Impulse 211922 226056311 2008-07-16T17:07:17Z CarsracBot 6929011 robot Adding: [[simple:Impulse]] {{otheruses}} In [[classical mechanics]], an '''impulse''' is defined as the [[integral]] of a [[force]] with respect to [[time]]: :<math>\mathbf{I} = \int \mathbf{F}\, dt </math> where :'''I''' is impulse (sometimes marked '''J'''), :'''F''' is the force, and : ''dt'' is an [[infinitesimal]] amount of time. A simple derivation using [[Newton's second law]] yields: :<math>\mathbf{I} = \int \frac{d\mathbf{p}}{dt}\, dt </math> :<math>\mathbf{I} = \int d\mathbf{p} </math> :<math>\mathbf{I} = \Delta \mathbf{p} </math> where :'''p''' is momentum This is often called the '''impulse-momentum theorem'''.<ref>See, for example, section 9.2, page 257, of Serway (2004). </ref> As a result, an impulse may also be regarded as the change in [[momentum]] of an object to which a force is applied. The impulse may be expressed in a simpler form when both the force and the mass are constant: :<math>\mathbf{I} = \mathbf{F}\Delta t = m \Delta \mathbf{v} = \Delta\ p</math> where :'''F''' is the ''constant'' total net force applied, :<math>\Delta t</math> is the time interval over which the force is applied, :''m'' is the ''constant'' mass of the object, :Δ'''v''' is the change in velocity produced by the force in the considered time interval, and :mΔ'''v''' = Δ(m'''v''') is the change in linear momentum. However, it is often the case that one or both of these two quantities vary. In the technical sense, impulse is a physical quantity, not an event or force. However, the term "impulse" is also used to refer to a fast-acting force. This type of impulse is often ''idealized'' so that the change in momentum produced by the force happens with no change in time. This sort of change is a [[step function|step change]], and is not physically possible. However, this is a useful model for certain purposes, such as computing the effects of ideal collisions, especially in game [[physics engine]]s. Impulse has the same units and dimensions as momentum ([[kilogram|kg]] [[metre per second|m/s]] = [[newton|N]]·[[second|s]]). Using basic math, Impulse can be calculated using the equation: <math>\mathbf{F}t = \Delta\ p</math> <math> \Delta\ p </math> can be calculated, if initial and final velocities are known, by using "m'''v(f)''' - m'''v(i)'''" or otherwise known as "mv - mu" where :'''F''' is the ''constant'' total net force applied, :<math>t</math> is the time interval over which the force is applied, :''m'' is the ''constant'' mass of the object, :'''v''' is the final velocity of the object at the end of the time interval, and :'''u''' is the initial velocity of the object when the time interval begins. Hence: <math>\mathbf{F}t = mv - mu</math> ==See also== * [[Specific impulse]] * [[Momentum]] * [[Wave-particle duality]] defines an impulse for waves. The preservation of momentum at a collision is then called [[Nonlinear optics#Phase matching|phase matching]]. Applications include: ** [[Compton effect]] ** [[nonlinear optics]] ** [[Acousto-optic modulator]] ** [[Umklapp scattering]] ** electron [[phonon]] scattering ==Notes== {{reflist}} ==Bibliography== *{{cite book | author=Serway, Raymond A.; Jewett, John W. | title=Physics for Scientists and Engineers | edition=6th ed. | publisher=Brooks/Cole | year=2004 | id=ISBN 0-534-40842-7}} *{{cite book | author=Tipler, Paul | title=Physics for Scientists and Engineers: Mechanics, Oscillations and Waves, Thermodynamics | edition=5th ed. | publisher=W. H. Freeman | year=2004 | id=ISBN 0-7167-0809-4}} ==External links and references== *[http://www.rwc.uc.edu/koehler/biophys/2c.html Dynamics] <!--Categories--> [[Category:Physical quantity]] [[Category:Classical mechanics]] <!--Interwiki--> [[cs:Impuls síly]] [[de:Impuls#Kraftstoß]] [[es:Impulso]] [[gl:Impulso]] [[hr:Impuls sile]] [[it:Impulso (fisica)]] [[ms:Impuls]] [[nl:Stoot]] [[ja:力積]] [[pl:Popęd (fizyka)]] [[pt:Impulso]] [[sq:Impulsi]] [[simple:Impulse]] [[fi:Impulssi]] [[tk:Impuls]] [[uk:Імпульс сили]] [[zh:冲量]]