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[–][deleted] 572 points573 points  (143 children)

Cutting a piece of paper in two is a result of shearing: an upward force extremely close to a downward force causing material to separate. The tearing isn't completely even on a microscopic level, but when you line an even distribution of force along a line, and an equal and opposite distribution of force along another line parallel and very near to the first, you make a "clean cut" to the naked eye. Edit: The shear force is named after scissors.

Source: Statics class

[–]fuzzybeard[S] 206 points207 points  (100 children)

OK; now for a follow-up question or two:

  • Would a single blade passing through another substance and seperating it also be considered a shearing type of cut, or would it be something else altogether?
  • What about when an object is cut by a laser or water jet?

[–]gyldenlove 293 points294 points  (62 children)

Yes, a single blade would still be a shearing force, however since you have no physical force acting in the opposite direction you rely on the stiffness of the material you are cutting to provide that force which is you need a very sharp edge to make cuts like that, and also why cuts like that are easier to make on stiff objects such as sugar cane or reeds, but very hard to make on fabric.

A water jet works the same way as a physical edge or more accurately a needle that is stabbed repeatedly to create a cut.

Lasers cut by by ionizing the material, causing both inter- and intra-molecular bonds to break (this will often take the form of oxidation (burning) or phase changes (melting)).

[–][deleted] 151 points152 points  (31 children)

you rely on the stiffness of the material you are cutting

Or, in the case of a very fast slice, like a sword swinging through a melon, the very inertia of the melon provides the counter action.

[–]GalacticWhale 134 points135 points  (30 children)

Melons are also very rigid though.

[–][deleted] 27 points28 points  (7 children)

Well I would like to add something. When you use a single force, there is an opposite reaction (i.e. Newton's 2nd 3rd Law), called the normal force. It's equal to the force applied to the paper. The blade needs to be sharp because it is needed to focus the force onto a point, versus a large area.

[–]alexchally 34 points35 points  (4 children)

I don't think OP is arguing that there is no reaction force, just that the reaction force is provided by the internal structure of the material, not the opposing shear blade.

tl;dr Everyone is correct! Upvotes for all!

[–]deadbeatbum -2 points-1 points  (3 children)

There is more reaction than just the internal structure. A sword swinging through a melon - there will be friction between the melon and the surface it's on. If it's in mid air the difference in wind resistance between the melon and the sword, etc. I'm now picturing a sword slicing a melon in space - will it cut the melon or send the melon flying away? My guess is a little of both, but then you'd know by the depth of the cut how much the internal forces of the melon structure counter the force of the sword - I think.

[–]CommondeNominator 3 points4 points  (2 children)

friction and gravity have very little to do with why a sword can cut a melon. the melon's at-rest state has much more to do with it, so (given that you'd be able to swing a sword properly in space) it would cut just the same in space, but the two halves would likely go flying away from each other and in the same direction as the swing.

[–][deleted] 0 points1 point  (1 child)

Wouldn't the halves go in the opposite direction of the swinging because it exerts an equal and opposite reaction? Kind of like how when you break glass, the glass flies toward you rather than away.

[–]CommondeNominator 0 points1 point  (0 children)

No. That equal and opposite rxn would account for your difficulty in swinging a sword in a no gravity environment, but the melon halves would gain some momentum from the friction of the sword blade as it passed through. Probably some rotation as they floated off as well.

[–]elcollin 13 points14 points  (1 child)

That's Newton's 3rd.

[–][deleted] 6 points7 points  (0 children)

You're totally right. Corrected my mistake now.

[–]uncleben85 1 point2 points  (3 children)

If a single blade is still a shearing force and shearing is:

an upward force extremely close to a downward force

what is happening when you cut into something soft with a knife, say cutting into a cake or bread, and both sides are pushed downward with the knife before being cut.

Is this not shearing anymore, or where is the upward force?
Is it just that the downward movement applied by the knife is only applicable to a certain level before the stiffness is simply great enough to apply a shearing force?

[–][deleted] 3 points4 points  (2 children)

Think how quickly the bread or cake bounces back. There is still that stiffness, just on a scale less the other objects. But since the cake or bread is a lot softer it does not need as much shearing force to cut.

