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h1. Impulse

{excerpt}The time integral of [force|force].  The net [external|external force] impulse acting on a [system|system] over a given time interval is equal to the system's change in [momentum|momentum].{excerpt}

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h3. {toggle-cloak:id=mot} Motivation for Concept

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Although some everyday [interactions|interaction] like [gravity|gravitation] and [friction|friction] result in stable [forces|force] whose effects can easily be analyzed with [dynamics|Point Particle Dynamics], many interactions are not steady.  Consider, for example, the difference between a push and a punch.  When you push something, you consciously use your muscles to apply a steady [force|force] to the target object.  For this reason, pushing a bowling ball or a bean bag feels much the same, apart from the fact that the bean bag will probably deform more in response to the [force].  When you punch something, however, you simply let your fist fly.  The [force|force] felt by the target object and the [reaction force|Newton's Third Law] exterted on your fist are the result of the impact of your moving fist with the object.  This impact is essentially out of your control.  The [force] exterted are not determined directly by your muscles (though the faster your fist is moving, the greater the force will tend to be), but rather it is principally determined by the properties of your hand and the target object.  Because of this fact, there is a dramatic difference between the results of punching a bean bag versus punching a bowling ball.

Such impact or collision forces are extremely common in everyday life.  Almost any sport will involve collisions.  Household activities like hammering nails or kneading dough require collisions.  Understanding collisions is also of great importance to car manufacturers.  

Unfortunately, the forces during a collision are very difficult to characterize.  They change extremely rapidly in time (the entire duration of a typical collision is measured in milliseconds), and they manner in which they change is stronly dependent on the material properties of the objects undergoing the collision.  Because of these complications, it is rare to see a detailed force profile for a collision.  Instead, collisions are usually described by an effect that is much more easily observed:  the resulting change in the motion of the participants.  The impulse delivered by a collision is one measure of this change.  

|!ball03.jpg!!ball04.jpg!!ball05.jpg!!ball06.jpg!!ball07.jpg!!ball08.jpg!|
|Photos taken with a high-speed digital camera showing the impact of a (new) tennis ball dropped from a height of 100 inches onto a wooden platform.\\The images shown are spaced by approximately 1 ms.\\Special thanks to James Bales at the [MIT Edgerton Center|http://web.mit.edu.ezproxyberklee.flo.org/edgerton] for helping Andrew Pawl to capture the image.\\For footage of tennis ball impacts at _much_ higher speeds see the [ITF website|http://www.itftennis.com/technical/].|
{note}Note that the center images are less blurry than the first and last.  Can you explain this?{note}
{info}The ball rebounds because it is elastic.  The deformation of the ball observed in the center image is not permanent.  The ball's structure causes it to return to its initial shape, and in the process it pushes itself off the ground.  If the ball were made of clay, the deformation would remain, and the ball would simply "splat" onto the ground.{info}

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