Mechanical energy - wikipedia Mechanical energy An example of a mechanical system : A satellite is orbiting the Earth influenced only by the conservative gravitational force ; its mechanical energy is therefore conserved. The satellite is accelerated towards the Earth with an acceleration perpendicular to the velocity. 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 and moving and physical energy. In the physical sciences, mechanical energy is the sum of potential energy and kinetic energy. It is the energy associated with the motion and position of an object. The principle of conservation of mechanical energy states that in an isolated system that is only subject to conservative forces, 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, nonconservative 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 ( dissipation ) and an increase in temperature was discovered by James Prescott Joule. Many devices are used to convert mechanical energy to or from other forms of energy, e.g. an electric motor converts electrical energy to mechanical energy, an electric generator converts mechanical energy into electrical energy and a steam engine converts heat energy to mechanical energy. Contents 1 General 2 Conservation of mechanical energy 2.1 Swinging pendulum 2.2 Irreversibilities 2.3 Satellite 3 Conversion 4 Distinction from other types 5 References 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. The kinetic energy which is also called the energy of motion : E m e c h a n i c a l = U + K ( displaystyle E_ ( mathrm ( mechanical ) ) = 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. If F represents the conservative force and x the position, the potential energy of the force between the two positions x and x is defined as the negative integral of F from x to x : U = − ∫ x 1 x 2 F → ⋅ d x → ( displaystyle 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. 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 : K = 1 2 m v 2 ( displaystyle K = ( 1 over 2 ) mv ^ ( 2 ) ) The principle of conservation of mechanical energy states that if a body or system is subjected only to conservative forces, the mechanical energy of that body or system remains constant. 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. Conservation of mechanical energy Play media MIT professor Walter Lewin demonstrating conservation of mechanical energy According to the principle of conservation of mechanical energy, the mechanical energy of an isolated system remains constant in time, as long as the system is free of friction and other non-conservative forces. 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. Though energy can not be created or destroyed in an isolated system, it can be converted to another form of energy. Swinging pendulum 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. Main article : Pendulum 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. Irreversibilities Main article : Irreversible process 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 comprise matter. This equivalence between mechanical energy and heat is especially important when considering colliding objects. In an elastic collision, mechanical energy is conserved -- the sum of the mechanical energies of the colliding objects is the same before and after the collision. After an inelastic collision, however, the mechanical energy of the system will have changed. Usually, the mechanical energy before the collision is greater than the mechanical energy after the collision. In inelastic collisions, some of the mechanical energy of the colliding objects is transformed into kinetic energy of the constituent particles. This increase in kinetic energy of the constituent particles is perceived as an increase in temperature. The collision can be described by saying some of the mechanical energy of the colliding objects has been converted into an equal amount of heat. Thus, the total energy of the system remains unchanged though the mechanical energy of the system has reduced. Satellite Main article : Vis - viva equation plot of kinetic energy K ( displaystyle K ), gravitational potential energy, U ( displaystyle U ) and mechanical energy E m e c h a n i c a l ( displaystyle E_ ( mathrm ( mechanical ) ) ) versus distance away from centre of earth, r at R = Re, R = 2 * Re, R = 3 * Re and lastly R = geostationary radius A satellite of mass m ( displaystyle m ) at a distance r ( displaystyle r ) from the centre of Earth possesses both kinetic energy, K ( displaystyle K ), ( by virtue of its motion ) and gravitational potential energy, U ( displaystyle U ), ( by virtue of its position within the