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The law of conservation of energy is all around us as energy is transferred, not created or destroyed. Discover how with conservation of energy examples.

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Kinetic energy

KE, E k, K or T

SI unit

joule (J)

Derivations from
other quantities

E k = 1 / 2 m v ²
E k = E t + E r

Émilie du Châtelet (1706-1749) with a pair of compasses in her right hand. She was the first to publish the relation for kinetic energy . This means that an object with twice the speed hits four times - 2×2 - harder. (Portrait by Maurice Quentin de La Tour.)

In physics, the kinetic energy of an object is the form of energy that it possesses due to its motion.

In classical mechanics, the kinetic energy of a non-rotating object of mass m traveling at a speed v is .[2]

It can be shown that the kinetic energy of an object is equal to the work, force ( F) x displacement ( s), needed to achieve its stated velocity. Having gained this energy during its acceleration, the mass maintains this kinetic energy unless its speed changes. The same amount of work is done by the object when decelerating from its current speed to a state of rest.

The SI unit of kinetic energy is the joule, while the English unit of kinetic energy is the foot-pound.

In relativistic mechanics, is a good approximation of kinetic energy only when v is much less than the speed of light.

History and etymology

The adjective kinetic has its roots in the Greek word κίνησις kinesis, meaning "motion". The dichotomy between kinetic energy and potential energy can be traced back to Aristotle's concepts of actuality and potentiality.

The principle in classical mechanics that E ∝ mv ² was first developed by Gottfried Leibniz and Johann Bernoulli, who described kinetic energy as the living force, . Willem 's Gravesande of the Netherlands provided experimental evidence of this relationship in 1722. By dropping weights from different heights into a block of clay, Willem 's Gravesande determined that their penetration depth was proportional to the square of their impact speed. Émilie du Châtelet recognized the implications of the experiment and published an explanation.

The terms kinetic energy and work in their present scientific meanings date back to 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. 1849-1851. Rankine, who had introduced the term "potential energy" in 1853, and the phrase "actual energy" to complement it, later cites William Thomson and Peter Tait as substituting the word "kinetic" for "actual".

Energy occurs in many forms, including chemical energy, thermal energy, electromagnetic radiation, gravitational energy, electric energy, elastic energy, nuclear energy, and rest energy. These can be categorized in two main classes: potential energy and kinetic energy. Kinetic energy is the movement energy of an object. Kinetic energy can be transferred between objects and transformed into other kinds of energy.

Kinetic energy may be best understood by examples that demonstrate how it is transformed to and from other forms of energy. For example, a cyclist uses chemical energy provided by food to accelerate a bicycle to a chosen speed. On a level surface, this speed can be maintained without further work, except to overcome air resistance and friction. The chemical energy has been converted into kinetic energy, the energy of motion, but the process is not completely efficient and produces heat within the cyclist.

The kinetic energy in the moving cyclist and the bicycle can be converted to other forms. For example, the cyclist could encounter a hill just high enough to coast up, so that the bicycle comes to a complete halt at the top. The kinetic energy has now largely been converted to gravitational potential energy that can be released by freewheeling down the other side of the hill. Since the bicycle lost some of its energy to friction, it never regains all of its speed without additional pedaling. The energy is not destroyed; it has only been converted to another form by friction. Alternatively, the cyclist could connect a dynamo to one of the wheels and generate some electrical energy on the descent. The bicycle would be traveling slower at the bottom of the hill than without the generator because some of the energy has been diverted into electrical energy. Another possibility would be for the cyclist to apply the brakes, in which case the kinetic energy would be dissipated through friction as heat.

Like any physical quantity that is a function of velocity, the kinetic energy of an object depends on the relationship between the object and the observer's frame of reference. Thus, the kinetic energy of an object is not invariant.

Spacecraft use chemical energy to launch and gain considerable kinetic energy to reach orbital velocity. In an entirely circular orbit, this kinetic energy remains constant because there is almost no friction in near-earth space. However, it becomes apparent at re-entry when some of the kinetic energy is converted to heat. If the orbit is elliptical or hyperbolic, then throughout the orbit kinetic and potential energy are exchanged; kinetic energy is greatest and potential energy lowest at closest approach to the earth or other massive body, while potential energy is greatest and kinetic energy the lowest at maximum distance. Disregarding loss or gain however, the sum of the kinetic and potential energy remains constant.

