Unfortunately, kinetic energy is the energy something contains due to velocity... as velocity drops by half, energy drops at the same 4-times rate. A lighter object looses velocity much faster when it meets resistance... such as an ax or maul striking wood. An example of this is demonstrated by ballistics... it's possible to send a lighter bullet from the muzzle at a much higher velocity (and it has a higher kinetic energy at launch). But both bullets meet air resistance as soon as they are launched, and the lighter bullet slows much faster... momentum causes the heavier bullet to lose less relative velocity. At some point down range, the heavier bullet will be traveling faster than the lighter bullet... and it now holds the higher kinetic energy. There's a bit more to it than that... but I believe you see my point.
Kinetic energy is the measure of energy contained by a moving object only at that moment in time (due to it's velocity at that brief moment).
Momentum (p=mv), on the other hand, is a measure of an object's ability to retain energy as it meets resistance.
That's why a light splitting ax works well for straight grained, relatively easy to split wood... it only needs to impart that energy for a relatively brief moment in time (before it loses most of that energy).
But for tough to split wood, even though it contains less energy at the moment of strike, the maul will impart more energy over the length of time needed to complete the split (because it retains more of its energy longer during resistance).
It flat ain't as simple as doing a bit of multiplication and making such claims as yours... there's much more to it.
Follow-through, follow-through, follow-through...
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