Earth 's gravitational field ; Earth 's mass is M ( displaystyle M ) ). Hence, mechanical energy E m e c h a n i c a l ( displaystyle E_ ( mathrm ( mechanical ) ) ) of a satellite is given by E m e c h a n i c a l = U + K ( displaystyle E_ ( mathrm ( mechanical ) ) = U + K ) E m e c h a n i c a l = − G M m r + 1 2 m v 2 ( displaystyle E_ ( mathrm ( mechanical ) ) = - G ( \frac ( Mm ) ( r ) ) + ( \frac ( 1 ) ( 2 ) ) mv ^ ( 2 ) ) If the satellite is in circular orbit, the energy conservation equation can be further simplified into E m e c h a n i c a l = − G M m 2 r ( displaystyle E_ ( mathrm ( mechanical ) ) = - G ( \frac ( Mm ) ( 2r ) ) ) since in circular motion, Newton 's 2nd Law of motion can be taken to be G M m r 2 = m v 2 r ( displaystyle G ( \frac ( Mm ) ( r ^ ( 2 ) ) ) = ( \frac ( mv ^ ( 2 ) ) ( r ) ) ) Conversion Today, many technological devices convert 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. A generator converts mechanical energy into electrical energy. A hydroelectric powerplant converts the mechanical energy of water in a storage dam into electrical energy. 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. A steam engine converts the heat energy of steam into mechanical energy. A turbine converts the kinetic energy of a stream of gas or liquid into mechanical energy. Distinction 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. Nuclear energy is energy stored in interactions between the particles in the atomic nucleus and is studied in nuclear physics. Electromagnetic energy is in the form of electric charges, magnetic fields, and photons. It is studied in electromagnetism. Various forms of energy in quantum mechanics ; e.g., the energy levels of electrons in an atom. References Notes Jump up ^ 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 therefore is internal and in the whole body. '' Jump up ^ 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. Citations ^ Jump up to : Wilczek, Frank ( 2008 ). `` Conservation laws ( physics ) ''. AccessScience. McGraw - Hill Companies. Retrieved 2011 - 08 - 26. ^ Jump up to : `` mechanical energy ''. The New Encyclopædia Britannica : Micropædia : Ready Reference. 7 ( 15th ed. ). 2003. access - date = requires url = ( help ) Jump up ^ Newton 1999, p. 409 Jump up ^ `` Potential Energy ''. Texas A&M University -- Kingsville. Retrieved 2011 - 08 - 25. Jump up ^ Brodie 1998, pp. 129 -- 131 Jump up ^ Rusk, Rogers D. ( 2008 ). `` Speed ''. AccessScience. McGraw - Hill Companies. Retrieved 2011 - 08 - 28. Jump up ^ Rusk, Rogers D. ( 2008 ). `` Velocity ''. AccessScience. McGraw - Hill Companies. Retrieved 2011 - 08 - 28. Jump up ^ Brodie 1998, p. 101 Jump up ^ Jain 2009, p. 9 Jump up ^ Jain 2009, p. 12 Jump up ^ Department of Physics. `` Review D: Potential Energy and the Conservation of Mechanical Energy '' ( PDF ). Massachusetts Institute of Technology. Retrieved 2011 - 08 - 03. Jump up ^ Resnick, Robert and Halliday, David ( 1966 ), Physics, Section 8 - 3 ( Vol I and II, Combined edition ), Wiley International Edition, Library of Congress Catalog Card No. 66 - 11527 Jump up ^ E. Roller, Duane ; Leo Nedelsky ( 2008 ). `` Conservation of energy ''. AccessScience. McGraw - Hill Companies. Retrieved 2011 - 08 - 26. Jump up ^ `` James Prescott Joule ''. Scientists : Their Lives and Works. Gale. 2006. access - date = requires url = ( help ) as cited on `` Student Resources in Context ''. Gale. Retrieved 2011 - 08 - 28. Jump up ^ Schmidt, Paul W. ( 2008 ). `` Collision ( physics ) ''. AccessScience. McGraw - Hill Companies. Retrieved 2011 - 09 - 03. Jump up ^ 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. access - date = requires url = ( help ) as cited on `` Student Resources in Context ''. Gale. Retrieved 2011 - 09 - 07. Jump up ^ Lerner, K. Lee ; Lerner, Brenda Wilmoth, eds. ( 2008 ). `` Electric motor ''. The Gale Encyclopedia of Science ( 4th ed. ). Detroit : Gale. access - date = requires url = ( help ) as cited on `` Student Resources in Context ''. Gale. Retrieved 2011 - 09 - 07. Jump up ^ `` Electric motor ''. U * X * L Encyclopedia of Science. U * X * L. 2007. access - date = requires url = ( help ) as cited on `` Student Resources in Context ''. Gale. Retrieved 2011 - 09 - 07. Jump up ^ `` Generator ''. U * X * L Encyclopedia of Science. U * X * L. 2007 - 07 - 16. access - date = requires url = ( help ) as cited on `` Student Resources in Context ''. Gale. Retrieved 2011 - 10 - 09. Jump up ^ `` Hydroelectric Power ''. Water Encyclopedia. Retrieved 2013 - 08 - 23 Jump up ^ Lerner, K. Lee ; Lerner, Brenda Wilmoth, eds. ( 2008 ). `` Internal combustion engine ''. The Gale Encyclopedia