Kinetic energy can be passed from one object to another. In the game of billiards, the player imposes kinetic energy on the cue ball by striking it with the cue stick. If the cue ball collides with another ball, it slows down dramatically, and the ball it hit accelerates as the kinetic energy is passed on to it. Collisions in billiards are effectively elastic collisions, in which kinetic energy is preserved. In inelastic collisions, kinetic energy is dissipated in various forms of energy, such as heat, sound and binding energy (breaking bound structures).

Flywheels have been developed as a method of energy storage. This illustrates that kinetic energy is also stored in rotational motion.

Several mathematical descriptions of kinetic energy exist that describe it in the appropriate physical situation. For objects and processes in common human experience, the formula ½mv² given by classical mechanics is suitable. However, if the speed of the object is comparable to the speed of light, relativistic effects become significant and the relativistic formula is used. If the object is on the atomic or sub-atomic scale, quantum mechanical effects are significant, and a quantum mechanical model must be employed.

Kinetic energy for non-relativistic velocity

Treatments of kinetic energy depend upon the relative velocity of objects compared to the fixed speed of light. Speeds experienced directly by humans are non-relativisitic; higher speeds require the theory of relativity.

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 1/2 the product of the mass and the square of the speed. In formula form:

where is the mass and is the speed (magnitude of the velocity) of the body. In SI units, mass is measured in kilograms, speed in metres per second, and the resulting kinetic energy is in joules.

For example, one would calculate the kinetic energy of an 80 kg mass (about 180 lbs) traveling at 18 metres per second (about 40 mph, or 65 km/h) as

When a person throws a ball, the person does work on it to give it speed as it leaves the hand. The moving ball can then hit something and push it, doing work on what it hits. The kinetic energy of a moving object is equal to the work required to bring it from rest to that speed, or the work the object can do while being brought to rest: net force × displacement = kinetic energy, i.e.,

Since the kinetic energy increases with the square of the speed, an object doubling its speed has four times as much kinetic energy. For example, a car traveling twice as fast as another requires four times as much distance to stop, assuming a constant braking force. As a consequence of this quadrupling, it takes four times the work to double the speed.

The kinetic energy of an object is related to its momentum by the equation:

where:

is 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:

is the mass of the body

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

The kinetic energy of any entity depends on the reference frame in which it is measured. However, the total energy of an isolated system, i.e. one in which energy can neither enter nor leave, does not change over time in the reference frame in which it is measured. Thus, the chemical energy converted to kinetic energy by a rocket engine is divided differently between the rocket ship and its exhaust stream depending upon the chosen reference frame. This is called the Oberth effect. But the total energy of the system, including kinetic energy, fuel chemical energy, heat, etc., is conserved over time, regardless of the choice of reference frame. Different observers moving with different reference frames would however disagree on the value of this conserved energy.

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

Derivation

Without vector calculus

The work W done by a force F on an object over a distance s parallel to F equals

Using Newton's Second Law

with m the mass and a the acceleration of the object and

the distance traveled by the accelerated object in time t, we find with for the velocity v of the object

With vector calculus

The work done in accelerating a particle with mass m during the infinitesimal time interval dt is given by the dot product of force F and the infinitesimal displacement d x

where we have assumed the relationship p = m v and the validity of Newton's Second Law. (However, also see the special relativistic derivation below.)

Applying the product rule we see that:

Therefore, (assuming constant mass so that dm = 0), we have,

Since this is a total differential (that is, it only depends on the final state, not how the particle got there), we can integrate it and call the result kinetic energy:

This equation states that the kinetic energy ( E k) is equal to the integral of the dot product of the momentum ( p) of a body and the infinitesimal change of the velocity ( v) of the body. It is assumed that the body starts with no kinetic energy when it is at rest (motionless).

