Application of kinetic energy as wind energy

Application of kinetic energy as wind energy
Introduction of wind energy


Wind can be used to do work. The kinetic energy of the wind can be changed into other forms of energy, either mechanical energy or electrical energy. Wind energy is the kinetic energy that is present in moving air. When a boat lifts a sail, it is using wind energy to push it through the water. This is one form of work. Farmers have been using wind energy for many years to pump water from wells using windmills like the one on the right. In Holland, windmills have been used for centuries to pump water from low-lying areas. Wind is also used to turn large grinding stones to grind wheat or corn, just like a water wheel is turned by water power. Today, the wind is also used to make electricity.
The amount of potential energy depends mainly on wind speed, but is also affected slightly by the density of the air, which is determined by the air temperature, barometric pressure, and altitude.

Wind turbine
A turbine is a device for converting the energy in a moving fluid into mechanical rotating energy. There are big turbines at the bottom of dams that convert the energy from pressure and velocity in water into rotating mechanical energy to drive huge generators. There are turbines in jet engines and turbochargers that convert the velocity, pressure, and temperature, in engine exhaust gasses into mechanical energy. After going through the turbine the exhaust gas is cooler and has a lower pressure. There are steam turbines that convert the pressure and velocity and high temperature of super-heated steam into mechanical rotating energy to drive electric generators. Wind turbines only take velocity or kinetic energy out of the wind. It's only the kinetic energy of the moving air molecules that we can convert to mechanical energy. A wind turbine is a device for converting the kinetic energy in wind into the mechanical energy of a rotating shaft. Usually that rotating mechanical energy is converted immediately by a generator into electrical energy.

The first law of thermodynamics tells us the energy out of a wind turbine has to equal the energy in. The energy in is the kinetic energy from the wind's velocity and air density. It is not possible to convert all of the wind's kinetic energy into mechanical energy. Some energy must remain in the wind. The "energy out" is the energy converted by the turbine blades into mechanical energy, plus whatever energy is left in the air after it passes through the turbin rotors. Power is how fast we are producing or using a quantity energy. Power has units of energy divided by time. A Watt is a unit a power. It represents one joule of energy transformed every second. A 60 Watt light bulb converts 60 joules of energy every second into light and heat. The formula below shows how to calculate the power in the wind (not the power available to us because we can't get it all).
Power in the wind = (density of air)2×(turbine blade diameter)2×(velocity of wind)3× constant
Notice that the power in the wind depends on the density of the air, the diameter of the turbine blades squared (D times D), and the velocity of the wind to the third power (V times V times V). There is also a constant in there.
Blowing wind spins the blades on a wind turbine -- just like a large toy pinwheel. This device is called a wind turbine and not a windmill. A windmill grinds or mills grain, or is used to pump water. The blades of the turbine are attached to a hub that is mounted on a turning shaft. The shaft goes through a gear transmission box where the turning speed is increased. The transmission is attached to a high speed shaft which turns a generator that makes electricity. If the wind gets too high, the turbine has a brake that will keep the blades from turning too fast and being damaged.


Turbine Efficiency
If the turbine could convert all the wind's power to mechanical power we would say it was 100% efficient. But as you probably know, the real world is never so generous. To even achieve 50% is unlikely, and would be a very efficient machine. A 50% efficient turbine would convert half of the power in the wind to mechanical power.

Benefits of wind energy
Wind energy is an ideal renewable energy. Wind energy is a pollution-free, infinitely sustainable form of energy. It doesn’t use fuel; it doesn’t produce greenhouse gasses, and it doesn’t produce toxic or radioactive waste.
Wind energy is quiet and does not present any significant hazard to birds or other wildlife. When large arrays of wind turbines are installed on farmland, only about 2% of the land area is required for the wind turbines. The rest is available for farming, livestock, and other uses. Landowners often receive payment for the use of their land, which enhances their income and increases the value of the land. Ownership of wind turbine generators by individuals and the community allows people to participate directly in the preservation of our environment. Each megawatt-hour of electricity that is generated by wind energy helps to reduce 0.8 to 0.9 tonnes of greenhouse gas emissions that are produced by coal or diesel fuel generation each year.

