Note that the fact that these two equations are different explains why [Newton’s Cradle](https://en.wikipedia.org/wiki/Newton%27s_cradle) works the way it does. The only way to conserve both momentum and kinetic energy is to also conserve mass, because both *v* and *v*^2 are involved. That’s why, if you drop one ball on one end, one ball bounces out the other, and not two or more balls at a lower speed.
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