Rotating bodies

If a rigid body Q is rotating about any line through the center of mass then it has rotational kinetic energy ( ) which is simply the sum of the kinetic energies of its moving parts, and is thus given by:

where:

(In this equation the moment of inertia must be taken about an axis through the center of mass and the rotation measured by ω must be around that axis; more general equations exist for systems where the object is subject to wobble due to its eccentric shape).

Kinetic energy of systems

A system of bodies may have internal kinetic energy due to the relative motion of the bodies in the system. For example, in the Solar System the planets and planetoids are orbiting the Sun. In a tank of gas, the molecules are moving in all directions. The kinetic energy of the system is the sum of the kinetic energies of the bodies it contains.

A macroscopic body that is stationary (i.e. a reference frame has been chosen to correspond to the body's center of momentum) may have various kinds of internal energy at the molecular or atomic level, which may be regarded as kinetic energy, due to molecular translation, rotation, and vibration, electron translation and spin, and nuclear spin. These all contribute to the body's mass, as provided by the special theory of relativity. When discussing movements of a macroscopic body, the kinetic energy referred to is usually that of the macroscopic movement only. However, all internal energies of all types contribute to a body's mass, inertia, and total energy.

Fluid dynamics

In fluid dynamics, the kinetic energy per unit volume at each point in an incompressible fluid flow field is called the dynamic pressure at that point.

Dividing by V, the unit of volume:

where is the dynamic pressure, and ρ is the density of the incompressible fluid.

Frame of reference

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 to 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.

The total kinetic energy of a system depends on the inertial frame of reference: it is the sum of the total kinetic energy in a center of momentum frame and the kinetic energy the total mass would have if it were concentrated in the center of mass.

This may be simply shown: let be the relative velocity of the center of mass frame i in the frame k. Since

Then,

However, let the kinetic energy in the center of mass frame, would be simply the total momentum that is by definition zero in the center of mass frame, and let the total mass: . Substituting, we get:[13]

Thus the kinetic energy of a system is lowest to center of momentum reference frames, i.e., frames of reference in which the center of mass is stationary (either the center of mass frame or any other center of momentum frame). In any different frame of reference, there is additional kinetic energy corresponding to the total mass moving at the speed of the center of mass. The kinetic energy of the system in the center of momentum frame is a quantity that is invariant (all observers see it to be the same).

Rotation in systems

It sometimes is convenient to split the total kinetic energy of a body into the sum of the body's center-of-mass translational kinetic energy and the energy of rotation around the center of mass ( rotational energy):

where:

Thus the kinetic energy of a tennis ball in flight is the kinetic energy due to its rotation, plus the kinetic energy due to its translation.

Relativistic kinetic energy

If a body's speed is a significant fraction of the speed of light, it is necessary to use relativistic mechanics to calculate its kinetic energy. In relativity, the total energy is given by the energy-momentum relation:

Here we use the relativistic expression for linear momentum: , where . with being an object's (rest) mass, speed, and c the speed of light in vacuum. Then kinetic energy is the total relativistic energy minus the rest energy:

At low speeds, the square root can be expanded and the rest energy drops out, giving the Newtonian kinetic energy.

Log of relativistic kinetic energy versus log relativistic momentum, for many objects of vastly different scales. The intersections of the object lines with the bottom axis approaches the rest energy. At low kinetic energy the slope of the object lines reflect Newtonian mechanics. As the lines approach the slope bends at the lightspeed barrier.

Derivation

Start with the expression for linear momentum , where . Integrating by parts yields

Since ,

is a constant of integration for the indefinite integral.

Simplifying the expression we obtain

is found by observing that when and , giving

resulting in the formula

This formula shows that the work expended accelerating an object from rest approaches infinity as the velocity approaches the speed of light. Thus it is impossible to accelerate an object across this boundary.

The mathematical by-product of this calculation is the mass-energy equivalence formula-the body at rest must have energy content

At a low speed ( v ≪ c), the relativistic kinetic energy is approximated well by the classical kinetic energy. This is done by binomial approximation or by taking the first two terms of the Taylor expansion for the reciprocal square root:

So, the total energy can be partitioned into the rest mass energy plus the non-relativistic kinetic energy at low speeds.

