Nick Connor

What is Kinetic Energy

The kinetic energy, K, is defined as the energy stored in an object because of its motion. An object in motion has the ability to do work and thus can be said to have energy. It is called kinetic energy, from the Greek word kinetikos, meaning “motion.”

The kinetic energy depends on the speed of an object and is the ability of a moving object to do work on other objects when it collides with them. On the other hand, the kinetic energy of an object represents the amount of energy required to increase the velocity of the object from rest (v = 0) to its final velocity. The kinetic energy also depends linearly on the mass, which is a numerical measure of object’s inertia and the measure of an object’s resistance to acceleration when a force is applied.

We define the quantity:

K = ½ mv²

to be the translational kinetic energy of the object. It must be added, it is called the “translational” kinetic energy to distinguish it from rotational kinetic energy.

Examples of Kinetic Energy

Block sliding down a frictionless incline slope

The 1 kg block starts out a height H (let say 1 m) above the ground, with potential energy mgH and kinetic energy that is equal to 0. It slides to the ground (without friction) and arrives with no potential energy and kinetic energy K = ½ mv². Calculate the velocity of the block on the ground and its kinetic energy.

E_mech = U + K = const

=> ½ mv² = mgH

=> v = √2gH = 4.43 m/s

=> K₂ = ½ x 1 kg x (4.43 m/s)² = 19.62 kg.m².s^-2 = 19.62 J

Pendulum

Assume a pendulum (ball of mass m suspended on a string of length L that we have pulled up so that the ball is a height H < L above its lowest point on the arc of its stretched string motion. The pendulum is subjected to the conservative gravitational force where frictional forces like air drag and friction at the pivot are negligible.

We release it from rest. How fast is it going at the bottom?

The pendulum reaches greatest kinetic energy and least potential energy when in the vertical position, because it will have the greatest speed and be nearest the Earth at this point. On the other hand, it will have its least kinetic energy and greatest potential energy at the extreme positions of its swing, because it has zero speed and is farthest from Earth at these points.

If the amplitude is limited to small swings, the period T of a simple pendulum, the time taken for a complete cycle, is:

where L is the length of the pendulum and g is the local acceleration of gravity. For small swings the period of swing is approximately the same for different size swings. That is, the period is independent of amplitude.

Example: Proton’s kinetic energy

A proton (m = 1.67 x 10^-27 kg) travels at a speed v = 0.9900c = 2.968 x 10⁸m/s. What is its kinetic energy?

According to a classical calculation, which is not correct, we would obtain:

K = 1/2mv² = ½ x (1.67 x 10^-27 kg) x (2.968 x 10⁸m/s)² = 7.355 x 10^-11 J

With relativistic correction the relativistic kinetic energy is equal to:

K = (ɣ – 1)mc²

where the Lorentz factor

ɣ = 7.089

therefore

K = 6.089 x (1.67 x 10^-27 kg) x (2.9979 x 10⁸m/s)² = 9.139 x 10^-10 J = 5.701 GeV

This is about 12 times higher energy as in the classical calculation. According to this relationship, an acceleration of a proton beam to 5.7 GeV requires energies that are in the order different.

See also:

Kinetic Energy

Example: Proton’s kinetic energy

A proton (m = 1.67 x 10^-27 kg) travels at a speed v = 0.9900c = 2.968 x 10⁸m/s. What is its kinetic energy?

According to a classical calculation, which is not correct, we would obtain:

K = 1/2mv² = ½ x (1.67 x 10^-27 kg) x (2.968 x 10⁸m/s)² = 7.355 x 10^-11 J

With relativistic correction the relativistic kinetic energy is equal to:

K = (ɣ – 1)mc²

where the Lorentz factor

ɣ = 7.089

therefore

K = 6.089 x (1.67 x 10^-27 kg) x (2.9979 x 10⁸m/s)² = 9.139 x 10^-10 J = 5.701 GeV

This is about 12 times higher energy as in the classical calculation. According to this relationship, an acceleration of a proton beam to 5.7 GeV requires energies that are in the order different.