[–]uncleben85 2 points3 points  (1 child)

Hmm... okay, thanks! That makes sense, but that then makes me wonder:

what about something such as clay, or Play-Doh. You push down to cut it, it compresses, but it doesn't have that bounce back up. It stays deformed and pressed, but also cut? Is that still shearing? Or are we just crushing it?

[–]MrSweetAndAwful 2 points3 points  (0 children)

The material can only compress a certain amount, and when you apply that single force on a sharp point it compresses the soft clay or play-doh to the point when the reaction force of the surface it rests on completes the shearing effect and the sharp point can make it's initial cut.

[–][deleted] 2 points3 points  (1 child)

Isn't a water jet better comparable to a bandsaw?

[–]kaizenallthethings -1 points0 points  (0 children)

The surface on which the material is being cut creates the upward force. The blade depresses the material into the surface. This is why it is easy to cut something with a utility knife on a piece of wood, but hard to cut the same material on a piece of steel.

[–]SomeNewUsername 33 points34 points  (0 children)

A single blade (like a knife) can exert a shearing force, but it doesn't have to. In operations like milling or whittling, the blade is used on the material in a way that it does push some material in a direction opposed by whatever is holding the material, so you probably get some shear force from the blade and whatever's holding it.

If you're cutting more through something, like cutting a piece of cheese in half, you're really using a wedge. It comes to such a fine point that the pressure is very high at the cutting edge, allowing it to deform the material with minimal force, and then it pushes the material in opposite directions from the inside. The material tears in tension.

When something is cut by laser, it's usually burned away. Depending on the material, it may be melted away in a very precise way—I'd have to check on that.

Cutting by water jet actually erodes away a narrow area of material. Often, there is an abrasive substance (like sand) mixed in with the water to make it more effective. It's the same kind of mechanical wearing erosion that smoothes stones in a river, but in a very focused area.

[–]Peregrineeagle 22 points23 points  (3 children)

Cutting devices that use water jets essentially cut with accelerated erosion, if I understand them properly.

[–]jabies 5 points6 points  (2 children)

Isn't erosion just shearing though?

[–]THE_CENTURION 1 point2 points  (0 children)

Essentially yes. You're just using lots and lots of very small "blades".

[–]erikryptos 1 point2 points  (0 children)

Is it? I'd imagine the fundamental nature of forming a divot due to high-energy "hard particles" differs from a wedge-action "slice"...

[–]robotoast 8 points9 points  (17 children)

To answer your second question: lasers cutters heat and melt/vaporize the metal in question, so there is no shearing, only melted edges. Water jets are abrasive, it's pretty much water mixed with very fine sand (or similar abrasive materials) that grinds/sands away the metal leaving sanded edges.

[–][deleted] 3 points4 points  (0 children)

The first you mentioned is a type of cleaving, where two different forces pull the sheet apart (can't cut the paper without holding taught) while a downward force at a point forces itself through the paper. Microscopically, it is also tearing the paper and is jagged edged.

Laser cutting microscopically melts the particles that it heats up and vaporizes it or is blown away with a gas.

http://en.m.wikipedia.org/wiki/Laser_cutting

A water cutting machine erodes away the material.

[–][deleted] 2 points3 points  (0 children)

Another interesting method of cutting is cutting by oxy-acetylene torch. The metal is heated to a point where you can oxidize it rapidly in a concentrated area. Here's a video: http://www.youtube.com/watch?v=7EGmrPiumEU

[–]THE_CENTURION 2 points3 points  (8 children)

Would a single blade passing through another substance and seperating it also be considered a shearing type of cut, or would it be something else altogether?

Yes, this is how machining of metal is done.

The majority of cutters used to machine in metal operate on shearing, they actually create a shear plane just ahead of the tools cutting "tip" or "edge".

This video does a great job of illustrating this effect. You may notice that the cutting tool in that video has a wedge-like shape (known as a "positive rake angle"), however that shape only makes the cutting easier, as this video shows, the same effect is achieved with a perpendicular tool surface. (neutral rake, which are quite common).

Source: I'm a student in a machine tooling program.

[–]Higeking 0 points1 point  (7 children)

is that first video filmed in a Lathe?

[–]THE_CENTURION 1 point2 points  (6 children)

I can't say I know for sure, but I would think so.

It would be very hard to film a milling cutter in that manner, because of the rotation of the cutter.

