{Energy

Prepared By Engr. Ahmad Sameer Nawab Kardan University Kabul, Afghanistan

Thomas Young – the first to use the term "energy" in the modern sense. The concept of energy emerged out of the idea of vis viva (living force),

which Gottfried Leibniz 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 random motion of the constituent parts of matter, a view shared by Isaac Newton, although it would be more than a century until this was generally accepted. 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". It was argued for some years whether energy was a substance (the caloric) or merely a physical quantity, such as momentum.

History

There is a fact, or if you wish, a law, governing all natural phenomena that are known to date. There is no known exception to this law—it is exact so far as we know. The law is called the conservation of energy. It states that there is a certain quantity, which we call energy, that does not change in manifold changes which nature undergoes. That is a most abstract idea, because it is a mathematical principle; it says that there is a numerical quantity which does not change when something happens. It is not a description of a mechanism, or anything concrete; it is just a strange fact that we can calculate some number and when we finish watching nature go through her tricks and calculate the number again, it is the same.

—The Feynman Lectures on Physics Since 1918 it has been known that the law of conservation of energy is the

direct mathematical consequence of the translational symmetry of the quantity conjugate to energy, namely time. That is, energy is conserved because the laws of physics do not distinguish between different instants of time (see Noether's theorem).

William Thomson (Lord Kelvin) amalgamated all of these laws into the laws of thermodynamics, which aided in 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.

During a 1961 lecture.for undergraduate students at the California Institute of Technology, Richard Feynman, a celebrated physics teacher and Nobel Laureate, said this about the concept of energy:

History

In Physics, energy (Ancient Greek)ἐνέργεια Engergia ("activity, operation") is an indirectly observed quantity that is often understood as the ability of a Physical Systdem to do Work on other physical systems.

Since work is defined as a Force acting through a distance (a length of space), energy is always equivalent to the ability to exert pulls or pushes against the basic forces of nature, along a path of a certain length.

The total energy contained in an object is identified with its Mass, and energy (like mass), cannot be created or destroyed. When Matter (ordinary material particles) is changed into energy (such as energy of motion, or into radiation), the mass of the system does not change through the transformation process.

Energy, like mass, is a Scalar physical quantity International System OF Units (SI), energy is measured in Joules, but in many fields other units, such as kilowatt-hours and kilocalories, are customary. All of these units translate to units of work, which is always defined in terms of forces and the distances that the forces act through.

What IS Energy

A system can transfer energy to another system by simply transferring matter to it (since matter is equivalent to energy, in accordance with its mass). However, when energy is transferred by means other than matter-transfer, the transfer produces changes in the second system, as a result of work done on it.

This work manifests itself as the effect of force(s) applied through distances within the target system. For example, a system can emit energy to another by transferring (radiating) electromagnetic energy, but this creates forces upon the particles that absorb the radiation.

Similarly, a system may transfer energy to another by physically impacting it, but in that case the energy of motion in an object, called kinetic energy, results in forces acting over distances (new energy) to appear in another object that is struck.

Transfer of thermal energy by heat occurs by both of these mechanisms: heat can be transferred by electromagnetic radiation, or by physical contact in which direct particle-particle impacts transfer kinetic energy.

Transformation OF Energy

The energy "stored" by force-fields and particles that have been forced into a new physical configuration in the field by doing work on them by another system, is referred to as potential energy. A simple example of potential energy is the work needed to lift an object in a gravity field, up to a support. Each of the basic forces of nature is associated with a different type of potential energy, and all types of potential energy (like all other types of energy) appears as system mass, whenever present. For example, a compressed spring will be slightly more massive than before it was compressed. Likewise, whenever energy is transferred between systems by any mechanism, an associated mass is transferred with it.

Any form of energy may be transformed into another form. For example, all types of potential energy are converted into kinetic energy when the objects are given freedom to move to different position (as for example, when an object falls off a support). When energy is in a form other than thermal energy, it may be transformed with good or even perfect efficiency, to any other type of energy, including electricity or production of new particles of matter. With thermal energy, however, there are often limits to the efficiency of the conversion to other forms of energy, as described by the second law of thermodynamics.

Transformation OF Energy

In all such energy transformation processes, the total energy remains the same, and a transfer of energy from one system to another, results in a loss to compensate for any gain. This principle, the conservation of energy, was first postulated in the early 19th century, and applies to any isolated system. According to Noether's theorem, the conservation of energy is a consequence of the fact that the laws of physics do not change over time.

Although the total energy of a system does not change with time, its value may depend on the frame of reference. For example, a seated passenger in a moving airplane has zero kinetic energy relative to the airplane, but non-zero kinetic energy (and higher total energy) relative to the Earth.

