How do sharp things "cut?"

[tim314]

In summary:

• Any solid object can push on the molecules of another solid object.

• This can have two effects: (1) moving the whole object you’re pushing, and (2) moving the specific molecules you’re pushing on relative to the other molecules.

• Effect (2) results in cutting the object if you push its molecules far enough apart from each other, causing the molecular bonds to break.

• Solids resist having their molecules pushed apart from each other. So if you try to do this to too many molecules at once, you’ll find it very hard.

• Sharp objects (like a knife) can displace fewer molecules at a time, so it’s easier to displace the molecules far enough to break the molecular bonds and achieve cutting.

• The side-to-side cutting motion is I think to reduce friction on the sides of the knife as it pushes through the apple.

[tim314]

@tim314

Friction is less on a moving object than on a stationary one

I should clarify that what I mean is that the coefficient of friction is less. This relates to the maximum frictional force that can be exerted on the object.

Obviously, if you aren’t exerting any force to try to move the object, then the force of friction is zero (since no force is needed to keep it in place).

But the point is, if you’re trying to push a knife through an apple, this means the apple will scrape against the flat sides of the knife. The effect of this scraping is greater if you’re starting with the knife at rest than if you already have the knife moving side-to-side.

[CalMeacham]

When you’re cutting polymers, you’re most certainly breaking bonds in a molecular chain, but this isn’t occurring through any chemical mechanism. Just stress, similar to how you can break a polymer by pulling or tearing it.

Actually, I’ll bet that most of the cutting you do on a polymer isn’t breaking the polymer bonds at all. Most familiar polymers are thermoplastic long-chain molecules, without a lot of cross-linking. When you heat them, they melt and become pliable and ultimately moldable because you’re giving the molecules enough energy to overcome the forces holding those long chains together, which, I believe, is van der Waal’s forces. Think of your average polymer as a plate of spaghetti with a bad case of static cling, or maybe frozen together as if you stuck it in the freezer, sauce and all. When you heat it, the spaghetti is free to slide around. If you grab two handfuls and pull them apart, you’re breaking the sauce holding them together, but you’re not breaking many noodles. That’ what’s going on in your polymer. When you cut with a knife, you’ll break the occasional bond between atoms in the long chains, but more of your cutting will simply separate chains held together by van der Waals (which is electrostatic, and not as strong as the atomic bonds in your molecule).

[Tom_Tildrum]

@DSYoungEsq

Now, all of a sudden, some invader molecules (themselves made up of atoms bound together) show up, and they are bound together, and they have a “shape” that is “sharp.” And for some reason, they manage to push the two molecules of apple skin apart, despite the fact that a lot of other forces and/or chemical processes won’t do that.

It seems to me that your question isn’t specific to sharpness. If I hit an apple with a ball-peen hammer, it’s going to break the molecules of the apple apart, just not as neatly. If I climb into a bathtub full of chocolate pudding, my body is going to push the molecules of pudding apart, even though both my body and the pudding are somewhat shapeless.

[Duhkecco]

@Tom Tildrum

It seems to me that your question isn’t specific to sharpness. If I hit an apple with a ball-peen hammer, it’s going to break the molecules of the apple apart, just not as neatly.

I don’t know about DSYoungEsq, but, for me, one of the key (academic) questions about “cutting” is: Why does a “sharp” object break the molecules of the apple apart “neatly”?

Of course, part of the answer is that the force is spread out over a smaller area, but that’s not the complete answer.

@beowulff

Force is applied by the repulsion of the electrons in the molecules. Since the binding force of the atoms in a molecule is stronger than the force holding different molecules together, the knife will separate molecules as it’s applied to the object being cut.

This, however, does not specifically explain cutting, nor does it provide a measure of “stronger”.

Also, remember that a knife is typically made from a substance which is “strong.” Strength in this case means that the molecules in the knife blade tend to bind together really well (knives are usually made of metal, which is a crystalline material).

Are you saying that crystalline materials are strong or that metals are strong? Both, neither, something else?

What is it at the molecular level that makes a material “strong”, or strong enough to cut through another material?

Think of a room full of balloons. If I force a balloon into this room, the others will be forced out of the way. If my balloon is wedge-shaped, it will tend to force the balloons in the room into two halves.

Visually, not a bad example, but a room full of balloons is not a good representation of a solid. Unless you’re talking about cutting through the walls of the room …

[Duhkecco]

@tim314

As to Duhkecco’s question about the cutting motion, I think (but could be wrong) that the idea is to reduce friction on the flat sides of the knife as it pushes through the apple. Friction is less on a moving object than on a stationary one, and it’s easier to keep the knife moving when you’re cutting back and forth than when you’re directly pushing into the apple (because you don’t have to oppose as many “springs” to keep it moving back and forth).

I think I might have come up with a better explanation: It’s not just a back and forth motion – it’s back and forth at an angle. That’s why most knives have curved blades. (Cleavers are straight but you use them to chop not cut, and bread knives are flat but they’re serrated, meaning that they have a “bunch of curves”.)

When you slice back and forth, only a small part of the knife is cutting at any given moment, thereby concentrating the force even more.

Not sure if this is the correct explanation, but it seems to make sense.

[Tom_Tildrum]

@Duhkecco

…most knives have curved blades.

But most saw blades are straight (apart from a circular saw, of course).

[beowulff]

[QUOTE=Duhkecco]
Are you saying that crystalline materials are strong or that metals are strong? Both, neither, something else? /QUOTE]

Metals are strong because they are made of crystals. The strongest metal objects are made of a single crystal. Crystals are strong because it’s atoms are bonded in a regular fashion to all of it’s neighbors. The strongest material (diamond) has it’s atoms bonded to all of it’s neighbors in a cubic crystal structure.
(There are differences between “hardness” and “toughness” which explains why diamonds aren’t always the best cutting material.)

[lobotomyboy63]

An extreme case would be the guillotine. They ended up angling the blade for maximum effectiveness. I would guess that’s so that at a tangent, the full force of the blade would be concentrated and break the skin—you’d lose a lot of energy trying to cut a wide strip. Once compromised, the angled blade would keep on going and slicing through the meat of the neck would not take much force. But you’d still need a lot for the bone.

The Nazis had their own, with a shorter drop for the blade (they must have used more mass to give it enough momentum).

[Duhkecco]

@Tom Tildrum

But most saw blades are straight (apart from a circular saw, of course).

Not sure if you’re joking here, about the straight saw blades.

The point was that, with a curved blade, only a small part of the blade is in contact with the object that you’re cutting, even if you are moving the knife parallel to the object’s surface.

With a hand saw, you usually hold the saw at an angle so that only a small part of the saw is contact with what you’re sawing. If you hold it parallel, it’s more difficult to saw.

Also, a saw is not so much a sharp object as it is a collection of sharp objects, the teeth. The teeth can be curved, but sometimes they’re straight. In either case, I think that they serve a similar purpose to a curved blade, namely, to concentrate the force on a smaller area.