Resources
1) http://www.energyquest.ca.gov/story/chapter16.html
2) http://canren.gc.ca/tech_appl/index.asp?CaId=6&PgId=232
3) http://ftexploring.com/energy/wind-enrgy.html

variation of kinetic energy

Kinetic energy is motion––of waves, electrons, atoms, molecules, substances, and objects.

Electrical Energy is the movement of electrical charges. Everything is made of tiny particles called atoms. Atoms are made of even smaller particles called electrons, protons, and neutrons. Applying a force can make some of the electrons move. Electrical charges moving through a wire is called electricity. Lightning is another example of electrical energy.

Radiant Energy is electromagnetic energy that travels in transverse waves. Radiant energy includes visible light, x-rays, gamma rays and radio waves. Light is one type of radiant energy. Solar energy is an example of radiant energy.

Thermal Energy, or heat, is the internal energy in substances––the vibration and movement of the atoms and molecules within substances. Geothermal energy is an example of thermal energy.

Motion Energy is the movement of objects and substances from one place to another. Objects and substances move when a force is applied according to Newton’s Laws of Motion. Wind is an example of motion energy.

Sound is the movement of energy through substances in longitudinal (compression/rarefaction) waves. Sound is produced when a force causes an object or substance to vibrate––the energy is transferred through the substance in a wave.

Basic Terminology and Concepts

Kinetic energy is the energy of motion. An object which has motion - whether it be vertical or horizontal motion - has kinetic energy. There are many forms of kinetic energy - vibrational (the energy due to vibrational motion), rotational (the energy due to rotational motion), and translational (the energy due to motion from one location to another). To keep matters simple, we will focus upon translational kinetic energy. The amount of translational kinetic energy (from here on, the phrase kinetic energy will refer to translational kinetic energy) which an object has depends upon two variables: the mass (m) of the object and the speed (v) of the object. The following equation is used to represent the kinetic energy (KE) of an object.


where m = mass of object

v = speed of object

This equation reveals that the kinetic energy of an object is directly proportional to the square of its speed. That means that for a twofold increase in speed, the kinetic energy will increase by a factor of four. For a threefold increase in speed, the kinetic energy will increase by a factor of nine. And for a fourfold increase in speed, the kinetic energy will increase by a factor of sixteen. The kinetic energy is dependent upon the square of the speed. As it is often said, an equation is not merely a recipe for algebraic problem-solving, but also a guide to thinking about the relationship between quantities.

Kinetic energy is a scalar quantity; it does not have a direction. Unlike velocity, acceleration, force, and momentum, the kinetic energy of an object is completely described by magnitude alone. Like work and potential energy, the standard metric unit of measurement for kinetic energy is the Joule. As might be implied by the above equation, 1 Joule is equivalent to 1 kg*(m/s)^2.

Kinetic Theory

Kinetic theory (or kinetic theory of gases) attempts to explain macroscopic properties of gases, such as pressure, temperature, or volume, by considering their molecular composition and motion. Essentially, the theory posits that pressure is due not to static repulsion between molecules, as was Isaac Newton's conjecture, but due to collisions between molecules moving at different velocities. Kinetic theory is also known as the kinetic-molecular theory or the collision theory.