When objects move at a speed much slower than light (e.g. in everyday phenomena on Earth), the first two terms of the series predominate. The next term in the Taylor series approximation

is small for low speeds. For example, for a speed of 10 km/s (22,000 mph) the correction to the non-relativistic kinetic energy is 0.0417 J/kg (on a non-relativistic kinetic energy of 50 MJ/kg) and for a speed of 100 km/s it is 417 J/kg (on a non-relativistic kinetic energy of 5 GJ/kg).

The relativistic relation between kinetic energy and momentum is given by

This can also be expanded as a Taylor series, the first term of which is the simple expression from Newtonian mechanics:

This suggests that the formulae for energy and momentum are not special and axiomatic, but concepts emerging from the equivalence of mass and energy and the principles of relativity.

General relativity

Using the convention that

where the four-velocity of a particle is

and is the proper time of the particle, there is also an expression for the kinetic energy of the particle in general relativity.

If the particle has momentum

as it passes by an observer with four-velocity u obs, then the expression for total energy of the particle as observed (measured in a local inertial frame) is

and the kinetic energy can be expressed as the total energy minus the rest energy:

where v α is the ordinary velocity measured w.r.t. the coordinate system, we get

Thus for a stationary observer ( v = 0)

and thus the kinetic energy takes the form

Factoring out the rest energy gives:

This expression reduces to the special relativistic case for the flat-space metric where

In the Newtonian approximation to general relativity

where Φ is the Newtonian gravitational potential. This means clocks run slower and measuring rods are shorter near massive bodies.

Kinetic energy in quantum mechanics

In quantum mechanics, observables like kinetic energy are represented as operators. For one particle of mass m, the kinetic energy operator appears as a term in the Hamiltonian and is defined in terms of the more fundamental momentum operator . The kinetic energy operator in the non-relativistic case can be written as

Notice that this can be obtained by replacing by in the classical expression for kinetic energy in terms of momentum,

In the Schrödinger picture, takes the form where the derivative is taken with respect to position coordinates and hence

The expectation value of the electron kinetic energy, , for a system of N electrons described by the wavefunction is a sum of 1-electron operator expectation values:

where is the mass of the electron and is the Laplacian operator acting upon the coordinates of the i th electron and the summation runs over all electrons.

The density functional formalism of quantum mechanics requires knowledge of the electron density only, i.e., it formally does not require knowledge of the wavefunction. Given an electron density , the exact N-electron kinetic energy functional is unknown; however, for the specific case of a 1-electron system, the kinetic energy can be written as

where is known as the von Weizsäcker kinetic energy functional.

References

External links

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Kinetic energy KE, E k, K or T SI unit joule (J) Derivations fromother quantities E k = 1 / 2 m v 2 E k = E t + E r In physics, the kinetic energy of an object is the form of energy that it possesses due to its motion.

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What is the nuclear energy. How does a nuclear power plant work. History and nuclear accidents. Advantages and disadvantages of nuclear energy. Nuclear waste management.

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potential energy, stored energy that depends upon the relative position of various parts of a system. A spring has more potential energy when it is compressed or stretched. A steel ball has more potential energy raised above the ground than it has after falling to Earth. In the raised position it is capable of doing more work. Potential energy is a property of a system and not of an individual body or particle; the system composed of Earth and the raised ball, for example, has more potential energy as the two are farther separated.

Potential energy arises in systems with parts that exert forces on each other of a magnitude dependent on the configuration, or relative position, of the parts. In the case of the Earth-ball system, the force of gravity between the two depends only on the distance separating them. The work done in separating them farther, or in raising the ball, transfers additional energy to the system, where it is stored as gravitational potential energy.

Potential energy also includes other forms. The energy stored between the plates of a charged capacitor is electrical potential energy. What is commonly known as chemical energy, the capacity of a substance to do work or to evolve heat by undergoing a change of composition, may be regarded as potential energy resulting from the mutual forces among its molecules and atoms. Nuclear energy is also a form of potential energy.

