difference whether we place the chief good in possession or in use, in state of mind or in activity. For the state of mind may exist without producing any good result, as in a man who is asleep or in some other way quite inactive, but the activity cannot; for one who has the activity will of necessity be acting, and acting well. And as in the Olympic Games it is not the most beautiful and the strongest that are crowned but those who compete (for it is some of these that are victorious), so those who act win, and rightly win, the noble and good things in life.
Aristotle, ca. 320 BCE
  • Dead force vis mortua.
  • 1669 Dutch physicist Christiaan Huygens, vis viva or living force is conserved in perfectly elastic collistions
  • 1689 German mathematician Gottfried Leibniz defined vis viva as mass times the square of velocity
  • Émilie du Châtelet (1706–1749) France along with Voltaire (1694–1778) France.
  • 1811 Italian mathematician Joseph Lagrange used calculus to show that a factor of two is involved in the relationship "potential" (potential energy) and vis viva (kinetic energy). As defined via the symbols used by Lagrange, i.e. T as kinetic energy, in his 1788 Analytical Mechanics
  • Thomas Young (1773–1829) England: first use of the word energy in the modern sense. His definition is almost the same as our current definition of kinetic energy. He's missing a one-half multiplier out front that makes the energies intercovertable. A Course of Lectures on Natural Philosophy and the Mechanical Arts. London: J. Johnson (1807).
    • "Hence is derived the idea conveyed by the term living or ascending force; for since the height to which a body will rise perpendicularly, is as the square of its velocity, it will preserve a tendency to rise to a height which is as the square of its velocity whatever may be the path into which it is directed, provided that it meet with no abrupt angle, or that it rebound at each angle in a new direction without losing any velocity. The same idea is somewhat more concisely expressed by the term energy, which indicates the tendency of a body to ascend or to penetrate to a certain distance, in opposition to a retarding force." Lecture V. On Confined Motion.
    • "The term energy may be applied, with great propriety, to the product of the mass or weight of a body, into the square of the number expressing its velocity." Lecture VIII. On Collision.
  • Carnot, changed his mind from the caloric to dynamic theory of heat but dies before he was recognised
  • Coriolis, (re)defined work, travail, used calculus to propery derive KE as 1/2mv2, work equals change in energy, Du calcul d l'effet des machines.
  • Joule, mechanical equivalent of heat
  • William Thomson, Lord Kelvin (1824–1907) Ireland-Scotland replaced "actual" with "kinetic", but no one has dared replace "potential" with something better, so we're stuck with it. Kelvin originally proposed the terms dynamical and statical. On a universal tendency in nature to the dissipation of mechanical energy. William Thomson. Philosophical Magazine Series 4. Vol. 4 No. 25 (1852): 304–306.
    • "The object of the present communication is to call attention to the remarkable consequences which follow from Carnot's proposition, established as it is on a new foundation, in the dynamical theory of heat; that there is an absolute waste of mechanical energy available to man, when heat is allowed to pass from one body to another at a lower temperature, by any means not fulfilling his criterion of a "perfect thermo dynamic engine". As it is most certain that Creative Power alone can either call into existence or annihilate mechanical energy, the "waste" referred to cannot be annihilation, but must be some transformation of energy. To explain the nature of this transformation, it is convenient, in the first place, to divide stores of mechanical energy into two classes — statical and dynamical. A quantity of weights at a height, ready to descend and do work when wanted, an electrified body, a quantity of fuel, contain stores of mechanical energy of the statical kind. Masses of matter in motion, a volume of space through which undulations of light or radiant heat are passing a body having thermal motions among its particles (that is not infinitely cold), contain stores of mechanical energy of the dynamical kind."
    William Rankine (1820–1872) Scotland: first mention of "potential energy" as distinguished from "actual energy". Since kinetic energy was the first form identified, he attached a modifier to the form of energy he discovered. Thus the unfortunate notion that kinetic energy is actual energy and potential energy is energy that has the potential to be actual energy. Energy is energy. No form of energy is any more or less "actual" than any other. The unfortunate terminology is due to Aristotle who applied the dichotomous terms potentiality and actuality to several disciplines — motion (Physics, Physica, Τα Φυσικη), causality (Metaphysics, Metaphysica, Τα Μετά Τα Φυσικά), ethics (Nicomachean Ethics, Ethica Nicomachea, Ηθικά Νικομάχεια), and physiology (On the Soul, De Anima, Περὶ Ψυχῆς). Philosophy is not science (although there is such a thing as philiosophy of science). Science should always strive to describe reality as close as possible when it relies on words to do so. Grand philosophical modes of organization may be used to some extent, but they shouldn't override the physical reality. On the general law of the transformation of energy. William John Macquorn Rankine. Philosophical Magazine Series 4. Vol. 5 No. 30 (1853): 106–117.
    • "Actual, or Sensible Energy, is a measurable, transmissible, and transformable condition, whose presence causes a substance to tend to change its state in one or more respects. By the occurrence of such changes, actual energy disappears, and is replaced by Potential or Latent Energy; which is measured by the product of a change of state into the resistance against which that change is made. (The vis viva of matter in motion, thermometric heat, radiant heat, light, chemical action, and electric currents, are forms of actual energy; amongst those of potential energy are the mechanical powers of gravitation, elasticity, chemical affinity, statical electricity, and magnetism). The law of the Conservation of Energy is already known—viz., that the sum of all the energies of the universe, actual and potential, is unchangeable. The object of the present paper is to investigate the law according to which all transformations of energy, between the actual and potential forms, take place."
  • 1855 potential and kinetic?
  • The term "kinetic energy" first appeared in an article by Kelvin (then William Thomson) and Peter Tait in the magazine Good Words — a magazine with a largely religious readership. Thomson incorporated several quotations from the King James Version of the Bible. Energy. William Thomson and Peter Guthrie Tait. Good Words (1862): 601–607.
    • When an eight-day clock has been wound up, it is thereby enabled to go for a week in spite of friction and the resistance which the air at every instant offers to the pendulum. It has got what in scientific language we call a supply of Energy. In this ense the energy simply consists in the fact of a mass of lead being suspended some four feet or so above the bottom of the clock-case. The mere fact of its being in that position gives it a power of "doing work" which it would not possess if lying on the ground. This is called Potential Energy.
    • A 64 lb. shot, fired vertically from a gun loaded with an ordinary service charge of powder, would, if unresisted by the air, rise to about 35,000 feet, and if seizeed and secured at the highest point of its course, would possess there, in virtue of its position, a potential energy of 2,240,000 foot-pounds. When it left the gun it had none of this, but it was moving at the rate of fifteen hundred feet per second. It had KINETIC or (as it has sometimes been called) actual energy. We prefer the first term, which indicates motion as the form in which the energy is displayed. Kinetic energy depends on motion; and observation shows that its amount in each case is calculable from the mass which moves and the velocity with which it moves.


