With your additions, it probably could be a really neat mini game to have in a survival-crafting game... Game, so, it doesn’t have to be perfect.

But the axe could wobble a bit, depending on some combination of chopping skill and how tired your guy is (simulating shoulder pain and lower back pain). Number of hits required depends on character strength and how straight on the hits are.

I’m not sure how the game would track the pieces of various sizes, though. I guess this would just be for firewood (building wood might have to be handled separately) so maybe it would be fine to just calculate the volume of each slice and have it provide fuel based on that…