The potential energy of a system of particles depends only on their initial and final configurations; it is independent of the path the particles travel. In the case of the steel ball and Earth, if the initial position of the ball is ground level and the final position is 10 feet above the ground, the potential energy is the same, no matter how or by what route the ball was raised. The value of potential energy is arbitrary and relative to the choice of reference point. In the case given above, the system would have twice as much potential energy if the initial position were the bottom of a 10-foot-deep hole.

Gravitational potential energy near Earth's surface may be computed by multiplying the weight of an object by its distance above the reference point. In bound systems, such as atoms, in which electrons are held by the electric force of attraction to nuclei, the zero reference for potential energy is a distance from the nucleus so great that the electric force is not detectable. In this case, bound electrons have negative potential energy, and those very far away have zero potential energy.

Potential energy may be converted into energy of motion, called kinetic energy, and in turn to other forms such as electric energy. Thus, water behind a dam flows to lower levels through turbines that turn electric generators, producing electric energy plus some unusable heat energy resulting from turbulence and friction.

Historically, potential energy was included with kinetic energy as a form of mechanical energy so that the total energy in gravitational systems could be calculated as a constant.

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Potential energy | Definition, Examples, & Facts

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potential energy, stored energy that depends upon the relative position of various parts of a system. A spring has more potential energy when it is compressed or stretched. A steel ball has more potential energy raised above the ground than it has after falling to Earth.

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This article was most recently revised and updated by

thermal energy, internal energy present in a system in a state of thermodynamic equilibrium by virtue of its temperature. Thermal energy cannot be converted to useful work as easily as the energy of systems that are not in states of thermodynamic equilibrium. A flowing fluid or a moving solid, for example, possesses energy that can be converted to work in some mechanical device, such as a windmill or a waterwheel, but the same fluid or solid in a thermodynamic equilibrium state having the same energy (as thermal energy) can do no work unless it is combined with another substance at a different temperature, as in a heat engine.

Kara Rogers.

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Thermal energy | Heat Transfer, Temperature & Kinetic Energy

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Thermal energy, internal energy present in a system in a state of thermodynamic equilibrium by virtue of its temperature. Thermal energy cannot be converted to useful work as easily as the energy of systems that are not in states of thermodynamic equilibrium. A flowing fluid or a moving solid, for

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Chemical energy is the potential of a chemical substance to undergo a chemical reaction to transform into other substances. Some examples of storage media of chemical energy include batteries, food, and gasoline. Breaking or making of chemical bonds involves energy, which may be either absorbed or evolved from a chemical system.

Energy that can be released or absorbed because of a reaction between a set of chemical substances is equal to the difference between the energy content of the products and the reactants, if the initial and final temperatures are the same. This change in energy can be estimated from the bond energies of the various chemical bonds in the reactants and products. It can also be calculated from , the internal energy of formation of the reactant molecules, and the internal energy of formation of the product molecules. The internal energy change of a chemical process is equal to the heat exchanged if it is measured under conditions of constant volume and equal initial and final temperature, as in a closed container such as a bomb calorimeter. However, under conditions of constant pressure, as in reactions in vessels open to the atmosphere, the measured heat change is not always equal to the internal energy change, because pressure-volume work also releases or absorbs energy. (The heat change at constant pressure is called the enthalpy change; in this case the enthalpy of reaction, if initial and final temperatures are equal).

Another useful term is the heat of combustion, which is the energy mostly of the weak double bonds of molecular oxygen released due to a combustion reaction and often applied in the study of fuels. Food is similar to hydrocarbon and carbohydrate fuels, and when it is oxidized to carbon dioxide and water, the energy released is analogous to the heat of combustion (though not assessed in the same way as a hydrocarbon fuel - see food 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 of molecular oxygen is converted to heat, and the same is the case with digestion of food metabolized in a biological organism. Green plants transform solar energy to chemical energy (mostly of oxygen) through the process known as photosynthesis, and electrical energy can be converted to chemical energy and vice versa 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. It is not a form of potential energy itself, but is more closely related to free energy. The confusion in terminology arises from the fact that in other areas of physics not dominated by entropy, all potential energy is available to do useful work and drives the system to spontaneously undergo changes of configuration, and thus there is no distinction between "free" and "non-free" potential energy (hence the one word "potential"). However, in systems of large entropy such as chemical systems, the total amount of energy present (and conserved by the first law of thermodynamics) of which this Chemical Potential Energy is a part, is separated from the amount of that energy- Thermodynamic Free Energy (which Chemical potential is derived from)-which (appears to) drive the system forward spontaneously as its entropy increases (in accordance with the second law).

