So I’ve been thinking about the feasibility of cutting stuff with a thin wire. As the thickness of the wire goes to zero, and the tensile strength goes correspondingly up, does the effort required for cutting actually go to zero?
It seems to me that it can’t go to exactly zero, because you still need to counteract whatever forces were holding the material together. But does it go to a small value or a large value, in the case of cutting a strong material like bone? Say, if we tried using a thin wire to decapitate a person standing up, would they actually get decapitated, or would they just fall over?
Seems to me the force needed to penetrate tracks the diameter, but the strength tracks the area of the cross-section. That is, decrease the thickness by N and it decreases the force needed by N but the strength by N squared. Below a critical thickness, the wire would just break. Spiderwebs don’t slice you up if you run into them.
There is nonzero finite surface energy involved in cleaving an object in two, which you need to impart (minimum applied force). But for a living thing the minimum would be low. And you can prevent falling over by using a circular wire that shrinks (or 2 or more wires arranged symmetrically) to counter any pushing non-cutting forces
The Wikipedia page on surface energy gives values in the hundreds to thousands of mJ/m^2 for solids. I haven’t a clue where meat and bone would fall in that table, and I haven’t been able to find out with five minutes of Google, but even if we assume they’re on the high side we’re not talking particularly high total energies.
(Tangentially, “surface energy of meat” is one of the better phrases I’ve Googled lately.)
So I’ve been thinking about the feasibility of cutting stuff with a thin wire. As the thickness of the wire goes to zero, and the tensile strength goes correspondingly up, does the effort required for cutting actually go to zero?
It seems to me that it can’t go to exactly zero, because you still need to counteract whatever forces were holding the material together. But does it go to a small value or a large value, in the case of cutting a strong material like bone? Say, if we tried using a thin wire to decapitate a person standing up, would they actually get decapitated, or would they just fall over?
Seems to me the force needed to penetrate tracks the diameter, but the strength tracks the area of the cross-section.
That is, decrease the thickness by N and it decreases the force needed by N but the strength by N squared.
Below a critical thickness, the wire would just break.
Spiderwebs don’t slice you up if you run into them.
There is nonzero finite surface energy involved in cleaving an object in two, which you need to impart (minimum applied force). But for a living thing the minimum would be low. And you can prevent falling over by using a circular wire that shrinks (or 2 or more wires arranged symmetrically) to counter any pushing non-cutting forces
How low are we talking?
The Wikipedia page on surface energy gives values in the hundreds to thousands of mJ/m^2 for solids. I haven’t a clue where meat and bone would fall in that table, and I haven’t been able to find out with five minutes of Google, but even if we assume they’re on the high side we’re not talking particularly high total energies.
(Tangentially, “surface energy of meat” is one of the better phrases I’ve Googled lately.)