Mechanical energy

An example of a mechanical system: A satellite is orbiting the Earth only influenced by the conservative gravitational force and the mechanical energy is therefore conserved. The satellite is accelerated towards the Earth with an acceleration perpendicular to the orbit. This acceleration is represented by a green acceleration vector and the velocity is represented by a red velocity vector. Though the velocity is constantly changed with the direction of the vector because of the acceleration vector, the speed of the satellite is not since the magnitude of the velocity vector remains unchanged.

In physics, mechanical energy is the sum of potential energy and kinetic energy present in the components of a mechanical system. It is the energy associated with the motion and position of an object. The law of conservation of energy states that in an isolated system that is only subject to conservative forces, like the gravitational force, the mechanical energy is constant. If an object is moved in the opposite direction of a conservative net force, the potential energy will increase and if the speed (not the velocity) of the object is changed, the kinetic energy of the object is changed as well. In all real systems, however, non-conservative forces, like frictional forces, will be present, but often they are of negligible values and the mechanical energy's being constant can therefore be a useful approximation. In elastic collisions, the mechanical energy is conserved but in inelastic collisions, some mechanical energy is converted into heat. The equivalence between lost mechanical energy and an increase in temperature was discovered by James Prescott Joule.

Many modern devices, such as the electric motor or the steam engine, are used today to convert mechanical energy into other forms of energy, e.g. electrical energy, or to convert other forms of energy, like heat, into mechanical energy.

General

Energy is a scalar quantity and the mechanical energy of a system is the sum of the potential energy which is measured by the position of the parts of the system, and the kinetic energy which is also called the energy of motion:^[1][2]

$E_{mechanical}=U+K\,$

The law of conservation of mechanical energy states that if a body or system is subjected only to conservative forces, the total mechanical energy of that body or system remains constant.^[3] 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. On the contrary, when a non-conservative force acts upon an object, the work done by the non-conservative force is dependent of the path.^[4]

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.^{[nb 1][1]} If F represents the conservative force and x the position, the potential energy of the force between the two positions x₁ and x₂ is defined as the negative integral of F from x₁ to x₂:^[6]

$U = - \int\limits_{x_1}^{x_2} \vec{F}\cdot d\vec{x}$

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.^{[nb 2][10]} It is defined as one half the product of the object's mass with the square of its speed, and the total kinetic energy of a system of objects is the sum of the kinetic energies of the respective objects:^[1][11]

$K={1 \over 2}mv^2$

Conservation and interconversion of energy

Of the three great conservation laws of classical mechanics, the conservation of energy is regarded as the most important.^{[nb 3]} According to this law, the mechanical energy of an isolated system remains constant in time, as long as the system is free of all frictional forces, including eventual internal friction from collisions of the objects of the system. In any real situation, frictional forces and other non-conservative forces are always 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. Though energy cannot be created nor destroyed in an isolated system, it can be internally converted to any other form of energy.^[1][12]

A swinging pendulum with the velocity vector (green) and acceleration vector (blue). The magnitude of the velocity vector, the speed, of the pendulum is greatest in the vertical position and the pendulum is farthest from Earth in its extreme positions.

Thus, in a mechanical system like a swinging pendulum subjected to the conservative gravitational force where frictional forces like air drag and friction at the pivot are negligible, energy passes back and forth between kinetic and potential energy but never leaves the system. 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. However, when taking the frictional forces into account, the system loses mechanical energy with each swing because of the work done by the pendulum to oppose these non-conservative forces.^[2]

That the loss of mechanical energy in a system always resulted in an increase of the system's temperature has been known for a long time, but it was the amateur physicist James Prescott Joule who first experimentally demonstrated how a certain amount of work done against friction resulted in a definite quantity of heat which should be conceived as the random motions of the particles that matter is composed of. ^[13] This equivalence between mechanical energy and heat is especially important when considering colliding objects. In an elastic collision, mechanical energy is conserved; i.e. the sum of the kinetic energies of the colliding objects is the same before and after the collision. After an inelastic collision, however, the total mechanical energy of the system will have changed. Usually, the total mechanical energy after the collision is smaller than the initial total mechanical energy and the lost mechanical energy is converted into heat. However, the total mechanical energy can be greater after an inelastic collision if for example the collision causes an explosion which converts chemical energy into mechanical energy. In inelastic collisions, the smaller particles of which the colliding objects consist are shaken up and rattle around. These small-scale motions are perceived as an increase in heat and need kinetic energy which must be taken from the large-scale motion of the objects that are observed directly. Thus, the total energy of the system remains unchanged though the mechanical energy has been changed.^[1][14]

Conversion

Today, many technological devices converts mechanical energy into other forms of energy or vice versa. These devices can be placed in these categories:

• An electric motor converts electrical energy into mechanical energy.^[15][16][17]
• A generator converts mechanical energy into electrical energy.^[18]
• An internal combustion engine is a heat engine that obtains mechanical energy from chemical energy by burning fuel. From this mechanical energy, the internal combustion engine often generates electricity.^[19]
• A steam engine converts the heat energy of steam into mechanical energy.^[20]
• A turbine converts the kinetic energy of a stream of gas or liquid into mechanical energy.^[21]

Distinguished from other types

The classification of energy into different types often follows the boundaries of the fields of study in the natural sciences.