Energy gives rise to weight when it 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 = mc², derived by Albert Einstein (1905) quantifies the relationship between rest-mass and rest-energy within 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

Transformation OF Energy

In the context of physical sciences, several forms of energy have been defined. These include:

Thermal energy, thermal energy in transit is called heat Chemical energy Electric energy Radiant energy, the energy of electromagnetic radiation Nuclear energy Magnetic energy Elastic energy Sound energy Mechanical energy Luminous energy Mass (E=mc²) These forms of energy may be divided into two main groups; kinetic

energy and potential energy. Other familiar types of energy are a varying mix of both potential and kinetic energy.

Energy may be transformed between these forms, some with 100% energy conversion efficiency and others with less. Items that transform between these forms are called transducers.

The above list of the known possible forms of energy is not necessarily complete. Whenever physical scientists discover that a certain phenomenon appears to violate the law of energy conservation, new forms may be added, as is the case with dark energy, a hypothetical form of energy that permeates all of space and tends to increase the rate of expansion of the universe.

Forms OF Energy

Classical mechanics distinguishes between potential energy, which is a function of the position of an object, and kinetic energy, which is a function of its movement. Both position and movement are relative to a frame of reference, which must be specified: this is often (and originally) an arbitrary fixed point on the surface of the Earth, the terrestrial frame of reference. It has been attempted to categorize all forms of energy as either kinetic or potential: this is not incorrect, but neither is it clear that it is a real simplification, as Feynman points out:

These notions of potential and kinetic energy depend on a notion of length scale. For example, one can speak of macroscopic potential and kinetic energy, which do not include thermal potential and kinetic energy. Also what is called chemical potential energy is a macroscopic notion, and closer examination shows that it is really the sum of the potential and kinetic energy on the atomic and subatomic scale. Similar remarks apply to nuclear "potential" energy and most other forms of energy. This dependence on length scale is non-problematic if the various length scales are decoupled, as is often the case ... but confusion can arise when different length scales are coupled, for instance when friction converts macroscopic work into microscopic thermal energy.

Forms OF Energy

Imperial system Before SI units were widely adopted around the world, the British systems of English units and

later imperial units were used in Britain, the Commonwealth and the United States. The system came to be known as United States customary units in the United States and is still in use there and in a few Caribbean countries. These various systems of measurement have at times been called foot-pound-second systems after the Imperial units for length, weight and time even though the tons, hundredweights, gallons, and nautical miles, for example, are different for the U.S. units. Many Imperial units remain in use in Britain which has officially partially switched to the SI system. Road signs are still in miles, yards, miles per hour; milk, beer and cider are sold by the pint; people measure their height in feet and inches and their weight in stone and pounds, to give just a few examples. Imperial units are used in many other places, for example, in many Commonwealth countries that are considered metricated, land area is measured in acres and floor space in square feet, particularly for commercial transactions (rather than government statistics). Similarly, gasoline is sold by the gallon in many countries that are considered metricated.

Metric system The metric system is a decimal system of measurement based on its units for length, the metre

and for mass, the kilogram. It exists in several variations, with different choices of base units, though these do not affect its day-to-day use. Since the 1960s, the International System of Units (SI) is the internationally recognized metric system. Metric units of mass, length, and electricity are widely used around the world for both everyday and scientific purposes.

The metric system features a single base unit for many physical quantities. Other quantities are derived from the standard SI units. Multiples and fractions of the units are expressed as Powers of 10 of each unit. Unit conversions are always simple because they are in the ratio of ten, one hundred, one thousand, etc., so that convenient magnitudes for measurements are achieved by simply moving the decimal place: 1.234 metres is 1234 millimetres or 0.001234 kilometres. The use of fractions, such as 2/5 of a metre, is not prohibited, but uncommon. All lengths and distances, for example, are measured in metres, or thousandths of a metre (millimetres), or thousands of metres (kilometres). There is no profusion of different units with different conversion factors as in the Imperial system which uses, for example, inches, feet, yards, fathoms, rods.

