How Do Sharp Things "cut?" - Straight Dope Message Board

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Factual Questions DSYoungEsq May 21, 2008, 7:25pm 1 Yes, we know that a sharp thing “cuts” by a combination of mashing and tearing, as it were. But what I want to know is, have we figured out what is going on at the atomic level that causes the bonds between the molecules to separate just because you are slicing through them with a thin wedge? Absolute May 21, 2008, 7:30pm 2 I don’t see much mystery here - the sharp thing’s molecules apply a force that pushes the other material’s molecules apart. The force applied by the sharp thing’s molecules is greater than the force holding the other molecules together, so they separate. KneadToKnow May 21, 2008, 7:41pm 3

have we figured out what is going on at the atomic level that causes the bonds between the molecules to separate just because you are slicing through them with a thin wedge?

It doesn’t make sense to me that anything would be going on at the atomic level (aside from some possible electron swapping, resulting in a static electrical charge). I look forward to the replies to this thread. Santo_Rugger May 21, 2008, 8:24pm 4 Cutting happens at the macroscopic, physical level, not at the microscopic, molecular level. beowulff May 21, 2008, 8:32pm 5

Cutting happens at the macroscopic, physical level, not at the microscopic, molecular level.

Oh yeah? And what is causing that macroscopic force? It’s the electron clouds of the cutter pushing against the electron clouds of the object. Snarky_Kong May 21, 2008, 8:56pm 6

Oh yeah? And what is causing that macroscopic force? It’s the electron clouds of the cutter pushing against the electron clouds of the object.

Right, the fundamental forces aren’t strong nuclear, weak nuclear, gravity, and sword. Magiver May 21, 2008, 9:00pm 7 Isn’t it a function of density and force? a knife is denser than most of the objects it cuts and this is enhanced by the amount of force. You can’t normally cut steel with water unless you apply a tremendous amount of force but you can slice through water with relative ease. DSYoungEsq May 21, 2008, 10:11pm 8

Right, the fundamental forces aren’t strong nuclear, weak nuclear, gravity, and sword.

I love this answer! I guess my point is this: there are forces holding molecules together to make a solid substance solid. We know that binding effect stops occurring when we heat a substance enough, or lower the pressure enough. The question is, what is it about a “sharp” object that causes the binding effect to be broken? chrisk May 21, 2008, 10:19pm 9

I would hazard a guess that the binding effect between the molecules of the ‘cut’ object are broken because the molecules of the cutting object, reinforced by a generally stronger binding effect to allow them to act together, are working as a wedge to drive them apart.This explains why sharpness isn’t enough for a blade made of glass or copper to cut through a similar thickness of steel. The cutting object also has to be tougher, bound more tightly together. (Or at least as tightly, in which case the force pushing the wedge in carries the day.)Think of it like a group of kids lined up to play red rover, except instead of one kid barreling into them at top speed, you get a crowd of adults all holding hands pushing the line apart. The kids are holding onto each other as hard as they can, but they’re not as strong as the grownups barging in.

beowulff May 21, 2008, 10:23pm 10

How many PSI does the edge of a knife apply? I’d bet many tens of thousands, maybe millions. That force is applied to the electrons in the molecules of the object being cut by the electrons in the edge of the knife. At some point, that force is greater than the Van Der Waals force holding the molecules together, and they are forced apart. lazybratsche May 21, 2008, 10:24pm 11 Molecular bonds will readily break, given the right physical stresses. The mashing and tearing you mention creates a lot of shearing forces, among other things. A sharp object just focuses a lot of force on a small area, creating high amounts of stress locally.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. Driver8 May 21, 2008, 11:05pm 12 This raises a question in my mind. Lets say I’m cutting through some cheese with a steel knife. Typically are the steel molecules bound together so strongly that not a single molecule is broken off the knife? Is it just the cheese molecules that come apart?In other words, am I left with steel in my cheese? I am sure that if it does happen the amount is so minuscule that there is no practical effect, but I am curious. beowulff May 21, 2008, 11:10pm 13

This raises a question in my mind. Lets say I’m cutting through some cheese with a steel knife. Typically are the steel molecules bound together so strongly that not a single molecule is broken off the knife? Is it just the cheese molecules that come apart?