References

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Chemical energy is the potential of a chemical substance to undergo a chemical reaction to transform into other substances. Some examples of storage media of chemical energy include batteries, food, and gasoline. Breaking or making of chemical bonds involves energy, which may be either absorbed or evolved from a chemical system.

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In a previous part of Lesson 1, it was said that work is done upon an object whenever a force acts upon it to cause it to be displaced. Work involves a force acting upon an object to cause a displacement. In all instances in which work is done, there is an object that supplies the force in order to do the work. If a World Civilization book is lifted to the top shelf of a student locker, then the student supplies the force to do the work on the book. If a plow is displaced across a field, then some form of farm equipment (usually a tractor or a horse) supplies the force to do the work on the plow. If a pitcher winds up and accelerates a baseball towards home plate, then the pitcher supplies the force to do the work on the baseball. If a roller coaster car is displaced from ground level to the top of the first drop of a roller coaster ride, then a chain driven by a motor supplies the force to do the work on the car. If a barbell is displaced from ground level to a height above a weightlifter's head, then the weightlifter is supplying a force to do work on the barbell. In all instances, an object that possesses some form of energy supplies the force to do the work. In the instances described here, the objects doing the work (a student, a tractor, a pitcher, a motor/chain) possess chemical potential energy stored in food or fuel that is transformed into work. In the process of doing work, the object that is doing the work exchanges energy with the object upon which the work is done. When the work is done upon the object, that object gains energy. The energy acquired by the objects upon which work is done is known as mechanical energy.
Mechanical energy is the energy that is possessed by an object due to its motion or due to its position. Mechanical energy can be either kinetic energy (energy of motion) or potential energy (stored energy of position). Objects have mechanical energy if they are in motion and/or if they are at some position relative to a zero potential energy position (for example, a brick held at a vertical position above the ground or zero height position). A moving car possesses mechanical energy due to its motion ( kinetic energy). A moving baseball possesses mechanical energy due to both its high speed ( kinetic energy) and its vertical position above the ground (gravitational potential energy). A World Civilization book at rest on the top shelf of a locker possesses mechanical energy due to its vertical position above the ground (gravitational potential energy). A barbell lifted high above a weightlifter's head possesses mechanical energy due to its vertical position above the ground (gravitational potential energy). A drawn bow possesses mechanical energy due to its stretched position (elastic potential energy).

Mechanical Energy as the Ability to Do Work

An object that possesses mechanical energy is able to do work. In fact, mechanical energy is often defined as the ability to do work. Any object that possesses mechanical energy - whether it is in the form of potential energy or kinetic energy - is able to do work. That is, its mechanical energy enables that object to apply a force to another object in order to cause it to be displaced.

Numerous examples can be given of how an object with mechanical energy can harness that energy in order to apply a force to cause another object to be displaced. A classic example involves the massive wrecking ball of a demolition machine. The wrecking ball is a massive object that is swung backwards to a high position and allowed to swing forward into building structure or other object in order to demolish it. Upon hitting the structure, the wrecking ball applies a force to it in order to cause the wall of the structure to be displaced. The diagram below depicts the process by which the mechanical energy of a wrecking ball can be used to do work.

A hammer is a tool that utilizes mechanical energy to do work. The mechanical energy of a hammer gives the hammer its ability to apply a force to a nail in order to cause it to be displaced. Because the hammer has mechanical energy (in the form of kinetic energy), it is able to do work on the nail. Mechanical energy is the ability to do work.

Another example that illustrates how mechanical energy is the ability of an object to do work can be seen any evening at your local bowling alley. The mechanical energy of a bowling ball gives the ball the ability to apply a force to a bowling pin in order to cause it to be displaced. Because the massive ball has mechanical energy (in the form of kinetic energy), it is able to do work on the pin. Mechanical energy is the ability to do work.

