Impulse
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2008-07-16T17:07:17Z
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robot Adding: [[simple:Impulse]]
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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]
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[[Category:Classical mechanics]]
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