See also:

Kinetic Energy

Relativistic Kinetic Energy

The previous relationship between work and kinetic energy are based on Newton’s laws of motion. When we generalize these laws according to the principle of relativity, we need a corresponding generalization of the equation for kinetic energy. If an object’s speed is close to the speed of light, it is necessary to use relativistic mechanics to calculate its kinetic energy.

In classical mechanics, kinetic energy and momentum are expressed as:

Derivation of its relativistic relationships is based on the relativistic energy-momentum relation:

It can be derived, the relativistic kinetic energy and the relativistic momentum are:

The first term (ɣmc²) of the relativistic kinetic energy increases with the speed v of the particle. The second term (mc²) is constant; it is called the rest energy (rest mass) of the particle, and represents a form of energy that a particle has even when at zero velocity. As velocity of an object approaches the speed of light, the kinetic energy approaches infinity. It is caused by the Lorentz factor, which approaches infinity for v → c. Therefore the speed of light cannot be reached by any massive particles.

The first term (ɣmc²) is known as the total energy E of the particle, because it equals the rest energy plus the kinetic energy:

E = K + mc²

For a particle at rest, i.e. K is zero, so the total energy is its rest energy:

E = mc²

This is one of the striking results of Einstein’s theory of relativity is that mass and energy are equivalent and convertible one into the other. Equivalence of the mass and energy is described by Einstein’s famous formula E = mc². This result have been experimentally confirmed countless times in nuclear and elementary particle physics. For example, see Positron-electron Pair Production or Conservation of Energy in Nuclear Reactions.

See also: Relativistic Mass

Example: Proton’s kinetic energy

A proton (m = 1.67 x 10^-27 kg) travels at a speed v = 0.9900c = 2.968 x 10⁸m/s. What is its kinetic energy?

According to a classical calculation, which is not correct, we would obtain:

K = 1/2mv² = ½ x (1.67 x 10^-27 kg) x (2.968 x 10⁸m/s)² = 7.355 x 10^-11 J

With relativistic correction the relativistic kinetic energy is equal to:

K = (ɣ – 1)mc²

where the Lorentz factor

ɣ = 7.089

therefore

K = 6.089 x (1.67 x 10^-27 kg) x (2.9979 x 10⁸m/s)² = 9.139 x 10^-10 J = 5.701 GeV

This is about 12 times higher energy as in the classical calculation. According to this relationship, an acceleration of a proton beam to 5.7 GeV requires energies that are in the order different.

See also:

Kinetic Energy

What is Kinetic Energy

The kinetic energy, K, is defined as the energy stored in an object because of its motion. An object in motion has the ability to do work and thus can be said to have energy. It is called kinetic energy, from the Greek word kinetikos, meaning “motion.”

The kinetic energy depends on the speed of an object and is the ability of a moving object to do work on other objects when it collides with them. On the other hand, the kinetic energy of an object represents the amount of energy required to increase the velocity of the object from rest (v = 0) to its final velocity. The kinetic energy also depends linearly on the mass, which is a numerical measure of object’s inertia and the measure of an object’s resistance to acceleration when a force is applied.

We define the quantity:

K = ½ mv²

to be the translational kinetic energy of the object. It must be added, it is called the “translational” kinetic energy to distinguish it from rotational kinetic energy.

Conservation of Mechanical Energy

First the principle of the Conservation of Mechanical Energy was stated:

The total mechanical energy (defined as the sum of its potential and kinetic energies) of a particle being acted on by only conservative forces is constant.

See also: Conservation of Mechanical Energy

An isolated system is one in which no external force causes energy changes. If only conservative forces act on an object and U is the potential energy function for the total conservative force, then

E_mech = U + K

The potential energy, U, depends on the position of an object subjected to a conservative force.

It is defined as the object’s ability to do work and is increased as the object is moved in the opposite direction of the direction of the force.

The potential energy associated with a system consisting of Earth and a nearby particle is gravitational potential energy.

The kinetic energy, K, depends on the speed of an object and is the ability of a moving object to do work on other objects when it collides with them.