Postulates

The theory for ideal gases makes the following assumptions:

• The gas consists of very small particles, each of which has a mass or weight in SI units, kilograms.
• The number of molecules is large such that statistical treatment can be applied.
• These molecules are in constant, random motion. The rapidly moving particles constantly collide with each other and with the walls of the container.
• The collisions of gas particles with the walls of the container holding them are perfectly elastic.
• The interactions among molecules are negligible. They exert no forces on one another except during collisions.
• The total volume of the individual gas molecules added up is negligible compared to the volume of the container. This is equivalent to stating that the average distance separating the gas particles is relatively large compared to their size.
• The molecules are perfectly spherical in shape, and elastic in nature.
• The average kinetic energy of the gas particles depends only on the temperature of the system.
• Relativistic effects are negligible.
• Quantum-mechanical effects are negligible. This means that the inter-particle distance is much larger than the thermal de Broglie wavelength and the molecules can be treated as classical objects.
• The time during collision of molecule with the container's wall is negligible as comparable to the time between successive collisions.
• The equations of motion of the molecules are time-reversible.

In addition, if the gas is in a container, the collisions with the walls are assumed to be instantaneous and elastic.

More modern developments relax these assumptions and are based on the Boltzmann equation. These can accurately describe the properties of dense gases, because they include the volume of the molecules. The necessary assumptions are the absence of quantum effects, molecular chaos and small gradients in bulk properties. Expansions to higher orders in the density are known as virial expansions. The definitive work is the book by Chapman and Enskog but there have been many modern developments and there is an alternative approach developed by Grad based on moment expansions. In the other limit, for extremely rarefied gases, the gradients in bulk properties are not small compared to the mean free paths. This is known as the Knudsen regime and expansions can be performed in the Knudsen number.

The kinetic theory has also been extended to include inelastic collisions in granular matter by Jenkins and others.

State Variables

A state variable is a precisely measurable physical property which characterizes the state of a system, independently of how the system was brought to that state. It must be inherently single-valued to characterize a state. For example in the heat-work example, the final state is characterized by a specific temperature (a state variable) regardless of whether it was brought to that state by heating, or by having work done on it, or both.

Common examples of state variables are the pressure P, volume V, and temperature T. In the ideal gas law, the state of n moles of gas is precisely determined by these three state variables. If a property, e.g., enthalpy H, is defined as a combination of other state variables, then it too is a state variable. Enthalpy is one of the four "thermodynamic potentials", and the other three, internal energy U, Helmholtz free energy F and Gibbs free energy G are also state variables. The entropy S is also a state variable.

Some texts just use the term "thermodynamic variable" instead of the description "state variable".

Kinetics

Chemistry: Foundations and Applications

Chemical kinetics is the study of the rates of chemical reactions. Such reaction rates range from the almost instantaneous, as in an explosion, to the almost unnoticeably slow, as in corrosion. The aim of chemical kinetics is to make predictions about the composition of reaction mixtures as a function of time, to understand the processes that occur during a reaction, and to identify what controls its rate.

Rates and Rate Laws

The rate of a chemical reaction is defined as the rate of change of the concentration of one of its components, either a reactant or a product. The experimental investigation of reaction rates therefore depends on being able to monitor the change of concentration with time. Classical procedures for reactions that take place in hours or minutes make use of a variety of techniques for determining concentration, such as spectroscopy and electro-chemistry. Very fast reactions are studied spectroscopically. Spectroscopic procedures are available for monitoring reactions that are initiated by a rapid pulse of electromagnetic radiation and are over in a few femtoseconds (1 fs = 10⁻¹⁵ s).

The analysis of kinetic data commonly proceeds by establishing a rate law, a mathematical expression for the rate in terms of the concentrations of the reactants (and sometimes products) at each stage of the reaction. For instance, it may be found that the rate of consumption of a reactant is proportional to the concentration of the reactant, in which case the rate law is

Rate = k [Reactant]

where [Reactant] denotes the concentration of the reactant and k is called the rate constant. The rate constant is independent of the concentrations of any species in the reaction mixture but depends on the temperature. A reaction with a rate law of this form is classified as a first-order rate law. More generally, a reaction with a rate law of the form

Rate = k [Reactant A]^a [Reactant B]^b …

is said to be of order a in A, of order b in B, and to have an overall order of a + b + …. Some rate laws are far more complex than these two simple examples and many involve the concentrations of the products.

