Wednesday, May 2, 2018

newtonian mechanics - Kinetic energy and momentum conservation in an explosion?


My physics book says, "A firecracker sliding on ice has the same total momentum before and after it explodes." I understand this part. This is because of Newton's 3rd law, and no external forces. This is what I really don't get. "The same, however, is not true of a system's kinetic energy. Energetically, that firecracker is very different after it explodes; internal potential energy has become kinetic energy of fragments." It goes on to say, "Nevertheless, the centre-of-mass concept remains useful in categorizing the kinetic energy associated with a system of particles."


How is it that the kinetic energy increased but momentum stayed the same? My problem lies within the equation $K = \frac{1}{2}mv^2$ and $p= mv$.


If kinetic energy increased doesn't that mean that the velocities increased as well? How else would $K$ become more positive? And since $K$ increased $v$ increased and thus $p=mv$ must increase?




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