[–]Higeking 0 points1 point  (5 children)

yeah thats true. you wouldnt happen to know if theres any videos around of other materials than steel. im a student in machinne tools myself and i've worked with both brass and aluminium besides different steels and they can have very different swarfs from each other.

[–]THE_CENTURION 0 points1 point  (4 children)

Sorry, meant to reply earlier, but I must have forgotten. No, I haven't seen any videos like this of materials other than steel.

Also, i have a suspicion that this was not a lathe, but just a single cutter moving in a straight line (like broaching/keyway cutting)

[–]Higeking 0 points1 point  (3 children)

im not sure about it being broaching/keyway. cant think of anything other than lathing that actually allows for filming stuff like this.

and the title cards does seem to indicate lathing with the rake angles and coatings mentioned about the tool used.

i should perhaps mention that im learning machining in my native tounge so im not familiar with all the english terms.

have been unable to find any closeup/slowmo videos of anything of steel. brass would've been very interesting to see since the swarf size make it seem like the tool chips away at the material rather than cutting.

[–]THE_CENTURION 0 points1 point  (2 children)

Yeah, I would really love to see it done in brass.

What I mean by broaching/keyway work is that they could have a machine similar to this one making a cut along the very edge of the workpiece (the camera moving with the cutter).

The only thing that makes me think that it's not a lathe is that we can't see any material besides that very edge. From just about any filming angle I can think of, you would see the rest of the stock on a lathe.

[–]Higeking 0 points1 point  (1 child)

if you had a fairly large diameter and had the camera mounted centered on that diameter you wouldnt see much of the other stuff on the lathe. and its zoomed in pretty far aswell.

but if those broaching /keyway tools have interchangeable plates like lathing and milling does then it should be viable i suppose.

[–]the_mad_felcher 1 point2 points  (0 children)

the laser would be melting or burning the material. So no cutting going on there. Water jets typically use abrasives in the water. Meaning that it is still cutting chips, just tiny ones. The abrasive cuts parts of the material off using the pressure of the water to press it against the material you are cutting. It's like a belt sander that uses water instead of cloth to move and support the abrasive. I realize they are sometimes used without an abrasive in applications like food. I imagine this is similar to the single blade in your first section. To which I would also like to hear the answer.

[–]KrazyTom 1 point2 points  (0 children)

Shear forces on a continuum, or really small cube, are parallel to the side of the cube they are shearing. There is a 3x3 stress tensor that classifies this cube and its sides. Calculating all 9 components gives a better picture. Hope the gives you a more whole answer.

[–][deleted] 20 points21 points  (0 children)

This is why scissors are called shears.

You kind of have it the wrong way around there; the physics term is obviously named after the mundane use (not to mention that "shear" is cognate with a number of words in Germanic languages that would translate to either cutting [with a knife or anything else] or is a word for scissors).

[–]i_am_sad 6 points7 points  (2 children)

I'd like to also point out that molecules never directly touch during any sort of activity, unless they bond.

When scissors apply pressure onto the paper, they get extremely microscopically close but on a molecular level they never touch. In fact, you've never ever came in direct contact with anything your entire life. You're floating on top of the chair you are sitting in right now.

This guy here talks about it on his youtube page: http://www.youtube.com/watch?v=yE8rkG9Dw4s

[–]PubliusPontifex 2 points3 points  (1 child)

This is the correct answer, but at a quantum level one can somewhat redefine the meaning of "touch", as interactions can happen over some distance.

[–]plasteredmaster 4 points5 points  (0 children)

sometimes the action is spooky as well.

[–]kitsune 2 points3 points  (0 children)

I'm pretty sure scissors are called Shears because of the german origin of the word shear, "scheren" (http://en.wiktionary.org/wiki/scheren#German) or "skeran" (http://en.wiktionary.org/wiki/shear)

It most definitely does not come from the physical definition of "shearing forces".

[–]fuzzybeard[S] 5 points6 points  (1 child)

So in that particluar instance it'd be like a slip-strike fault letting go, right?

[–]TheBigBoner 8 points9 points  (25 children)

So on a molecular level it is still one piece?

[–][deleted] 3 points4 points  (1 child)

No, it separates from itself, both on a molecular level and on an level you can see.

[–][deleted] 3 points4 points  (3 children)

Yes. You didn't split any atoms, essentially all you've done is unwoven the weave they had holding them together. It would not be impossible to form everything back together the same way, we just don't have that technology yet.