The advantage of identifying the reaction order is that all reactions with the same rate law (but different characteristic rate constants) behave similarly. For example, the concentration of a reactant in a first-order reaction decays exponentially with time at a rate determined by the rate constant

[Reactant] = [Reactant]₀e ^−kt

where [Reactant]₀ is the initial concentration of the reactant. On the other hand, all second-order reactions lead to the following time-dependence of the concentration:

Figure 1 shows the time-dependence predicted by these expressions. It is common to report the time-dependence of first-order reactions in terms of the half-life, t _½, of the reactant, the time needed for its concentration to fall to half its initial value. For a first-order reaction (but not for other orders)

Thus, reactions with large rate constants have short half-lives.

Reaction Mechanisms

The identification of a rate law provides valuable insight into the reaction mechanism, the sequence of elementary steps by which a reaction takes place. The aim is to identify the reaction mechanism by constructing the rate law that it implies. This procedure may be simplified by identifying the rate-determining step of a reaction, the slowest step in a sequence that determines the overall rate. Thus, if the proposed mechanism is A → B followed by B → C, and the former is much faster than the latter, then the overall rate of the reaction will be equal to the rate of A → B, for once B is formed, it immediately converts into C.

In general, for a mechanism of many steps (including their reverse), the construction of the overall rate law is quite difficult, requiring an approximation or a computer for a numerical analysis. One common approximation

is the steady-state assumption, in which the net rate of formation of any intermediate (B in the present example) is set equal to zero. A hazard of using kinetic information to identify a reaction mechanism, however, is that more than one mechanism might result in the same rate law, especially when approximate solutions are derived. For this reason, proposed reaction mechanism must be supported by additional evidence.

The Origin of Reaction Rates

Once a reaction mechanism has been identified, attention turns to the molecular properties that govern the values of the rate constants that occur in the individual elementary steps. A clue to the factors involved is provided by the experimental observation that the rate constants of many reactions depend on temperature according to the Arrhenius expression

where E _a is called the activation energy.

The simplest model that accounts for the Arrhenius expression is the collision theory of gas-phase reaction rates, in which it is supposed that reaction occurs when two reactant molecules collide with at least a minimum kinetic energy (which is identified with the activation energy, Figure 2). A more sophisticated theory is the activated complex theory (also known as the transition state theory ), in which it is supposed that the reactants encounter each other, form a loosened cluster of atoms, then decompose into products.

Reactions in solution require more detailed consideration than reactions in gases. It is necessary to distinguish between "diffusion-controlled" and

"activation-controlled" reactions. In a diffusion-controlled reaction, the rate is controlled by the ability of the reactants to migrate through the solvent and encounter each other. In an activation-controlled reaction, the rate is controlled by the ability of the reactants that have met each other to acquire enough energy to react.

The rate of a reaction may also be increased by finding a catalyst , a substance that takes part in a reaction by providing an alternative pathway with a lower activation energy but is regenerated in the process and is therefore not consumed. Catalysis is the foundation of the chemical industry and a great effort is made to discover or fabricate efficient, economical catalysts. It is also the foundation of life, because the biological catalysts known as enzymes (elaborate protein molecules) control almost every aspect of an organism's function.

about chemical kinetics

Chemical Kinetics

Chemical kinetics is the study and discussion of chemical reactions with respect to reaction rates, effect of various variables, re-arrangement of atoms, formation of intermediates etc. There are many topics to be discussed, and each of these topics is a tool for the study of chemical reactions. By the way, the study of motion is called kinetics, from Greek kinesis, meaning movement.

At the macroscopic level, we are interested in amounts reacted, formed, and the rates of their formation. At the molecular or microscopic level, the following considerations must also be made in the discusion of chemical reaction mechanism.

• Molecules or atoms of reactants must collide with each other in chemical reactions.
• The molecules must have sufficient energy (discussed in terms of activation energy) to initiate the reaction.
• In some cases, the orientation of the molecules during the collision must also be considered.

