How is it possible that momentum is conserved in a collision while the total kinetic energy goes down? Intuitively it seems as if the total kinetic energy in the system goes down, momentum should go down as well.
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Related: http://physics.stackexchange.com/questions/92051/how-can-momentum-but-not-energy-be-conserved-in-an-inelastic-collision – SNB Nov 02 '16 at 17:32
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Keep in mind that kinetic energy is a scalar, which can not be negative, while momentum is a vector. There is only one way for the total kinetic energy of a system to be zero - all the parts must have a kinetic energy of zero i.e. nothing is moving. On the other hand, since momentum is a vector, it's quite possible a system could have a total momentum of zero while two or more of the parts are moving.
Consider a simple setup with two objects of equal mass and speed moving towards each other. The total momentum of this system is zero. How can it go down?
M. Enns
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$F_{internal}+ F_{external} = \frac{dp}{dt}$ but according to Newton's third laws the sum of the internal forces is zero. This leaves the external forces. If the system is closed then the the sum of external forces is zero and thus we have $0 = \frac{dp}{dt} \implies p = \text{ some constant} $. Conservation of momentum is related to the fact, that in introductory courses, we consider closed systems and then it follows momentum is conserved regardless of whether the collision is elastic or not.
Secondly, kinetic energy is only one of the forms of energy that you care about. It can be converted to other forms on energy even in a closed system. All that matters is that the total energy is conserved.
Amara
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