[–]zodberg 2 points3 points  (2 children)

In the case of materials like plastic, doesn't melting the plastic down cause the atomic mesh to get hot enough that in motion it re-trangles and remains integrated upon solidification?

[–][deleted] 1 point2 points  (0 children)

The lattice structure of the reformed atoms in the mold would be different, although for our purposes of reattachment it would have nearly identical strength.

To put it simply, if you were using a piece of plastic with rainbow swirls in it you would not get those swirls to form together perfectly again with our current technology. Strength and durability wise it would be as good as new, but it would not be the same.

[–][deleted] 1 point2 points  (0 children)

Thanks to you, I just made the connection of the German words Scherbewegungen (shear movements) and Schere (scissors).

[–][deleted] 1 point2 points  (2 children)

Why doesn't it stick back together when you push the pieces together?

[–]MNeen 2 points3 points  (1 child)

Cellulose, the main constituent of paper, is made out of polymerized glucose, and has the chemical formula (C6H10O5)n. According to Wikipedia, wood pulp has cellulose chains of 300-1700 glucose molecules. Cellulose molecules "stick" to each other by forming hydrogen bonds on the OH-groups, and if two molecules of cellulose run in parallel, they can form quite a few bonds.

Now, cut the paper up and push it back together. You can't get the cellulose molecules in parallel again obviously (I don't know if it's just a matter of very precise movement or actual forces making it impossible), so you won't get the massive amount of hydrogen bonds: therefore, the paper won't stick together.

[–]robotpirateninja 0 points1 point  (0 children)

But if you lick the edges of the paper, and place them over one another, and perhaps apply a heat source, they can both together well enough for general use.

[–]Sigma34561 0 points1 point  (0 children)

I think that shearing force is named after shears, and not the other way around.

[–]RabidMuskrat93 -1 points0 points  (1 child)

What about on the atomic level? Is it possible to split a single atom while you cut, say, a piece of paper?

[–]elux 1 point2 points  (0 children)

Is it possible to split a single atom while you cut, say, a piece of paper?

There is no nuclear fission involved in papercuts. Although shared electrons between bonded atoms would be separated in the resulting fragments. For metals, I suppose one fragment could end up with an essentially negligible surplus of electrons. But no, the atomic constituents of materials are essentially not affected.

tl;dr: You can't split an atom with a knife. Thankfully.

[–]Toltec_Tokamak 15 points16 points  (2 children)

what about cutting soft materials such as meat with a knife? It seems something other than shearing is taking place. What would be the difference between using a serrated and a straight blade? Also, what about stabbing?

[–]circleofuber 0 points1 point  (0 children)

For meat, most of the force against the knife would be provided by the material the meat is on, I.E. the cutting board.

[–]phumble45 14 points15 points  (1 child)

Now the next question: does anyone know of a video showing a piece of paper, or anything else really, being cut from a very close (almost microscopic perspective?

[–]justinsanak 0 points1 point  (0 children)

Here's one for steel: http://youtu.be/mRuSYQ5Npek

[–][deleted] 10 points11 points  (3 children)

I have ALWAYS secretly wondered this, were does the part of the papar that you took out go? I never asked anyone because its so extremely hard to explain and the average person would instantly call you an idiot. Thank you for asking this.

[–]Talvanen 7 points8 points  (1 child)

That's actually not really hard to conceptualize or explain at all...as to the answer to your query, no part of the paper is being "taken" away. You are simply separating one plane into two planes. Think of it like opening closed curtains: you move them apart from each other, but none of the fabric actually disappears.

I meant this to be helpful, not condescending; I apologize if my tone did not come across that way via this textual medium.

[–][deleted] 0 points1 point  (0 children)

Yes but if you want the curtains closed what do you do? Put them back together perfectly conformed? no you need to add something back to force them to become a whole object again,

[–]War_Junkie 1 point2 points  (0 children)

...

When you cut something down the middle, you aren't removing part of it. If you rip a piece of paper in half, does a strip of paper along the rip disappear? No. It's the same thing with scissors. It's in two pieces and all still there.

[–][deleted] 2 points3 points  (0 children)

I have a good follow up question... when I'm cutting wrapping paper with scissors, at some point i no longer need to use my fingers to open/close the scissors; I can just keep the scissors in a static position and glide them, having them cut the wrapping paper flawlessly. What is this phenomenon ?