 K = ½ mv²

The above mentioned definition (E_mech = U + K) assumes that the system is free of friction and other non-conservative forces. The difference between a conservative and a non-conservative force is that when a conservative force moves an object from one point to another, the work done by the conservative force is independent of the path.

In any real situation, frictional forces and other non-conservative forces are present, but in many cases their effects on the system are so small that the principle of conservation of mechanical energy can be used as a fair approximation. For example the frictional force is a non-conservative force, because it acts to reduce the mechanical energy in a system.

Note that non-conservative forces do not always reduce the mechanical energy. A non-conservative force changes the mechanical energy, there are forces that increase the total mechanical energy, like the force provided by a motor or engine, is also a non-conservative force.

Block sliding down a frictionless incline slope

The 1 kg block starts out a height H (let say 1 m) above the ground, with potential energy mgH and kinetic energy that is equal to 0. It slides to the ground (without friction) and arrives with no potential energy and kinetic energy K = ½ mv². Calculate the velocity of the block on the ground and its kinetic energy.

E_mech = U + K = const

=> ½ mv² = mgH

=> v = √2gH = 4.43 m/s

=> K₂ = ½ x 1 kg x (4.43 m/s)² = 19.62 kg.m².s^-2 = 19.62 J

Pendulum

Assume a pendulum (ball of mass m suspended on a string of length L that we have pulled up so that the ball is a height H < L above its lowest point on the arc of its stretched string motion. The pendulum is subjected to the conservative gravitational force where frictional forces like air drag and friction at the pivot are negligible.

We release it from rest. How fast is it going at the bottom?

The pendulum reaches greatest kinetic energy and least potential energy when in the vertical position, because it will have the greatest speed and be nearest the Earth at this point. On the other hand, it will have its least kinetic energy and greatest potential energy at the extreme positions of its swing, because it has zero speed and is farthest from Earth at these points.

If the amplitude is limited to small swings, the period T of a simple pendulum, the time taken for a complete cycle, is:

where L is the length of the pendulum and g is the local acceleration of gravity. For small swings the period of swing is approximately the same for different size swings. That is, the period is independent of amplitude.

Relativistic Kinetic Energy

The previous relationship between work and kinetic energy are based on Newton’s laws of motion. When we generalize these laws according to the principle of relativity, we need a corresponding generalization of the equation for kinetic energy. If an object’s speed is close to the speed of light, it is necessary to use relativistic mechanics to calculate its kinetic energy.

In classical mechanics, kinetic energy and momentum are expressed as:

Derivation of its relativistic relationships is based on the relativistic energy-momentum relation:

It can be derived, the relativistic kinetic energy and the relativistic momentum are:

The first term (ɣmc²) of the relativistic kinetic energy increases with the speed v of the particle. The second term (mc²) is constant; it is called the rest energy (rest mass) of the particle, and represents a form of energy that a particle has even when at zero velocity. As velocity of an object approaches the speed of light, the kinetic energy approaches infinity. It is caused by the Lorentz factor, which approaches infinity for v → c. Therefore the speed of light cannot be reached by any massive particles.

The first term (ɣmc²) is known as the total energy E of the particle, because it equals the rest energy plus the kinetic energy:

E = K + mc²

For a particle at rest, i.e. K is zero, so the total energy is its rest energy:

E = mc²

This is one of the striking results of Einstein’s theory of relativity is that mass and energy are equivalent and convertible one into the other. Equivalence of the mass and energy is described by Einstein’s famous formula E = mc². This result have been experimentally confirmed countless times in nuclear and elementary particle physics. For example, see Positron-electron Pair Production or Conservation of Energy in Nuclear Reactions.

See also: Relativistic Mass

Example: Proton’s kinetic energy

A proton (m = 1.67 x 10^-27 kg) travels at a speed v = 0.9900c = 2.968 x 10⁸m/s. What is its kinetic energy?