Reaction Rates

Chemical reaction rates are the rates of change in concentrations or amounts of either reactants or products. For changes in amounts, the units can be one of mol/s, g/s, lb/s, kg/day etc. For changes in concentrations, the units can be one of mol/(L s), g/(L s), %/s etc.

With respect to reaction rates, we may deal with average rates, instantaneous rates, or initial rates depending on the experimental conditions.

Thermodynamics and kinetics are two factors that affect reaction rates. The study of energy gained or released in chemical reactions is called thermodynamics, and such energy data are called thermodynamic data. However, thermodynamic data have no direct correlation with reaction rates, for which the kinetic factor is perhaps more important. For example, at room temperature (a wide range of temperatures), thermodynamic data indicates that diamond shall convert to graphite, but in reality, the conversion rate is so slow that most people think that diamond is forever.

Factors Influence Reaction Rates

Many factors influence rates of chemical reactions, and these are summarized below. Much more extensive discussion will be given in other pages.

1. Nature of Reactants
   Acid-base reactions, formation of salts, and exchange of ions are fast reactions. Reactions in which large molecules are formed or break apart are usually slow. Reactions breaking strong covalent bonds are also slow.
2. Temperature
   Usually, the higher the temperature, the faster the reaction. The temperature effect is discussed in terms of activation energy.
3. Concentration Effect
   The dependences of reaction rates on concentrations are called rate laws. Rate laws are expressions of rates in terms of concentrations of reactants. Keep in mind that rate laws can be in differential forms or integrated forms. They are called differential rate laws and integrated rate laws. The following is a brief summary of topics regarding rate laws.
   • rate laws: differential and integrated rate laws.
   • Integrated rate laws: First Order Reactions
     Second Order Reactions
     
   Rate laws apply to homogeneous reactions in which all reactants and products are in one phase (solution).
4. Heterogeneous reactions: reactants are present in more than one phase
   For heterogeneous reactions, the rates are affected by surface areas.
5. Catalysts: substances used to facilitate reactions
   By the nature of the term, catalysts play important roles in chemical reactions.

Reaction Mechanisms

The detailed explanation at the molecular level how a reaction proceeds is called reaction mechanism. The explanation is given in some elementary steps. Devising reaction mechanisms requires a broad understanding of properties of reactants and products, and this is a skill for matured chemists. However, first year chemistry students are often given a mechanism, and be asked to derive the rate law from the proposed mechanism. The steady-state approximations is a technique for deriving a rate law from the proposed mechanism.

Chemical kinetics

Chemical kinetics, also known as reaction kinetics, is the study of rates of chemical processes. Chemical kinetics includes investigations of how different experimental conditions can influence the speed of a chemical reaction and yield information about the reaction's mechanism and transition states, as well as the construction of mathematical models that can describe the characteristics of a chemical reaction. In 1864, Peter Waage and Cato Guldberg pioneered the development of chemical kinetics by formulating the law of mass action, which states that the speed of a chemical reaction is proportional to the quantity of the reacting substances.

Rate of reaction

Main article: reaction rate

Chemical kinetics deals with the experimental determination of reaction rates from which rate laws and rate constants are derived. Relatively simple rate laws exist for zero order reactions (for which reaction rates are independent of concentration), first order reactions, and second order reactions, and can be derived for others. In consecutive reactions the rate-determining step often determines the kinetics. In consecutive first order reactions, a steady state approximation can simplify the rate law. The activation energy for a reaction is experimentally determined through the Arrhenius equation and the Eyring equation. The main factors that influence the reaction rate include: the physical state of the reactants, the concentrations of the reactants, the temperature at which the reaction occurs, and whether or not any catalysts are present in the reaction.

Factors affecting reaction rate

Nature of the Reactants

Depending upon what substances are reacting, the time varies. Acid reactions, the formation of salts, and ion exchange are fast reactions. When covalent bond formation takes place between the molecules and when large molecules are formed, the reactions tend to be very slow.