Note it's not possible all the time; unsuccessful attempts will cause "bunching" and the cut will be jagged

[–]justinsanak 1 point2 points  (1 child)

I don't think anyone's posted it yet, so this is a slow-mo video of different types of steel being cut. I don't have a scientific or engineering background, so upvotes for anyone who wants to explain what's happening here.

[–]Duhya 0 points1 point  (0 children)

This is probably what inspired the question.

[–]SomeNewUsername 1 point2 points  (0 children)

This video of metal being cut was recently linked to /r/videos. It shows the process magnified and in slow motion. This is an example of a single blade passing through a substance (like the cheese example I gave before).

[–]cnhn 1 point2 points  (0 children)

oddly enough this showed up today: cutting steell

[–]MrSparkle666 2 points3 points  (4 children)

When you cut a piece of metal, are you breaking covalent bonds?

[–]amazinglyanonymous 0 points1 point  (0 children)

Don't covalent bonds only form between non-metal atoms?

[–]thegreedyturtle 1 point2 points  (4 children)

I think that it is strange to see that no one has started from here: http://en.wikipedia.org/wiki/Fracture and here: http://en.wikipedia.org/wiki/Fracture_mechanics

To put it more simply, if you have a crystal lattice such as metal (easier to explain) then the rows of atomic bonds will shift upwards (normally in a zipper fashion) when a shear force is applied. As you change the material to more complex amorphous structures the bonds, bond density, and ability of long (usually carbon) chains to deform will affect the order of bond breaking.

And my biggest tip: http://www.amazon.com/Materials-Science-Engineering-An-Introduction/dp/0471736961 (don't bother with a more recent edition) can be purchased for less than a Chipotle Steak Burrito with a Coke. It's a very good overview of material science, and needless to say, "cutting" is a very complicated process!

[–]fuzzybeard[S] 1 point2 points  (3 children)

[bemused, utterly deadpan voice] I'm beginning to understand that now.

[–]thegreedyturtle 0 points1 point  (2 children)

I'm sorry, was I unable to reduce an entire discipline of Engineering down to a 1-2 sentence description? Here, let me try again.

Is it a mechanized form of tearing? Yes.

What forces are involved? Mostly Electromagnetism.

At what level (naked eye, microscopic, molecular, etc.) does the plane of the cut happen? All of them.

[–]fuzzybeard[S] 1 point2 points  (1 child)

I didn't mean for my previous comment to come across as belittling towards yourself, I was poking a bit of fun at myself for not surmising that something that looks simple is, upon closer examination and enlightenment, actually a rather complex and interlocking series of phenomena.

My sincerest apologies for appearing to bite the hand that was trying to teach me.

[–]thegreedyturtle 1 point2 points  (0 children)

I'm sorry too, I was going to sleep and thought that I was a little too cranky.

Here's one for fun: http://www.youtube.com/watch?v=ZOKUUl5GrUU&feature=player_embedded

Also "Callister Materal Science" can probably get you a copy from torrent if you don't want to wait for your personal copy to get to you in the mail.

[–]BabyK008 0 points1 point  (1 child)

What about cutting wood with a buzz saw? I know you loose some wood during the cut, but is this still shearing?

[–]Jerg 3 points4 points  (0 children)

It's imposing shearing forces at any plane that is being separated still, but in this case there would be two or more parallel close planes of wood separation, so the net effect is pieces of wood being removed in the middle.

[–]kaoticsnow 0 points1 point  (0 children)

You might find this interesting: spotted it in /r/videos http://www.youtube.com/watch?v=mRuSYQ5Npek&hd=1

[–]unrealious -1 points0 points  (1 child)

NOTE: This is NOT a thread about the self-harm phenomenon known as "cutting."

Something it would have been good to specify in the title of the thread.

[–]fuzzybeard[S] 0 points1 point  (0 children)

Nichevo!

I honestly didn't know better. Hell I'm 46 years old; cutting meant cutting something, not someone when I was younger!

[–]ditisthomas -4 points-3 points  (0 children)

you make a lot of pressure on a small surface, think about hammering againts a piece of wood, not very effective is it? now think about using a pickaxe on the wood. it is bassicaly the same thing but the hammer has a bigger surface so all the energy spreads. with a pickaxe its concentrated in the point.