According to a classical calculation, which is not correct, we would obtain:

K = 1/2mv² = ½ x (1.67 x 10^-27 kg) x (2.968 x 10⁸m/s)² = 7.355 x 10^-11 J

With relativistic correction the relativistic kinetic energy is equal to:

K = (ɣ – 1)mc²

where the Lorentz factor

ɣ = 7.089

therefore

K = 6.089 x (1.67 x 10^-27 kg) x (2.9979 x 10⁸m/s)² = 9.139 x 10^-10 J = 5.701 GeV

This is about 12 times higher energy as in the classical calculation. According to this relationship, an acceleration of a proton beam to 5.7 GeV requires energies that are in the order different.

See also:

Energy

What is Mechanical Energy

In physics, mechanical energy (E_mech) is the energy associated with the motion and position of an object usually in some force field (e.g. gravitational field). Mechanical energy (and also the thermal energy) can be separated into two categories, transient and stored. Transient energy is energy in motion, that is, energy being transferred from one place to another. Stored energy is the energy contained within a substance or object. Transient mechanical energy is commonly referred to as work. Stored mechanical energy exists in one of two forms: kinetic or potential:

• Potential energy. Potential energy, U, is defined as the energy stored in an object subjected to a conservative force. Common types include the gravitational potential energy of an object that depends on its mass and its distance from the center of mass of another object.
• Kinetic energy. The kinetic energy, K, is defined as the energy stored in an object because of its motion. It depends on the speed of an object and is the ability of a moving object to do work on other objects when it collides with them.

Conservation of Mechanical Energy

First the principle of the Conservation of Mechanical Energy was stated:

The total mechanical energy (defined as the sum of its potential and kinetic energies) of a particle being acted on by only conservative forces is constant.

See also: Conservation of Mechanical Energy

An isolated system is one in which no external force causes energy changes. If only conservative forces act on an object and U is the potential energy function for the total conservative force, then

E_mech = U + K

The potential energy, U, depends on the position of an object subjected to a conservative force.

It is defined as the object’s ability to do work and is increased as the object is moved in the opposite direction of the direction of the force.

The potential energy associated with a system consisting of Earth and a nearby particle is gravitational potential energy.

The kinetic energy, K, depends on the speed of an object and is the ability of a moving object to do work on other objects when it collides with them.

 K = ½ mv²

The above mentioned definition (E_mech = U + K) assumes that the system is free of friction and other non-conservative forces. The difference between a conservative and a non-conservative force is that when a conservative force moves an object from one point to another, the work done by the conservative force is independent of the path.

In any real situation, frictional forces and other non-conservative forces are present, but in many cases their effects on the system are so small that the principle of conservation of mechanical energy can be used as a fair approximation. For example the frictional force is a non-conservative force, because it acts to reduce the mechanical energy in a system.

Note that non-conservative forces do not always reduce the mechanical energy. A non-conservative force changes the mechanical energy, there are forces that increase the total mechanical energy, like the force provided by a motor or engine, is also a non-conservative force.

Block sliding down a frictionless incline slope

The 1 kg block starts out a height H (let say 1 m) above the ground, with potential energy mgH and kinetic energy that is equal to 0. It slides to the ground (without friction) and arrives with no potential energy and kinetic energy K = ½ mv². Calculate the velocity of the block on the ground and its kinetic energy.

E_mech = U + K = const

=> ½ mv² = mgH

=> v = √2gH = 4.43 m/s

=> K₂ = ½ x 1 kg x (4.43 m/s)² = 19.62 kg.m².s^-2 = 19.62 J

Pendulum

Assume a pendulum (ball of mass m suspended on a string of length L that we have pulled up so that the ball is a height H < L above its lowest point on the arc of its stretched string motion. The pendulum is subjected to the conservative gravitational force where frictional forces like air drag and friction at the pivot are negligible.

We release it from rest. How fast is it going at the bottom?

The pendulum reaches greatest kinetic energy and least potential energy when in the vertical position, because it will have the greatest speed and be nearest the Earth at this point. On the other hand, it will have its least kinetic energy and greatest potential energy at the extreme positions of its swing, because it has zero speed and is farthest from Earth at these points.

If the amplitude is limited to small swings, the period T of a simple pendulum, the time taken for a complete cycle, is:

where L is the length of the pendulum and g is the local acceleration of gravity. For small swings the period of swing is approximately the same for different size swings. That is, the period is independent of amplitude.