How do you solve energy problems in physics? ›

Potential energy is that pe graph is equal to mass times g times the height g here is 9.8 newtons

What is energy in physics formula? ›

Overview of Work, Energy and Power
What is Work, Energy and Power?
DefinitionEnergy is defined as the capacity to do work.
FormulaThe energy stored in an object due to its position and height is known as potential energy and is given by the formula: P.E. = mgh
8 more rows

How do we calculate energy? ›

As every engineer knows, energy calculation is straightforward. The unit of electrical energy is the kilowatt-hour (kWh), found by multiplying the power use (in kilowatts, kW) by the number of hours during which the power is consumed. Multiply that value by the cost per kWh, and you have the total energy cost.

What is energy in physics class 9? ›

Energy : The energy may be defined as the capacity of a body to do work. – The SI unit of energy is joule (J). or 1 kJ = 1000 J. Forms of energy : The various forms include potential energy, kinetic energy, heat energy, chemical energy, and light energy.

What are the 3 formulas for work? ›

Work formula is used to compute work done, force or displacement in any problem.
W= F × d × cos\theta.
WIt is the work done by the force.
FF is the force applied.
dIt is the displacement caused by the force
\thetaIt is the angle between the force vector and the displacement vector.

How do you calculate work energy and power? ›

use the following equations:
  1. work done = force × distance moved in direction of force.
  2. change in gravitational energy = mgh.
  3. power = work donetime taken, power = rate of energy transfer.
  4. power = force × velocity.
  5. efficiency = useful energy transferredtotal work done × 100 %


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