Units And Measurements

The International System of Units (abbreviated as SI from the French language name Système International d'Unités) is the modern revision of the metric system. It is the world's most widely used system of units, both in everyday commerce and in science. The SI was developed in 1960 from the metre-kilogram-second (MKS) system, rather than the centimetre-gram-second (CGS) system, which, in turn, had many variants. During its development the SI also introduced several newly named units that were previously not a part of the metric system. The original SI units for the six basic physical quantities were:

Units And Measurements

Unit Abbreviation Quantity measured

Metre m length

second s time

kilogram kg mass

ampere A electric current

kelvin Kthermodynamic temperature

candela cd luminous intensity

Because energy is defined via work, the SI unit for energy is the same as the unit of work – the joule (J), named in honor of James Prescott Joule and his experiments on the mechanical equivalent of heat. In slightly more fundamental terms, 1 joule is equal to 1 newton-metre and, in terms of SI base units:

An energy unit that is used in atomic physics, particle physics and high energy physics is the electronvolt (eV). One EV  is equivalent to 1.60217653×10−19 J. In spectroscopy the unit cm−1 = 0.000123986 EV is used to represent energy since energy is inversely proportional to wavelength from the equation .

In discussions of energy production and consumption, the units barrel of oil equivalent and ton of oil equivalent are often used.

When discussing amounts of energy released in explosions or bolide impact events, the TNT equivalent unit is often used. 1 ton of TNT equivalent is equal to 4.2 × 109 joules. Therefore, 1 kt TNT is 4.2 × 1012 joules, and 1 Mt TNT is 4.2 × 1015 joules.

Note that torque, the "rotational force" or "angular force" which causes a change in rotational motion is typically expressed in newton-metres. This is not a simple coincidence: a torque of 1 newton-metre applied on 1 radian requires exactly 1 newton-metre = 1 joule of energy.

Units And Measurements

The mole, the unit of amount of substance, was subsequently added to this list and the degree Kelvin renamed the kelvin.

There are two types of SI units, base units and derived units. Base units are the simple measurements for time, length, mass, temperature, amount of substance, electric current and light intensity. Derived units are constructed from the base units, for example, the watt, i.e. the unit for power, is defined from the base units as m2·kg·s−3. Other physical properties may be measured in compound units, such as material density, measured in kg·m-3.

Units And Measurements

In cgs units, one erg is 1 gcm2 s−2, equal to 1.0×10−7 J. US units The imperial/U.S. units for both energy and work include the foot-pound force (1.3558 J),

the British thermal unit (Btu) which has various values in the region of 1055 J, and the horsepower-hour (2.6845 MJ).

Electricity The energy unit used for everyday electricity, particularly for utility bills, is the kilowatt-

hour (kWh), and one kWh is equivalent to 3.6×106 J  (3600 kJ or 3.6 MJ). Electricity usage is often given in units of kilowatt-hours per year (kWh/yr). This is actually a measurement of average power consumption, i.e., the average rate at which energy is transferred.

Food industry The calorie equals the amount of thermal energy necessary to raise the temperature of

one gram of water by 1 Celsius degree, at a pressure of 1 atm. For thermochemistry a calorie of 4.184 J is used, but other calories have also been defined, such as the International Steam Table calorie of 4.1868 J. Food energy is measured in large calories or kilocalories, often simply written capitalized as "Calories" (= 103 calories).

Atom physics and chemistry In physics and chemistry, it is still common to measure energy on the atomic scale in the

non-SI, but convenient, units electronvolts (eV). The Hartree (the atomic unit of energy) is commonly used in calculations. Historically Rydberg units have been used.

Other Units Of Energy

Spectroscopy In spectroscopy and related fields it is common to measure energy

levels in units of reciprocal centimetres. These units (cm−1) are strictly speaking not energy units but units proportional to energies, with hc being the proportionality constant.

Explosions A gram of TNT releases 980–1100 calories upon explosion. To define

the tonne of TNT, this was arbitrarily standardized by letting 1000 thermochemical calories = 1 gram TNT = 4184 J (exactly).

Other Units Of Energy

When calculating kinetic energy (work to accelerate a mass 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 mass energy - energy which every mass must possess even when being at rest. The amount of energy is directly proportional to the mass of body: Where m is the mass, c is the speed of light in vacuum, E is the rest mass energy. For example, consider electron-positron annihilation, in which the rest mass of individual

particles is destroyed, but the inertia equivalent of the system of the two particles (its invariant mass) remains (since all energy is associated with mass), and this inertia and invariant mass is carried off by photons which individually are massless, but as a system retain their mass. This is a reversible process - the inverse process is called pair creation - in which the rest mass of particles is created from energy of two (or more) annihilating photons. In this system the matter (electrons and positrons) is destroyed and changed to non-matter energy (the photons). However, the total system mass and energy do not change during this interaction.

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.

It is not uncommon to hear that energy is "equivalent" to mass. It would be more accurate to state that every energy has an inertia and gravity equivalent, and because mass is a form of energy, then mass too has inertia and gravity associated with it.