• Chemical energy is the kind of potential energy stored in chemical bonds and is studied in chemistry.^[22]
• Nuclear energy is energy stored in interactions between the particles in the atomic nucleus and is studied in nuclear physics.^[23]
• Electromagnetic energy is in the form of electric charges, magnetic fields, and photons. It is studied in electromagnetism.^[24][25]
• Various forms of energy in quantum mechanics; e.g., the energy levels of electrons in an atom.^[26][27]

References

Notes

1. ^ It is important to note that when measuring mechanical energy, an object is considered as a whole, as it is stated by Isaac Newton in his Principia: "The motion of a whole is the same as the sum of the motions of the parts; that is, the change in position of its parts from their places, and thus the place of a whole is the same as the sum of the places of the parts and thereore is internal and in the whole body."^[5]
2. ^ In physics, speed is a scalar quantity and velocity is a vector. In other words, velocity is speed with a direction and can therefore change without changing the speed of the object since speed is the numerical magnitude of a velocity.^[7][8][9]
3. ^ The other conservation laws are the conservation of linear momentum and the conservation of angular momentum.^[1]

Citations

1. ^ ^{a b c d e f} Wilczek, Frank (2008). "Conservation laws (physics)". AccessScience. McGraw-Hill Companies. http://www.accessscience.com/abstract.aspx?id=757423&referURL=http%3a%2f%2fwww.accessscience.com%2fcontent.aspx%3fsearchStr%3dConservation%2blaws%2b%28physics%29%26id%3d757423. Retrieved 2011-08-26. 
2. ^ ^{a b} "mechanical energy". The New Encyclopædia Britannica: Micropædia: Ready Reference. 7 (15th ed.). 2003. 
3. ^ Jain 2009, p. 12
4. ^ Department of Physics. "Review D: Potential Energy and the Conservation of Mechanical Energy" (PDF). Massachusetts Institute of Technology. http://web.mit.edu/8.02t/www/materials/modules/ReviewD.pdf. Retrieved 2011-08-03. 
5. ^ Newton 1999, p. 409
6. ^ "Potential Energy". Texas A&M University–Kingsville. http://physics.tamuk.edu/~suson/html/2325/PotentialEnergy.html. Retrieved 2011-08-25. 
7. ^ Brodie 1998, pp. 129–131
8. ^ Rusk, Rogers D. (2008). "Speed". AccessScience. McGraw-Hill Companies. http://accessscience.com/abstract.aspx?id=643200&referURL=http%3a%2f%2faccessscience.com%2fcontent.aspx%3fsearchStr%3dspeed%26id%3d643200. Retrieved 2011-08-28. 
9. ^ Rusk, Rogers D. (2008). "Velocity". AccessScience. McGraw-Hill Companies. http://accessscience.com/abstract.aspx?id=729500&referURL=http%3a%2f%2faccessscience.com%2fcontent.aspx%3fsearchStr%3dvelocity%26id%3d729500. Retrieved 2011-08-28. 
10. ^ Brodie 1998, p. 101
11. ^ Jain 2009, p. 9
12. ^ E. Roller, Duane; Leo Nedelsky (2008). "Conservation of energy". AccessScience. McGraw-Hill Companies. http://www.accessscience.com/abstract.aspx?id=157600&referURL=http%3a%2f%2fwww.accessscience.com%2fcontent.aspx%3fsearchStr%3dconservation%2bof%2benergy%26id%3d157600. Retrieved 2011-08-26. 
13. ^ "James Prescott Joule". Scientists: Their Lives and Works. Gale. 2006.  as cited on "Student Resources in Context". Gale. http://www.gale.cengage.com/InContext/resources.htm. Retrieved 2011-08-28. 
14. ^ Schmidt, Paul W. (2008). "Collision (physics)". AccessScience. McGraw-Hill Companies. http://accessscience.com/abstract.aspx?id=149000&referURL=http%3a%2f%2faccessscience.com%2fcontent.aspx%3fsearchStr%3dCollision%2b%28physics%29%26id%3d149000. Retrieved 2011-09-03. 
15. ^ Kopicki, Ronald J. (2003). "Electrification, Household". In Kutler, Stanley I.. Dictionary of American History. 3 (3rd ed.). New York: Charles Scribner's Sons. pp. 179–183.  as cited on "Student Resources in Context". Gale. http://www.gale.cengage.com/InContext/resources.htm. Retrieved 2011-09-07. 