A dart gun is still another example of how mechanical energy of an object can do work on another object. When a dart gun is loaded and the springs are compressed, it possesses mechanical energy. The mechanical energy of the compressed springs gives the springs the ability to apply a force to the dart in order to cause it to be displaced. Because of the springs have mechanical energy (in the form of elastic potential energy), it is able to do work on the dart. Mechanical energy is the ability to do work.

A common scene in some parts of the countryside is a "wind farm." High-speed winds are used to do work on the blades of a turbine at the so-called wind farm. The mechanical energy of the moving air gives the air particles the ability to apply a force and cause a displacement of the blades. As the blades spin, their energy is subsequently converted into electrical energy (a non-mechanical form of energy) and supplied to homes and industries in order to run electrical appliances. Because the moving wind has mechanical energy (in the form of kinetic energy), it is able to do work on the blades. Once more, mechanical energy is the ability to do work.

The Total Mechanical Energy

As already mentioned, the mechanical energy of an object can be the result of its motion (i.e., kinetic energy) and/or the result of its stored energy of position (i.e., potential energy). The total amount of mechanical energy is merely the sum of the potential energy and the kinetic energy. This sum is simply referred to as the total mechanical energy (abbreviated TME).

TME = PE + KE

As discussed earlier, there are two forms of potential energy discussed in our course - gravitational potential energy and elastic potential energy. Given this fact, the above equation can be rewritten:

TME = PEgrav + PEspring + KE

The diagram below depicts the motion of Lee Ben Fardest (esteemed American ski jumper) as he glides down the hill and makes one of his record-setting jumps.

The total mechanical energy of Lee Ben Fardest is the sum of the potential and kinetic energies. The two forms of energy sum up to 50 000 Joules. Notice also that the total mechanical energy of Lee Ben Fardest is a constant value throughout his motion. There are conditions under which the total mechanical energy will be a constant value and conditions under which it will be a changing value. This is the subject of Lesson 2 - the work-energy relationship. For now, merely remember that total mechanical energy is the energy possessed by an object due to either its motion or its stored energy of position. The total amount of mechanical energy is merely the sum of these two forms of energy. And finally, an object with mechanical energy is able to do work on another object.

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In a previous part of Lesson 1, it was said that work is done upon an object whenever a force acts upon it to cause it to be displaced. Work involves a force acting upon an object to cause a displacement.

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Electrical energy is energy derived from electric potential energy or kinetic energy. When loosely used to describe energy absorbed or maybe delivered by an electrical circuit (for example, one provided by an electric power utility) "electrical energy" talks about energy which has been converted from electric potential energy.

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Gravitational energy is the potential energy a body with mass has in relation to another massive object due to gravity. It is potential energy associated with the gravitational field. Gravitational energy is dependent on the masses of two bodies, their distance apart and the gravitational constant ( G).

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In the case of a bow and arrow, when the archer does work on the bow, drawing the string back, some of the chemical energy of the archer's body is transformed into elastic potential energy in the bent limbs of the bow.

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In physics, energy is the quantitative property that must be transferred to an object in order to perform work on, or to heat, the object. Energy is a conserved quantity; the law of conservation of energy states that energy can be converted in form, but not created or destroyed.

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The watt is named after the Scottish inventor James Watt. This unit was proposed initially by C. William Siemens in August 1882 in his President's Address to the Fifty-Second Congress of the British Association for the Advancement of Science.

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The joule (; symbol: J) is a derived unit of energy in the International System of Units. It is equal to the energy transferred to (or work done on) 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 newton metre or N⋅m).

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The joule (; symbol: J) is a derived unit of energy in the International System of Units. It is equal to the energy transferred to (or work done on) 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 newton metre or N⋅m).

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According to Jammer, the term work was introduced in 1826 by the French mathematician Gaspard-Gustave Coriolis as "weight lifted through a height", which is based on the use of early steam engines to lift buckets of water out of flooded ore mines.