Physical State

The physical state (solid, liquid, or gas) of a reactant is also an important factor of the rate of change. When reactants are in the same phase, as in aqueous solution, thermal motion brings them into contact. However, when they are in different phases, the reaction is limited to the interface between the reactants. Reaction can only occur at their area of contact, in the case of a liquid and a gas, at the surface of the liquid. Vigorous shaking and stirring may be needed to bring the reaction to completion. This means that the more finely divided a solid or liquid reactant, the greater its surface area per unit volume, and the more contact it makes with the other reactant, thus the faster the reaction. To make an analogy, for example, when one starts a fire, one uses wood chips and small branches—one doesn't start with large logs right away. In organic chemistry On water reactions are the exception to the rule that homogeneous reactions take place faster than heterogeneous reactions.

Concentration

Concentration plays an important role in reactions according to the collision theory of chemical reactions, this is because molecules must collide in order to react together. As the concentration of the reactants increases, the frequency of the molecules colliding increases, striking each other faster by being in closer contact at any given point in time. Imagine two reactants being in a closed container. All the molecules contained within are colliding constantly. By increasing the amount of one or more of the reactants you cause these collisions to happen more often, increasing the reaction rate (Figure 1.1).

Temperature

Temperature usually has a major effect on the rate of a chemical reaction. Molecules at a higher temperature have more thermal energy. Although collision frequency is greater at higher temperatures, this alone contributes only a very samll proportion to the increase in rate of reaction. Much more important is the fact that the proportion of reactant molecules with sufficient energy to react (energy greater than activation energy: E > E_a) is significantly higher and is explained in detail by the Maxwell-Boltzmann distribution of molecular energies.

The 'rule of thumb' that the rate of chemical reactions double for every 10 °C temperature rise is a common misconception. This may have been generalized from the special case of biological systems, where the Q10 (temperature coefficient) is often between 1.5 and 2.5.

A reaction's kinetics can also be studied with a temperature jump approach. This involves using a sharp rise in temperature and observing the relaxation rate of an equilibrium process.

Catalysts

Generic potential energy diagram showing the effect of a catalyst in an hypothetical exothermic chemical reaction. The presence of the catalyst opens a different reaction pathway (shown in red) with a lower activation energy. The final result and the overall thermodynamics are the same.

A catalyst is a substance that accelerates the rate of a chemical reaction but remains chemically unchanged afterwards. The catalyst increases rate reaction by providing a different reaction mechanism to occur with a lower activation energy. In autocatalysis a reaction product is itself a catalyst for that reaction leading to positive feedback. Proteins that act as catalysts in biochemical reactions are called enzymes. Michaelis-Menten kinetics describe the rate of enzyme mediated reactions.

In certain organic molecules specific substituents can have an influence on reaction rate in neighbouring group participation.

Agitating or mixing a solution will also accelerate the rate of a chemical reaction, as this gives the particles greater kinetic energy, increasing the number of collisions between reactants and therefore the possibility of successful collisions.

Increasing the pressure in a gaseous reaction will increase the number of collisions between reactants, increasing the rate of reaction. This is because the activity of a gas is directly proportional to the partial pressure of the gas. This is similar to the effect of increasing the concentration of a solution. A catalyst does not affect the position of the equilibria, as the catalyst speeds up the backward and forward reactions equally.

Equilibrium

While chemical kinetics is concerned with the rate of a chemical reaction, thermodynamics determines the extent to which reactions occur. In a reversible reaction, chemical equilibrium is reached when the rates of the forward and reverse reactions are equal and the concentrations of the reactants and products no longer change. This is demonstrated by, for example, the Haber-Bosch process for combining nitrogen and hydrogen to produce ammonia. Chemical clock reactions such as the Belousov-Zhabotinsky reaction demonstrate that component concentrations can oscillate for a long time before finally reaching equilibrium.

