Thread by @anderssandberg

#FridayPhysicsFun - @maartengm brought up cutting as a topic, and it is an interesting one. How do knives work? How sharp can you go? Is it the path to Royalty?

https://twitter.com/maartengm/status/1449441341159653384

A knife is nearly a wedge. Wedges, one of the six simple machines, work (1) as a double incline, spreading out the splitting force over a long distance, and (2) by focusing the pushing force onto a thin edge. hyperphysics.phy-astr.gsu.edu/hbase/Mechanic…

The amplification of force, the mechanical advantage, is 1/tan(α) where α is the tip angle. Make α approach zero and very little force is needed to separate the target.
en.wikipedia.org/wiki/Mechanica…

In a plastic material most force is used to deform the material, which pushes back. Work goes into deformation. In a brittle material cutting creates a fracture that may race ahead of the blade. The work done goes into the surface energy of the crack.

A knife also cuts by slicing, especially in soft materials where pushing just squishes them. This induces a shear force that can tear the material. Bread knifes and saws are serrated to boost this effect. physics.aps.org/articles/v5/139
journals.aps.org/prl/abstract/1…

Incidentally, this is why curved swords are effective: the shape guarantees more movement along the target when slicing (and a small initial strike region). Thicker blades can be stronger but are less sharp.
claireryanauthor.com/blog/2016/6/6/…

Scissors cut by exerting a lot of shear force on things caught between the blades, amplified by the lever design. Cheap scissors mostly use shear, while quality ones also have good blades.
en.wikipedia.org/wiki/Scissors#…

One of my favourite slicers is the Knife-Edge Scanning Microscope (KESM) that uses a diamond edge to slice tissue while shining light through the edge to a sensor, acting as a simultaneous scanner. It can do 1 μm slices. en.wikipedia.org/wiki/Knife-edg…
ncbi.nlm.nih.gov/pmc/articles/P…

The sharpest blade in use is ancient: obsidian, natural volcanic glass. Standard razor blades have edges 30-60 nm wide, while obsidian blades go down to 3 nm. edition.cnn.com/2015/04/02/hea…

In addition, their edges are smooth rather than jagged like steel. Steel is composed of small crystals, so when it fractures it will have a serrated pattern following the crystal joins. Obsidian is amorphous so when it cracks the crack just follows the lines of stress.

A smooth blade that is finer than a cell (and some macromolecules) makes for very effective cutting with less scarring. europepmc.org/article/med/84…

The problem is that obsidian is hard and brittle, so it easily fractures if there is any lateral stress. Not so good in surgery. Maybe desirable in a weapon. But the elasticity of metal scalpels makes them last much longer.
en.wikipedia.org/wiki/Macuahuitl

Still, razors are dulled by human hair too. Apparently, the hair can trigger formation of microcracks (presumably between crystals) that lead to chipping.
news.mit.edu/2020/why-shavi…
science.org/doi/full/10.11…

The sharpest imagined blade is the monofiliament whip beloved by cyberpunk fiction: super-strong, a single molecule thick. (Gibson may have popularized it in the short story Johnny Mnemonic 1981, but Randall Garrett used it first, in 1963)
en.wikipedia.org/wiki/Monomolec…

The problem is that it is too fine: a 0.4 nm wire cutting through a 4 nm cell membrane will push molecules apart but they will happily rejoin behind it. Especially since they move faster than the wire. I would not be surprised if collagen chains broke & rejoined after the wire.

It might locally cause dislocations in the crystal structure of metal, but as steel shows, imperfect metal is strong too. I suspect it would just push through, leaving the metal lattice to realign behind.

I think the sharpest cut would be from cosmic strings, hypothetical 1D topological defects in field theories. They would be about 1 fm across. scholarpedia.org/article/Cosmic… guava.physics.uiuc.edu/~nigel/courses…

Isn't that too thin to cut? Maybe not, since their enormous mass causes a deficit angle in spacetime: passing through an object it would either separate or push together matter by that angle. Especially negative mass strings would be awesome knives.

They would be almost as sharp as Aunt Maya's lack of sword in the epic webcomic Kill Six Billion Demons. killsixbilliondemons.com/comic/wielder-…