In other words, am I left with steel in my cheese? I am sure that if it does happen the amount is so minuscule that there is no practical effect, but I am curious.

I’m sure a small amount of steel is left in your cheese. If you look at the edge of a knife under an electron microscope, it appears very jagged. Some of the little jaggies will break off even when cutting soft objects. dgroberts May 22, 2008, 12:16am 14 Here is a guess:The knife is impelled by kenetic energy. It’s molecular bonds are stronger than those of the cheese’s, and the blade focuses all of that kenetic energy on a small point or line on the cheese. So the cheese gives way.So it’s the kenetic energy of the knife causing the softer material to give way.I await rebuke by wiser men. WarmNPrickly May 22, 2008, 3:22am 15 Keep in mind that these “cheese” molecules are quite small even when compared to the sharpest knife. I don’t think you are breaking chemical bonds when you cut cheese so much as smashing through the fatty lattice. Mainly, I think you are just pushing the tiny little molecules aside.Cutting a polymer is a different story. In that case the stresses are breaking molecular bonds, but it is still not accurate to think of it as a blade slicing through the bonds, because on a molecular scale, the blade is as sharp as a hammer. Mostly I think the jagged edges are catching molecules and pulling them apart.What is interesting to consider, is whether the bonds are broken homolyticly or heterolyticly. Analysis of the products would easily distinguish the two, if somebody thought it worthwhile to find out. tim314 May 22, 2008, 3:45pm 16

I guess my point is this: there are forces holding molecules together to make a solid substance solid. We know that binding effect stops occurring when we heat a substance enough, or lower the pressure enough. The question is, what is it about a “sharp” object that causes the binding effect to be broken?

Isn’t it just that you’re pushing the molecules apart by sticking a knife in between them? That is, the bond strength decreases as you increase the distance between the atoms.Or is that too simplistic? Duhkecco May 22, 2008, 5:09pm 17 What *specifically * is happening at the molecular level at the moment that the cut starts.**Absolute ** says:

the sharp thing’s molecules apply a force that pushes the other material’s molecules apart. The force applied by the sharp thing’s molecules is greater than the force holding the other molecules together, so they separate.

And, **lazybratsche ** adds:

Molecular bonds will readily break, given the right physical stresses. The mashing and tearing you mention creates a lot of shearing forces, among other things. A sharp object just focuses a lot of force on a small area, creating high amounts of stress locally.

It seems to me that the force required will depend on the materials and shape of the cutting implement and of the object that is being cut. And, that some of the variables would be the hardness, ductility, elasticity, tensile strength, brittleness, and crystallinity (and, possibly, melting point) of those materials.But I don’t know how those variables can be quantified by referring to molecular structure, to the point that one could predict whether a force (applied in a particular direction, over a particular area) would cause an object to cut through another object, rather than dent, squash or shatter it, or, in effect, do nothing.Perhaps an expert in Materials Science knows.Also, a typical cutting motion has two directions: *into * the substance and across. But, in some cases, it seems that the motion across is not necessary, eg. when cutting a very soft substance, or when the motion into the substance is very fast (greater force), or the cutting implement is very sharp. But, is shear stress always a component of cutting?And, yeah, I’m going beyond what is being asked in the OP. :o DSYoungEsq May 22, 2008, 5:19pm 18

What *specifically * is happening at the molecular level at the moment that the cut starts.

**Absolute ** says:And, **lazybratsche ** adds:It seems to me that the force required will depend on the materials and shape of the cutting implement and of the object that is being cut. And, that some of the variables would be the hardness, ductility, elasticity, tensile strength, brittleness, and crystallinity (and, possibly, melting point) of those materials.