Relativity

Any living organism relies on an external source of energy—radiation from the Sun in the case of green plants; chemical energy in some form in the case of animals—to be able to grow and reproduce. The daily 1500–2000 Calories (6–8 MJ) recommended for a human adult are taken as a combination of oxygen and food molecules, the latter mostly carbohydrates and fats, of which glucose (C6H12O6) and stearin (C57H110O6) are convenient examples. The food molecules are oxidised to carbon dioxide and water in the mitochondria

C6H12O6 + 6O2 → 6CO2 + 6H2O C57H110O6 + 81.5O2 → 57CO2 + 55H2O and some of the energy is used to convert ADP into ATP ADP + HPO4

2− → ATP + H2O The rest of the chemical energy in the carbohydrate or fat is converted into heat: the ATP is used as a sort

of "energy currency", and some of the chemical energy it contains when split and reacted with water, is used for other metabolism (at each stage of a metabolic pathway, some chemical energy is converted into heat). Only a tiny fraction of the original chemical energy is used for work:[18]

gain in kinetic energy of a sprinter during a 100 m race: 4 kJ gain in gravitational potential energy of a 150 kg weight lifted through 2 metres: 3kJ Daily food intake of a normal adult: 6–8 MJ It would appear that living organisms are remarkably inefficient (in the physical sense) in their use of the

energy they receive (chemical energy or radiation), and it is true that most real 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 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 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: 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 the metabolism of green plants, i.e. reconverted into carbon dioxide and heat.

Energy And Life

Energy density is a term used for the amount of useful energy stored in a given system or region of space per unit volume.

For fuels, the energy per unit volume is sometimes a useful parameter. In a few applications, comparing, for example, the effectiveness of hydrogen fuel to gasoline it turns out that hydrogen has a higher specific energy than does gasoline, but, even in liquid form, a much lower energy density.

Energy Density

The kinetic energy of an object is the energy which it possesses due to its motion.It is defined as the work needed to accelerate a body of a given mass from rest to its stated velocity. Having gained this energy during its acceleration, the body maintains this kinetic energy unless its speed changes. The same amount of work is done by the body in decelerating from its current speed to a state of rest.

The speed, and thus the kinetic energy of 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 from the point of view of an observer moving with the same velocity as the bullet, and so has zero kinetic energy. By contrast, the total kinetic energy of 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.

In classical mechanics, the kinetic energy of a non-rotating object of mass m traveling at a speed v is ½ mv². In relativistic mechanics, this is only a good approximation when v is much less than

the speed of light.

Kinetic Energy

Kinetic energy of rigid bodies 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 is equal to the mass multiplied by the square of the speed, multiplied by the constant 1/2. In formula form:

where is the mass and is the speed (or the velocity) of the body. In SI units (used for most modern scientific work), mass is measured in kilograms, speed in metres per second, and the resulting kinetic energy is in joules.

For example, one would calculate 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

Ek = (1/2) · 80 · 182 J = 12.96 kJ When you throw a ball, you do work on it to give it speed as it leaves your 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 the work the object can do while being brought to rest: Net force x distance = kinetic energy. Or, in equation notation:

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 the work to double the speed.

The kinetic energy of an object is related to its momentum by the equation: where: Momentum is mass of the body. For the translational kinetic energy, that is the kinetic energy associated with rectilinear motion, of a

rigid body with constant mass , whose center of mass is moving in a straight line with speed , as seen above is equal to

where: the mass of the body is the speed of the center of mass of the body.

Newtonian Kinetic Energy

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 which energy can neither enter nor leave, does not change in whatever reference frame 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 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 disagree on the value of this conserved energy.

The kinetic energy of such systems depends on the choice of reference frame: 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.

Newtonian Kinetic Energy

In physics, potential energy is the energy of a body or a system due to the position of the body or the arrangement of the particles of the system.The SI unit for measuring work and energy is the Joule (symbol J).

The term "potential energy" was coined by the 19th century Scottish engineer and physicist William Rankine,although it has links to Greek philosopher Aristotle's concept of potentiality.

Potential Energy

However, over large variations in distance, the approximation that g is constant is no longer valid, and we have to use calculus and the general mathematical definition of work to determine gravitational potential energy. For the computation of the potential energy we can integrate the gravitational force, whose magnitude is given by Newton's law of gravitation, with respect to the distance r between the two bodies. Using that definition, the gravitational potential energy of a system of masses m1 and M2 at a distance r using gravitational constant G is

Given this formula for U, the total potential energy of a system of n bodies is found by summing, for all

pairs of two bodies, the potential energy of the system of those two bodies. Gravitational potential summation Considering the system of bodies as the combined set of small particles the

bodies consist of, and applying the previous on the particle level we get the negative gravitational binding energy. This potential energy is more strongly negative than the total potential energy of the system of bodies as such since it also includes the negative gravitational binding energy of each body. The potential energy of the system of bodies as such is the negative of the energy needed to separate the bodies from each other to infinity, while the gravitational binding energy is the energy needed to separate all particles from each other to infinity.