See also:

Energy

Energy Units

Energy is generally defined as the potential to do work or produce heat. This definition causes  the SI unit for energy is the same as the unit of work – the joule (J). Joule is a derived unit of energy and it is named in honor of James Prescott Joule and his experiments on the mechanical equivalent of heat. In more fundamental terms, 1 joule is equal to:

1 J = 1 kg.m²/s²

Since energy is a fundamental physical quantity and it is used in various physical and engineering branches, there are many energy units in physics and engineering.

• Joule (unit: J)
• Calorie (unit: cal)
• Britich Thermal Unit (unit: BTU)
• Foot-pound force (unit: ft.lbf)
• Kilowatt-hour (unit: kWh)
• Megawatt-day (unit: MWd)
• Electronvolt (unit: eV)

Joule – Energy Units

Joule (unit: J). Joule  is a derived unit of energy. It is equal to the energy transferred to an object when a force of one newton acts on that object in the direction of its motion through a distance of one metre.

• 1 joule = 0.239 Calories
• 1 joule = 9.48 x 10^-4 BTU
• 1 joule = 2.778 x 10^-7 kWh

Examples of Energy of 1 Joule

One joule in everyday life and in science corresponds to approximately:

• The kinetic energy of an object with mass 1 kg moving at √2 ≈ 1.4 m/s.
• The kinetic energy of a 50 kg object (e.g. human) moving very slowly – approximately 0.72 km/h.
• The energy required to lift a medium-size apple (100 g) 1 meter vertically from the surface of the Earth.
• The heat required to raise the temperature of 1 g of water by 0.24 °C.
• The heat required to evaporate of 0.00044 g of liquid water at 100°C.
• The amount of electricity required to light a 1 watt LED for 1 s.
• Is released by approximately 3.1⋅10¹⁰ fissions in a nuclear reactor.

See also:

Energy

Energy Units

Energy is generally defined as the potential to do work or produce heat. This definition causes  the SI unit for energy is the same as the unit of work – the joule (J). Joule is a derived unit of energy and it is named in honor of James Prescott Joule and his experiments on the mechanical equivalent of heat. In more fundamental terms, 1 joule is equal to:

1 J = 1 kg.m²/s²

Since energy is a fundamental physical quantity and it is used in various physical and engineering branches, there are many energy units in physics and engineering.

• Joule (unit: J)
• Calorie (unit: cal)
• Britich Thermal Unit (unit: BTU)
• Foot-pound force (unit: ft.lbf)
• Kilowatt-hour (unit: kWh)
• Megawatt-day (unit: MWd)
• Electronvolt (unit: eV)

Kilowatt to Kilowatthour – kW to kWh

Kilowatt-hour (unit: kWh). Kilowatt-hour is a derived unit of energy. It is used to measure energy, especially electrical energy in commercial applications.

One kilowatt-hour is equal to one kilowatt of power produced or consumed over a period of one hour (kilowatts multiplied by the time in hours).

1kW . h = 1kWh

The kilowatt hour is commonly used by electric utilities as a billing unit for energy delivered to consumers. 1kW . h = 1kWh . 3600s = 3600kWs = 3600kJ = 3600000J. One kilowatt-hour corresponds to the heat required to evaporate of 1.58 kg of liquid water at 100°C. A radio rated at 100 watts operating for 10 hours continuously uses one kilowatt hour.

• 1 kWh = 3.6 x 10⁶ J
• 1 kWh = 8.6 x 10⁵ cal
• 1 kWh = 3412 BTU

See also:

Energy

Energy Units

Energy is generally defined as the potential to do work or produce heat. This definition causes  the SI unit for energy is the same as the unit of work – the joule (J). Joule is a derived unit of energy and it is named in honor of James Prescott Joule and his experiments on the mechanical equivalent of heat. In more fundamental terms, 1 joule is equal to:

1 J = 1 kg.m²/s²

Since energy is a fundamental physical quantity and it is used in various physical and engineering branches, there are many energy units in physics and engineering.

