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Q: How fast would a human have to run in order to be cut in half at the bellybutton by a cheese-cutting wire?
Randall’s response: AAAAAAAAAAAAA!!!
My response: None. The wire would snap first.Alright, I’ve been waiting for this one. I’ve been wondering for a while about the common sci-fi trope of a super-strong wire, usually only one molecule thick, that can cut through anything. In more modern stories, the wire is usually made out of carbon nanotubes, which can be (depend how you measure it) up to a hundred times stronger than steel. Is such a thing really possible? Well…sort of, but not with a cheese-cutting wire–and not with a single-molecule thread, either.
This may be a surprising answer, but if you think about it, we already have an example of a super-strong very thin wire that doesn’t cut through anything: spider silk. Spider silk is stronger than steel and ten times thinner than a human hair: only 3 micrometers wide. It snaps at the slightest touch. Carbon nanotubes are a lot stronger than spider silk, but a carbon nanotube wire a thousand atoms wide would be as delicate as spider silk and couldn’t cut much of anything.
What does this have to do with a cheese cutter? Well, a cheese-cutting wire is about half a millimeter wide and is made of steel. It does a great job at cutting cheese, but cheese is soft. How does it do at cutting something tougher, like people? (I’m going to be simplifying a lot here because there’s a lot about the physics that I don’t understand myself, but it should be in the ballpark.)
Let’s start with a simple example. Suppose you have two wires of the same thickness, but different materials. One is a steel cheese-cutting wire, and the other is made of human skin. (Gross, yes, but bear with me.) Press the wires together at right angles to each other. How much force will it take to snap the thread of skin? Well, the tensile strength of steel varies a lot, but it’s around 1 GPa (about 145,000 psi), whereas for human skin, it’s about 20 MPa (3,000 psi). The wires in this example have a diameter of about half a millimeter, and if you do the math, it turns out that it takes about one pound of force to snap the tiny thread of skin.
Now imagine that instead of a single thread of skin, you had a ribbon an inch wide–just fifty times as wide–against the same half-millimeter-diameter cheese-cutting wire. Now, if you press them together with enough force–fifty pounds of force–the steel wire will snap first because it is weaker, leaving the wide ribbon of skin intact. A whole person is a lot wider than one inch, so whatever speed they run at, it may be painful, but the cheese-cutting wire will break when they hit it long before it cuts them in half.
Note that real skin is more like two millimeters thick than half a millimeter, but it’s also soft and flexible, so it probably won’t take the force over its full thickness. For a ballpark estimate, I will assume that the force is applied to a thickness of the skin equal to the diameter of the wire.
Okay, so let’s ask how fast a person has to run to break a half-millimeter diameter wire when they hit it. This is a little tricky because the tensile strength depends on tension force along the wire, perpendicular to the runner’s motion. The math is complicated and involves vectors, but there’s actually a mechanical advantage factor of four or so–although there’s force pulling from both ends of the wire, too. All told, you probably need about 25 pounds, or 100 newtons, of deceleration force to break the wire.
How far can the wire bend? That depends on how long it it and how tight it’s pulled, but for the sake of example, lets say it’s stretched across a road and can bend about a meter before it breaks. For an average human with a mass of 65 kg, you can work out that they would have to be running at 1.7 m/s, or not quite 4 miles per hour. So if you’re going at a nice jogging pace and happen to run into a cheese-cutting wire, don’t worry. You’re safe. But the wire isn’t.
In my next post I will investigate the sci-fi end of this topic: the cutting power of carbon nanotubes.