There fore ,

General Formula

Elastic potential energy Calculation of elastic potential energy The elastic potential energy stored in a stretched spring can be

calculated by finding the work necessary to stretch the spring a distance x from its un-stretched length:

an ideal spring will follow Hooke's Law: The work done (and therefore the stored potential energy) will

then be:

The units are in Joules. The equation is often used in calculations of positions of

mechanical equilibrium. More involved calculations can be found at elastic potential energy.

Kinds Of Potential Energy

The elastic potential energy stored in a stretched spring can be calculated by finding the work necessary to stretch the spring a distance x from its un-stretched length:

an ideal spring will follow Hooke's Law: The work done (and therefore the stored potential

energy) will then be:

Calculation OF Elastic Potential Energy

Chemical potential energy is a form of potential energy related to the structural arrangement of atoms or molecules. This arrangement may be the result of chemical bonds within a molecule or otherwise. Chemical energy of a chemical substance can be transformed to other forms of energy by a chemical reaction. As an example, when a fuel is burned the chemical energy is converted to heat, same is the case with digestion of food metabolized in a biological organism. Green plants transform solar energy to chemical energy through the process known as photosynthesis, and electrical energy can be converted to chemical energy through electrochemical reactions.

The similar term chemical potential is used to indicate the potential of a substance to undergo a change of configuration, be it in the form of a chemical reaction, spatial transport, particle exchange with a reservoir, etc.

Chemical potential Energy

An object can have potential energy by virtue of its electric charge and several forces related to their presence. There are two main types of this kind of potential energy: electrostatic potential energy, electro dynamic potential energy (also sometimes called magnetic potential energy).

Plasma formed inside a gas filled sphere

Electrical Potential Energy

In case the electric charge of an object can be assumed to be at rest, it has potential energy due to its position relative to other charged objects.

The electrostatic potential energy is the energy of an electrically charged particle (at rest) in an electric field. It is defined as the work that must be done to move it from an infinite distance away to its present location, in the absence of any non-electrical forces on the object. This energy is non-zero if there is another electrically charged object nearby.

The simplest example is the case of two point-like objects A1 and A2 with electrical charges q1 and q2. The work W required to move A1 from an infinite distance to a distance r away from A2 is given by:

where ε0 is the electric constant. This equation is obtained by integrating the Coulomb force between

the limits of infinity and r. A related quantity called electric potential (commonly denoted with

a V for voltage) is equal to the electric potential energy per unit charge.

Electro Static Potential Energy

The energy of a magnetic moment m in an externally produced magnetic B-field B has potential energy

The magnetization M in a field is where the integral can be over all space or, equivalently, where M is

non zero. Magnetic potential energy is the form of energy related not only to the distance between magnetic materials, but also to the orientation, or alignment, of those materials within the field. For example, the needle of a compass has the lowest magnetic potential energy when it is aligned with the north and south poles of the Earth's magnetic field. If the needle is moved by an outside force, torque is exerted on the magnetic dipole of the needle by the Earth's magnetic field, causing it to move back into alignment. The magnetic potential energy of the needle is highest when it is perpendicular to the Earth's magnetic field. Two magnets will have potential energy in relation to each other and the distance between them, but this also depends on their orientation. If the opposite poles are held apart, the potential energy will be the highest when they are near the edge of their attraction, and the lowest when they pull together. Conversely, like poles will have the highest potential energy when forced together, and the lowest when they spring apart.

Magnetic Potential Energy

Nuclear potential energy is the potential energy of the particles inside an atomic nucleus. The nuclear particles are bound together by the strong nuclear force. Weak nuclear forces provide the potential energy for certain kinds of radioactive decay, such as beta decay.

Nuclear particles like protons and neutrons are not destroyed in fission and fusion processes, but collections of them have less mass than if they were individually free, and this mass difference is liberated as heat and radiation in nuclear reactions (the heat and radiation have the missing mass, but it often escapes from the system, where it is not measured). The energy from the Sun is an example of this form of energy conversion. In the Sun, the process of hydrogen fusion converts about 4 million tones of solar matter per second into electromagnetic energy, which is radiated into space.

Nuclear Potential Energy