• Joule (unit: J)
• Calorie (unit: cal)
• Britich Thermal Unit (unit: BTU)
• Foot-pound force (unit: ft.lbf)
• Kilowatt-hour (unit: kWh)
• Megawatt-day (unit: MWd)
• Electronvolt (unit: eV)

Example of Energies in Electronvolts

• Thermal neutrons are neutrons in thermal equilibrium with a surrounding medium of temperature 290K (17 °C or 62 °F). Most probable energy at 17°C (62°F) for Maxwellian distribution is 0.025 eV (~2 km/s).
• Thermal energy of a molecule is at room temperature about 0.04 eV.
• Approximately 1 eV corresponds to an infrared photon of wavelength 1240 nm.
• Visible light photons have energies in range 1.65 eV (red) – 3.26 eV (violet).
• The first resonance in n + ²³⁸U reaction is at 6.67 eV (energy of incident neutron), which corresponds to the first virtual level in ²³⁹U, has a total width of only 0.027 eV, and the mean life of this state is 2.4×10^-14s.
• Ionization energy of atomic hydrogen is 13.6 eV.
• Carbon-14 decays into nitrogen-14 through beta decay (pure beta decay). The emitted beta particles have a maximum energy of 156 keV, while their weighted mean energy is 49 keV.
• High energy diagnostic medical x-ray photons have kinetic energies of about 200 keV.
• Thallium 208, which is one of nuclides in the ²³²U decay chain, emits gamma rays of 2.6 MeV which are very energetic and highly penetrating.
• Typical kinetic energy of alpha particle from radioactive decay is about 5 MeV. It is caused by the mechanism of their production.
• The total energy released in a reactor is about 210 MeV per ²³⁵U fission, distributed as shown in the table. In a reactor, the average recoverable energy per fission is about 200 MeV, being the total energy minus the energy of the energy of antineutrinos that are radiated away.
• Cosmic ray can have energies of 1 MeV – 1000 TeV.

See also:

Energy

Energy Units

Energy is generally defined as the potential to do work or produce heat. This definition causes  the SI unit for energy is the same as the unit of work – the joule (J). Joule is a derived unit of energy and it is named in honor of James Prescott Joule and his experiments on the mechanical equivalent of heat. In more fundamental terms, 1 joule is equal to:

1 J = 1 kg.m²/s²

Since energy is a fundamental physical quantity and it is used in various physical and engineering branches, there are many energy units in physics and engineering.

• Joule (unit: J)
• Calorie (unit: cal)
• Britich Thermal Unit (unit: BTU)
• Foot-pound force (unit: ft.lbf)
• Kilowatt-hour (unit: kWh)
• Megawatt-day (unit: MWd)
• Electronvolt (unit: eV)

Electronvolt (unit: eV)

Electronvolt (unit: eV). Electronvolts are a traditional unit of energy particularly in atomic and nuclear physics. Electronvolt is equal to energy gained by a single electron when it is accelerated through 1 volt of electric potential difference. The work done on the charge is given by the charge times the voltage difference, therefore the work W on electron is: W = qV = (1.6 x 10^-19 C) x (1 J/C) = 1.6 x 10^-19 J. Since this is very small unit, it is more convenient to use multiples of electronvolts: kilo-electronvolts (keV), mega-electronvolts (MeV), giga-electronvolts (GeV) and so on. Since Albert Einstein showed that mass and energy are equivalent and convertible one into the other, the electronvolt is also a unit of mass. It is common in particle physics, where units of mass and energy are often interchanged, to express mass in units of eV/c², where c is the speed of light in vacuum (from E = mc²). For example, it can be said the proton has mass of 938.3 MeV, although strictly speaking it should be 938.3 MeV/c². For another example, an electron–positron annihilation occurs when a negatively charged electron and a positively charged positron (each with a mass of 0.511 MeV/c²) collide. When an electron and a positron collide, they annihilate resulting in the complete conversion of their rest mass to pure energy (according to the E=mc² formula) in the form of two oppositely directed 0.511 MeV gamma rays (photons).

e⁻ + e⁺ → γ + γ (2x 0.511 MeV)

