If I cut a thing in two, are the two pieces together exactly the same size as the original?
Or to rephrase it: does a knife/scissors/etc just split something or does it remove something?
The term for the material removed to make a cut is kerf. You hear about it a lot with woodworking as not taking into account can lead to inaccuracies in the final dimensions of your materials.
I would think separating a material by passing another through it is cutting while separating materials with only force would be breaking if it happens along a length or tearing of it happens gradually from a single point.
A knife generally tears, it separates the material in front, causing it to tear ahead of the blade.
The CNC (computer controlled cutters) metals that slide into each other so tightly that you cannot see the seam, are created using 2 separate blocks of metal, one becomes the outer block and the other becomes the inner block, then they’re both polished together to appear seamless. There’s no practical way (as far as I know) to make significant cuts without losing or malforming some of the material (you can cut playdough without losing any of the mass, but it’s bunched up along the cut path.
My very old understanding of how materials behave
It will remove some amount of material when you cut.
If it is enough for anyone to care about is another question.
Or was the question what happens on a molecular level and if cutting is any different than sawing at that level?
If you shear (scissors) then there should be less loss, maybe some distortion though. If you saw, you lose the sawdust. if you slice (knife), it might be either way or a bit of both.
Most likely you lose something, whether it’s a loss that matters, that depends.
Or to rephrase it: does a knife/scissors/etc just split something or does it remove something?
So, solids aren’t really solid. Like, at an atomic level no two molecules are actually touching. Think of it like a magnet floating above another.
What you cut it with matters too, something insanely sharp like a medical grade obsidian blade wieled with skill is so sharp, it’s just going to separate the molecules. And remove very little material.
Try to cut a piece of paper in half with a baseball bat, and lot of material won’t be attached to either of the two biggest pieces. Because it’s a big blunt object.
I believe, chemically, molecules with a stronger bond push molecules with a weaker bond apart. And physically, the applied force over the affected area decides the amount and direction of the bonds being separated.
In most cases cutting causes a physical change not a chemical change.
I believe when they say chemically they are referencing, “at a molecular level”
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