16. ^ Lerner, K. Lee; Lerner, Brenda Wilmoth, ed (2008). "Electric motor". The Gale Encyclopedia of Science (4th ed.). Detroit: Gale.  as cited on "Student Resources in Context". Gale. http://www.gale.cengage.com/InContext/resources.htm. Retrieved 2011-09-07. 
17. ^ "Electric motor". U*X*L Encyclopedia of Science. U*X*L. 2007.  as cited on "Student Resources in Context". Gale. http://www.gale.cengage.com/InContext/resources.htm. Retrieved 2011-09-07. 
18. ^ "Generator". U*X*L Encyclopedia of Science. U*X*L. 2007-07-16.  as cited on "Student Resources in Context". Gale. http://www.gale.cengage.com/InContext/resources.htm. Retrieved 2011-10-09. 
19. ^ Lerner, K. Lee; Lerner, Brenda Wilmoth, ed (2008). "Internal combustion engine". The Gale Encyclopedia of Science (4th ed.). Detroit: Gale.  as cited on "Student Resources in Context". Gale. http://www.gale.cengage.com/InContext/resources.htm. Retrieved 2011-10-09. 
20. ^ "Steam engine". U*X*L Encyclopedia of Science. U*X*L. 2007-07-16.  as cited on "Student Resources in Context". Gale. http://www.gale.cengage.com/InContext/resources.htm. Retrieved 2011-10-09. 
21. ^ Lerner, K. Lee; Lerner, Brenda Wilmoth, ed (2008). "Turbine". The Gale Encyclopedia of Science (4th ed.). Detroit: Gale.  as cited on "Student Resources in Context". Gale. http://www.gale.cengage.com/InContext/resources.htm. Retrieved 2011-10-09. 
22. ^ Atkins, Peter W. (2008). "Chemical energy". AccessScience. McGraw-Hill Companies. http://accessscience.com/abstract.aspx?id=127100&referURL=http%3a%2f%2faccessscience.com%2fcontent.aspx%3fsearchStr%3dchemical%2benergy%26id%3d127100. Retrieved 2011-10-17. 
23. ^ Duckworth, Henry E.; Wilkinson, D. H. (2008). "Nuclear binding energy". AccessScience. McGraw-Hill Companies. http://accessscience.com/abstract.aspx?id=457950&referURL=http%3a%2f%2faccessscience.com%2fcontent.aspx%3fsearchStr%3dnuclear%2benergy%26id%3d457950. Retrieved 2011-10-17. 
24. ^ Hartwig, William H. (2008). "Electrical energy measurement". AccessScience. McGraw-Hill Companies. http://accessscience.com/abstract.aspx?id=218350&referURL=http%3a%2f%2faccessscience.com%2fcontent.aspx%3fsearchStr%3dElectrical%2benergy%2bmeasurement%26id%3d218350. Retrieved 2011-10-17. 
25. ^ Smythe, William R. (2008). "Electromagnetic radiation". AccessScience. McGraw-Hill Companies. http://accessscience.com/abstract.aspx?id=222700&referURL=http%3a%2f%2faccessscience.com%2fcontent.aspx%3fsearchStr%3dElectromagnetic%2bradiation%26id%3d222700. Retrieved 2011-10-17. 
26. ^ Gerjuoy, Edward (2008). "Quantum mechanics". AccessScience. McGraw-Hill Companies. http://accessscience.com/abstract.aspx?id=562900&referURL=http%3a%2f%2faccessscience.com%2fcontent.aspx%3fsearchStr%3dQuantum%2bmechanics%26id%3d562900. Retrieved 2011-10-17. 
27. ^ March-Russell, John (2008). "Energy level (quantum mechanics)". AccessScience. McGraw-Hill Companies. http://accessscience.com/abstract.aspx?id=232800&referURL=http%3a%2f%2faccessscience.com%2fcontent.aspx%3fsearchStr%3dEnergy%2blevel%2b%28quantum%2bmechanics%29%26id%3d232800. Retrieved 2011-10-17. 

Bibliography

• Brodie, David; Brown, Wendy; Heslop, Nigel; Ireson, Gren; Williams, Peter (1998). Terry Parkin. ed. Physics. Addison Wesley Longman Limited. ISBN 978-0582279844. 
• Jain, Mahesh C. (2009). Textbook of Engineering Physics, Part I. New Delhi: PHI Learning Pvt. Ltd.. ISBN 978-8120338623. http://books.google.com/books?id=DqZlU3RJTywC. Retrieved 2011-08-25. 
• Newton, Isaac (1999). I. Bernard Cohen, Anne Miller Whitman. ed. The Principia: mathematical principles of natural philosophy. United States of America: University of California Press. ISBN 978-0520088160.