But I don’t know how those variables can be quantified by referring to molecular structure, to the point that one could predict whether a force (applied in a particular direction, over a particular area) would cause an object to cut through another object, rather than dent, squash or shatter it, or, in effect, do nothing.

Perhaps an expert in Materials Science knows.

Also, a typical cutting motion has two directions: *into * the substance and across. But, in some cases, it seems that the motion across is not necessary, eg. when cutting a very soft substance, or when the motion into the substance is very fast (greater force), or the cutting implement is very sharp. But, is shear stress always a component of cutting?

And, yeah, I’m going beyond what is being asked in the OP. :o

No, actually, you are getting to the heart of the matter.Look, at the atomic level, we have some atoms, and they are all bound together to make a molecule. And that molecule happens to be next to another, relatively identical molecule. And something holds those two molecules together, so that they react to forces applied by staying next to each other. Let’s say those atoms and molecules are molecules in the skin of an apple.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.Saying that “Isn’t it just that you’re pushing the molecules apart by sticking a knife in between them?” is simply begging the question. WHY are they pushing the molecules apart? What allows them to get in between the other molecules when many other combinations of molecules can’t?So far, no one has offered an explanation at the appropriate level.

beowulff May 22, 2008, 5:36pm 19

No, actually, you are getting to the heart of the matter.

Look, at the atomic level, we have some atoms, and they are all bound together to make a molecule. And that molecule happens to be next to another, relatively identical molecule. And something holds those two molecules together, so that they react to forces applied by staying next to each other. Let’s say those atoms and molecules are molecules in the skin of an apple.

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.

Saying that “Isn’t it just that you’re pushing the molecules apart by sticking a knife in between them?” is simply begging the question. WHY are they pushing the molecules apart? What allows them to get in between the other molecules when many other combinations of molecules can’t?

So far, no one has offered an explanation at the appropriate level.

I think this has been covered. 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. 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).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. tim314 May 22, 2008, 6:04pm 20

So just to be clear, your question is:What is the physical mechanism by which the atoms of the knife exert a repulsive force on the atoms of the apple? And why aren’t other objects as good as a knife for creating space between the apple’s atoms?Is that right?Here’s the best I can do for an answer:As for the physical force that causes the knife to repel the apple atoms, I think it’s a combination of electrostatic forces (the electron cloud of the knife atoms repelling the electron cloud of the apple atoms when the two get close together), and the effects of the exclusion principle (which says you can’t pile multiple electrons, for instance, into the same quantum state).There is nothing special about the knife that causes it to repel the apple’s atoms. If I push on the apple with my hand, it will also repel the apple’s atoms – that’s why I can push the apple across a table. The difference is, my hand isn’t actually cutting the apple (that is, it’s pushing on the apples atoms without breaking the bonds between apple molecules).That brings us to the second question: Why does the knife cut better than another (duller) object (like my hand) . . .The apple is held together by electromagnetic forces between the various negatively charged electrons and positively charged nuclei in its atoms. But as a simple conceptual picture, we can pretend that the apple is made of a bunch of “apple atoms” wired together by springs. Originally, the atoms are located at the equilibrium positions where all these spring forces balance out. If you displace some of the apple atoms, the springs stretch, and exert a force to try to pull the atoms back to their original positions. However, if you stretch the springs too far, they break, and the atoms won’t return to their original positions.If you press on the apple with a dull object, it is displacing many apple atoms at once, meaning there are many springs trying to pull the atoms back into place. The result is you have to push really hard to overcome the force of all these springs. Meaning it’s hard to cut things with a dull knife. You can displace the apple as a whole (which doesn’t require stretching the springs) but you can’t displace one apple atom significantly from another apple atom.Now, if instead you press on the apple with a sharp knife, the blade edge is thinner and thus displaces fewer atoms. This means there are less springs pushing back against you, and thus it takes less force to push the springs to the breaking point.Obviously, we have to replace “springs” with “molecular bonds” to make the above description realistic, but I think the basic concept is the same.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).next page → Related topics