• 1 eV = 1.603 x 10^-19 J
• 1 eV = 3.83 x 10^-20 cal
• 1 eV = 1.52 x 10^-22 BTU

Example of Energies in Electronvolts

• Thermal neutrons are neutrons in thermal equilibrium with a surrounding medium of temperature 290K (17 °C or 62 °F). Most probable energy at 17°C (62°F) for Maxwellian distribution is 0.025 eV (~2 km/s).
• Thermal energy of a molecule is at room temperature about 0.04 eV.
• Approximately 1 eV corresponds to an infrared photon of wavelength 1240 nm.
• Visible light photons have energies in range 1.65 eV (red) – 3.26 eV (violet).
• The first resonance in n + ²³⁸U reaction is at 6.67 eV (energy of incident neutron), which corresponds to the first virtual level in ²³⁹U, has a total width of only 0.027 eV, and the mean life of this state is 2.4×10^-14s.
• Ionization energy of atomic hydrogen is 13.6 eV.
• Carbon-14 decays into nitrogen-14 through beta decay (pure beta decay). The emitted beta particles have a maximum energy of 156 keV, while their weighted mean energy is 49 keV.
• High energy diagnostic medical x-ray photons have kinetic energies of about 200 keV.
• Thallium 208, which is one of nuclides in the ²³²U decay chain, emits gamma rays of 2.6 MeV which are very energetic and highly penetrating.
• Typical kinetic energy of alpha particle from radioactive decay is about 5 MeV. It is caused by the mechanism of their production.
• The total energy released in a reactor is about 210 MeV per ²³⁵U fission, distributed as shown in the table. In a reactor, the average recoverable energy per fission is about 200 MeV, being the total energy minus the energy of the energy of antineutrinos that are radiated away.
• Cosmic ray can have energies of 1 MeV – 1000 TeV.

See also:

Energy

Energy Units

Energy is generally defined as the potential to do work or produce heat. This definition causes  the SI unit for energy is the same as the unit of work – the joule (J). Joule is a derived unit of energy and it is named in honor of James Prescott Joule and his experiments on the mechanical equivalent of heat. In more fundamental terms, 1 joule is equal to:

1 J = 1 kg.m²/s²

Since energy is a fundamental physical quantity and it is used in various physical and engineering branches, there are many energy units in physics and engineering.

• Joule (unit: J)
• Calorie (unit: cal)
• Britich Thermal Unit (unit: BTU)
• Foot-pound force (unit: ft.lbf)
• Kilowatt-hour (unit: kWh)
• Megawatt-day (unit: MWd)
• Electronvolt (unit: eV)

Megawatt-day (unit: MWd)

Megawatt-day (unit: MWd).  Megawatt-day is a derived unit of energy. It is used to measure energy produced, especially in power engineering. One megawatt-day is equal to one megawatt of power produced by power plant over a period of one day (megawatts multiplied by the time in days). 1 MWd = 24,000 kWh. At nuclear power plants there are also gigawatt-days, because it approximately corresponds to energy produced by power plant over a period of one day. This unit (MWd) was also used to derive unit of fuel burnup. The most commonly used measure of fuel burnup is the fission energy release per unit mass of fuel. Therefore fuel burnup of nuclear fuel is normally have units of megawatt-days per metric tonne (MWd/MTU), where tonne refers to a metric ton of uranium metal (sometimes MWd/tU HM as Heavy Metal). In this field, the megawatt-day refers to the thermal power of the reactor, not the fraction which is converted to electricity. For example, for a typical nuclear reactor with a thermal power of 3000 MWth, about ~1000MWe of electrical power is generated in the generator. For example, a reactor with 100 000 kg of fuel operating at 3000MWth power level for 1000 days would have a burnup increase of 30,000 MWd/MTU. In words of fissions,  fissioning of about 1 g of U-235 produces about 1 MWd of thermal energy (see: Energy Release per Fission).

• 1 MWd = 8.64 x 10¹⁰ J
• 1 MWd = 2.06 x 10¹⁰ cal
• 1 MWd = 8.19 x 10⁷ BTU

See also:

Energy