Practical tools post-collapse: Axes and Hatchets
An axe or hatchet is a good way of cutting wood. There are many kinds. Here's a post on their types and uses.
Cutting down a tree is tough. It's not easy work, but why would we expect that something that took decades or even hundreds of years to grow be simple to chop down.
Let's assume the tree is already down. It fell down in a storm, perhaps a long time ago, and we want to harvest it. The actual cutting of a tree is technical based upon it's weight, likely direction of travel, and length.
There are reasons we mostly want to harvest trees this way. First we don't indiscriminately cut down something which is preventing soil erosion. It may be producing fruit or nuts or medicines. It take an enormous amount of time to replace it. It's producing oxygen.
The reason most people don't think about is accidents. Accidents happened all the time from a tree falling a different way because someone didn't or couldn't accurately predict how it was going to fall. Should they use poor technique, a tree can twist and then fall quite differently. The lay of the land will certainly affect the direction. The weight from moisture will change the fall, especially if icy. If you have an injured person as a cost of cutting down a tree then it can be horrific.
Trees are full of resin. When a new tree is cut down, the axes, hatchets, and saws slow down their cutting action from the natural fluids produced from the sap and the wood. It will dull them. Your saw will fill up faster from the resin and sawdust. The longer it seasons from being down for a time, the easier it is to cut. It also will get somewhat lighter, and in a post-collapse, that's definitely an issue.
Since the wood must season anyway, even after cutting, that's some consideration too for burning and other uses. It takes a long long time to dry naturally since it's raining. Unless you have heat, a good pole barn, and time to commit to cutting/hauling/stacking/drying you're not going to have lots of seasoned lumber to draw from.
What is the cutting tool made to do? Using it for something other than its intended use will almost always mean a much longer amount of time to commit to it, and time is your enemy. You can't make it up, and if you waste time, something else didn't get accomplished. Many a craftsman has had this conversation pre-collapse because there's not an endless amount of free-time for projects. Post-collapse, it's an even bigger issue as routine jobs will fill most days.
Use this for splitting kindling and cutting off a small limb. It works in a short controlled burst(s). It can also be used as a weapon. It can also be used to drive in small stakes (for many uses besides a tent). It's extremely valuable and probably carried often on your homestead post-collapse.
This is a medium do-it-all tool. Wailing it to split wood is foolish and will break ax handles. Not a big deal today to replace, but still expensive. Try shaping an axe handle sometime, and then you'll protect that baby like it's fragile. You sure will hate breaking it post-collapse.
This is a heavier axe meant for heavy duty work. I'll bet if you have to limit your budget (99% of us), you'll buy this and not a forest axe.
Hands-down easier for splitting wood, but useless for anything else. Only works well if the splitting log is elevated to by being placed waist high on a sturdy platform (like a tree stump). Committing to going through the wood, not just making contact, a satisfying split will result. It is Zen-like and relaxing and warms you up. On very cold days, splitting is more difficult if your woodpile is wet and gets icy. Foolish. Cover it with a tarp. Split a lot to save time on bad days. Bringing in wood means possible termite infestation.
They can be quite heavy. Pick one suited for your strength and swing. The length of one's arm adds leverage. On a side note, an old proof of manliness is lifting a sledgehammer with one hand and touching your nose with the head of it. The ones with dexterity, timing, some strength, and arm length can do it easier and better. The same principle applies with maul weight.