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Consider the situation above where two objects whose masses are M1 and M2 are moving toward each other with uniform speeds, V1 and V2 respectively, in collinear paths. The objects collide and subsequently separate (or not) with velocities V1' and V2'. One can engage Newton's second and third laws and apply reasoning shown at left.

m1v1 represents the momentum of block 1 before the collision; m2v2, the same for block 2. Together the right-hand sum represents the total momentum before the collision.

Similar statements on the left-hand side seem to identify all of the momentum in the system after the collision.The statement presented above suggests that in this event momentum is conserved, that is to say, the momentum that exists in the system after the collision is equal to the momentum in the system before the collision. Like the other laws in nature, this one is only good until some experiment shows that it is not valid. To date, none has been found and the law of conservation of momentum represents one of the fundamental rules at the heart of physics.

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Most interactions between objects are said t be Inelastic wherein momentum is conserved, but not kinetic energy. Note that this is not a violation of the law of conservation of energy. In inelasatic events, some KE may be converted to heat. KE is considered "lost" not because we cannot find it but rather because we cannot retrieve it. Examples of inelastic events include moving objects colliding and sticking together, or two objects moving (or not) and springing apart. A quick calculation of KE before and after the event will confirm this. We can account for the missing energy; we just cannot get to it easily.

Sometimes the question is phrased "what fraction of the original KE is lost?" The answer to this question involves building a fraction that has a numerator and a denominator. The syntax of the question can be used as a guide building this fraction. What follows the word "of" in the question goes into the denominator; what follows the word "is"goes to the numerator. As an example, what fraction of 4 is 3? "What fraction of the original kinetic energy is lost?"becomes a fraction (KE before - KE after) / KE before. While this fraction seems ungainly, substituting masses and velocities often yield a very managab,e answer

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The law of conservation of momemtum applies in all interactions (collisions and explosions) in one, two, or three dimensions (all means all). Additionally, If the proper circumstances are in place, a collision can occur where kinetic energy as well as momentum is conserved. Such a collision is elastic If such an event takes place, two other equations apply and are presented below. If objects M1 and M2 move with velocities V1 & V2, respectively, before the elastic collision, then the velocities of objects after the collision are given by


 For a derivation of these equations, click here


It is common (though not absolutely necessary) when using these equations to let V2 = zero. This allows the reader to focus attention on each object before and after the collision.

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 M 31

 M 32

 M 33
 For another look at collisions go to
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A hallmark of mechanics is the consideration of word problems. Useful relationships are published here in a page called 
EQUATIONS. The reader should consult this page before attempting the problems assigned.

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 This page was last reviewed 10/16/05