of Science ( 4th ed. ). Detroit : Gale. access - date = requires url = ( help ) as cited on `` Student Resources in Context ''. Gale. Retrieved 2011 - 10 - 09. Jump up ^ `` Steam engine ''. U * X * L Encyclopedia of Science. U * X * L. 2007 - 07 - 16. access - date = requires url = ( help ) as cited on `` Student Resources in Context ''. Gale. Retrieved 2011 - 10 - 09. Jump up ^ Lerner, K. Lee ; Lerner, Brenda Wilmoth, eds. ( 2008 ). `` Turbine ''. The Gale Encyclopedia of Science ( 4th ed. ). Detroit : Gale. access - date = requires url = ( help ) as cited on `` Student Resources in Context ''. Gale. Retrieved 2011 - 10 - 09. Jump up ^ Atkins, Peter W. ( 2008 ). `` Chemical energy ''. AccessScience. McGraw - Hill Companies. Retrieved 2011 - 10 - 17. Jump up ^ Duckworth, Henry E. ; Wilkinson, D.H. ( 2008 ). `` Nuclear binding energy ''. AccessScience. McGraw - Hill Companies. Retrieved 2011 - 10 - 17. Jump up ^ Hartwig, William H. ( 2008 ). `` Electrical energy measurement ''. AccessScience. McGraw - Hill Companies. Retrieved 2011 - 10 - 17. Jump up ^ Smythe, William R. ( 2008 ). `` Electromagnetic radiation ''. AccessScience. McGraw - Hill Companies. Retrieved 2011 - 10 - 17. Jump up ^ Gerjuoy, Edward ( 2008 ). `` Quantum mechanics ''. AccessScience. McGraw - Hill Companies. Retrieved 2011 - 10 - 17. Jump up ^ March - Russell, John ( 2008 ). `` Energy level ( quantum mechanics ) ''. AccessScience. McGraw - Hill Companies. Retrieved 2011 - 10 - 17. Bibliography Brodie, David ; Brown, Wendy ; Heslop, Nigel ; Ireson, Gren ; Williams, Peter ( 1998 ). Terry Parkin, eds. Physics. Addison Wesley Longman Limited. ISBN 978 - 0 - 582 - 28736 - 5. CS1 maint : Uses editors parameter ( link ) Jain, Mahesh C. ( 2009 ). Textbook of Engineering Physics, Part I. New Delhi : PHI Learning Pvt. Ltd. ISBN 978 - 81 - 203 - 3862 - 3. Retrieved 2011 - 08 - 25. Newton, Isaac ( 1999 ). I. Bernard Cohen, Anne Miller Whitman, eds. The Principia : mathematical principles of natural philosophy. United States of America : University of California Press. ISBN 978 - 0 - 520 - 08816 - 0. CS1 maint : Uses editors parameter ( link ) Energy Fundamental concepts Energetics Energy Units Energy system Energy transformation Mass Mass -- energy equivalence Power Thermodynamics Laws of thermodynamics Exergy Forms Kinetic Potential Mechanical Electric Magnetic Gravitational Chemical Ionization Nuclear Chromodynamic Elastic Mechanical wave Sound wave Radiant Rest Thermal Energy carriers Enthalpy Fuel fossil fuel Heat Work Electricity Battery Capacitor Primary energy Fossil fuel Coal Petroleum Natural gas Gravitational energy Nuclear fuel Natural uranium Radiant energy Solar Wind Bioenergy Hydropower Marine energy Geothermal Energy system components Energy engineering Oil refinery Fossil - fuel power station Cogeneration Integrated gasification combined cycle Nuclear power Nuclear power plant Radioisotope thermoelectric generator Solar power Photovoltaic system Concentrated solar power Solar thermal energy Solar power tower Solar furnace Wind power Wind farm High - altitude wind power Hydropower Hydroelectricity Wave farm Tidal power Biomass Geothermal power Use and supply Energy consumption World energy consumption Energy security Energy conservation Efficient energy use Transport Agriculture Renewable energy Sustainable energy Energy policy Energy development Worldwide energy supply South America USA Mexico Canada Europe Asia Africa Australia Misc. Jevons 's paradox Carbon footprint Retrieved from `` https://en.wikipedia.org/w/index.php?title=Mechanical_energy&oldid=819055700 '' Categories : Energy ( physics ) Mechanics Hidden categories : Pages using citations with accessdate and no URL CS1 maint : Uses editors parameter Articles containing video clips Talk Contents About Wikipedia Беларуская Български Bosanski Català Čeština Dansk Eesti Ελληνικά Español Euskara فارسی Français Galego 한국어 Հայերեն हिन्दी Hrvatski Bahasa Indonesia Italiano עברית Қазақша Kiswahili Kreyòl ayisyen Latviešu Lietuvių Nederlands नेपाली 日本 語 Norsk Norsk nynorsk Polski Português Română Русский Scots Simple English Slovenčina Slovenščina Suomi Svenska తెలుగు ไทย Türkçe Українська Tiếng Việt 粵語 中文 Edit links This page was last edited on 7 January 2018, at 04 : 32. Text is available under the Creative Commons Attribution - ShareAlike License ; additional terms may apply. By using this site, you agree to the Terms of Use and Privacy Policy. Wikipedia ® is a registered trademark of the Wikimedia Foundation, Inc., a non-profit organization. About Wikipedia

Question: when is the mechanical energy of a system conserved
Answer: elastic collisions