Free energy

In general terms, the free energy change (ΔG) of a reaction determines if a chemical change will take place, but kinetics describes how fast the reaction is. A reaction can be very exothermic and have a very positive entropy change but will not happen in practice if the reaction is too slow. If a reactant can produce two different products, the thermodynamically most stable one will generally form except in special circumstances when the reaction is said to be under kinetic reaction control. The Curtin-Hammett principle applies when determining the product ratio for two reactants interconverting rapidly, each going to a different product. It is possible to make predictions about reaction rate constants for a reaction from Free-energy relationships.

The kinetic isotope effect is the difference in the rate of a chemical reaction when an atom in one of the reactants is replaced by one of its isotopes.

Chemical kinetics provides information on residence time and heat transfer in a chemical reactor in chemical engineering and the molar mass distribution in polymer chemistry.

Applications

The mathematical models that describe chemical reaction kinetics provide chemists and chemical engineers with tools to better understand and describe chemical processes such as food decomposition, microorganism growth, stratospheric ozone decomposition, and the complex chemistry of biological systems. These models can also be used in the design or modification of chemical reactors to optimize product yield, more efficiently separate products, and eliminate environmentally harmful by-products. When performing catalytic cracking of heavy hydrocarbons into gasoline and light gas, for example, kinetic models can be used to find the temperature and pressure at which the highest yield of heavy hydrocarbons into gasoline will occur.

Kinetic Energy

The kinetic energy of an object is the extra 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 current velocity. Having gained this energy during its acceleration, the body maintains this kinetic energy unless its speed changes. Negative work of the same magnitude would be required to return the body to a state of rest from that velocity.

Etymology

The adjective "kinetic" to the noun energy has its roots in the Greek word for "motion" (kinesis). The terms kinetic energy and work and their present scientific meanings date back to the mid 19th century. Early understandings of these ideas can be attributed to Gaspard-Gustave Coriolis who in 1829 published the paper titled Du Calcul de l'Effet des Machines outlining the mathematics of kinetic energy.

William Thomson, later Lord Kelvin, is given the credit for coining the term kinetic energy c. 1849.

Introduction

Main article: Energy

There are various forms of energy : chemical energy, heat, electromagnetic radiation, potential energy (gravitational, electric, elastic, etc.), nuclear energy, rest energy. These can be categorized in two main classes: potential energy and kinetic energy.

Kinetic energy can be best understood by examples that demonstrate how it is transformed from other forms of energy and to the other forms. For example, a cyclist will use chemical energy that was provided by food to accelerate a bicycle to a chosen speed. This speed can be maintained without further work, except to overcome air-resistance and friction. The energy has been converted into the energy of motion, known as kinetic energy but the process is not completely efficient and heat is also produced within the cyclist.

The kinetic energy in the moving bicycle and the cyclist 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 the other side of the hill. (Since the bicycle lost some of its energy to friction, it will never regain all of its speed without further pedaling. Note that 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 also generate some electrical energy on the descent. The bicycle would be traveling more slowly at the bottom of the hill because some of the energy has been diverted into making electrical power. Another possibility would be for the cyclist to apply the brakes, in which case the kinetic energy would be dissipated through friction as heat energy.

Like any physical quantity which is a function of velocity, the kinetic energy of an object does not depend only on the inner nature of that object. It also depends on the relationship between that object and the observer (in physics an observer is formally defined by a particular class of coordinate system called an inertial reference frame). Physical quantities like this are said to be not invariant. The kinetic energy is co-located with the object and contributes to its gravitational field.

Calculations

There are several different equations that may be used to calculate the kinetic energy of an object. In many cases they give almost the same answer to well within measurable accuracy. Where they differ, the choice of which to use is determined by the velocity of the body or its size. Thus, if the object is moving at a velocity much smaller than the speed of light, the Newtonian (classical) mechanics will be sufficiently accurate; but if the speed is comparable to the speed of light, relativity starts to make significant differences to the result and should be used. If the size of the object is sub-atomic, the quantum mechanical equation is most appropriate.