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I was wondering if it is possible to drive a nail through, for example, concrete by dropping a light object on the head of the nail over many iterations.

I.e. is there a certain threshold of force that must be reached for the nail to make even the slightest progress into the concrete? Or is it possible for a small force applied thousands of times to drive the nail?

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    $\begingroup$ Like peeing in the snow at night, you probably make a difference but it is difficult to tell... $\endgroup$ – user6760 Dec 30 '19 at 4:40
  • $\begingroup$ You seem to be relating weight with force incorrectly. You also need to include speed. If your light object is moving very fast, when it hits the nail it transfer much more energy. Then you also need to consider air resistance, as that robs energy from the moving object. Consider a bullet fired from a gun, light object with lots of energy because it is moving fast, until gravity and air resistance slow and stop it. $\endgroup$ – James Jenkins Dec 30 '19 at 18:35
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    $\begingroup$ Certainly you should be able to do it with a light sabre. $\endgroup$ – Hot Licks Dec 30 '19 at 19:09
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    $\begingroup$ It does not answer the question, but it is closely related: In concrete, you can make a hole with light objects, and then put the nail into it, with water molecules, or even photons, by erosion or by melting, using a water jet cutter, or a laser cutter. Erosion does not work with metal, but melting does if it is not polished, I think. $\endgroup$ – Volker Siegel Dec 31 '19 at 2:49
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    $\begingroup$ @RBarryYoung: If you've ever driven a nail into concrete with a hammer, you'd know that the energy transferred from the hammer is often dissipated/wasted by deforming the nail rather than driving it into the concrete. There's a reason behind those elaborate concrete nailing tools. $\endgroup$ – Flydog57 Dec 31 '19 at 22:31
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Driving a nail through something, physically speaking, amounts to breaking crystalline, chemical or extra-molecular (e.g. van der Waals) structure: a certain material forms some sort of structure and you destroy it by passing a nail in the middle. Now, in quantum mechanics, we have the interesting phenomenon that not all interactions produce meaningful effects. For example: an electron in an atom will not react after being hit by photons with random energies - only the ones that have just the right ones will result in a quantum jump between levels. Since photons carry momentum, we can interpret a standing-still nail as being constantly hit by a huge amount of very tiny hammer blows, one for each photon that hits it perpendicularly to the surface. These tiny hammer blows are not enough to destroy the bonds in the material you want to nail, showing that there is indeed a [quantum] threshold that must be surpassed in order to drive a nail through some solid material.

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    $\begingroup$ Interesting microscopic picture $\endgroup$ – Alchimista Dec 30 '19 at 8:57
  • $\begingroup$ Maybe I'm misunderstanding, but this really doesn't seem to me to be correct. I mean, if I hammer a nail into wood, I'm not breaking apart the wood molecules. I'm compressing the material far enough to make way for the nail. Think of it this way: if you remove the nail and examine the hole from the inside, I'd expect to see, well, wood lining the sides. Not exotic compounds formed by breaking apart molecules. (Also, this explanation doesn't make sense to explain where the matter goes, since the volume of the nail is displacing that same amount of material from the original object.) $\endgroup$ – Kevin Dec 31 '19 at 18:11
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    $\begingroup$ @Kevin Cellulose is a very long chain polymer; you are indeed breaking the polymer at one point, and compressing it to each side. $\endgroup$ – Ross Presser Dec 31 '19 at 18:15
  • $\begingroup$ Downvoted since you do not mention friction. For the correct answer see: physics.stackexchange.com/a/522360/5563 (this is not MY answer) $\endgroup$ – FrankH Dec 31 '19 at 21:14
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    $\begingroup$ @Kevin : Any "exotic compounds" would literally be about one molecule thick, at most - in effect the broken ends of cellulose chains, following reaction with [likely] air. (Not sure what that comes out to chemically - likely several things are possible.) You will not be able to see that with your eye. $\endgroup$ – The_Sympathizer Jan 1 at 20:43
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My initial answer to that is no. This is because there is some maximum normal force $\vec{F_n}$ that the material can exert back on an object before it is deformed. Unless the object can exceed this $\vec{F_n}$, then it will not deform, and therefore not be driven through the material.

There are of course so further questions to be asked. If the nail has a wedged head, then it is "mathematically plausible" for a nail to have such a high slope that the mechanical advantage is high enough to drive through, but this is clearly unrealistic. There is also the chance that slight forces on the nail might create a form of erosion over time, but this isn't really the nail being "driven" so I'd settle on saying that no it's not possible.

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    $\begingroup$ But materials also can have fatigue which results in deformation over time from many events which do not exceed their deformation limits. $\endgroup$ – UuDdLrLrSs Dec 30 '19 at 14:04
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    $\begingroup$ This answer is in apparent conflict with erosive forces, e.g. a gentle stream cutting through rock over millions of years. $\endgroup$ – whatsisname Dec 30 '19 at 18:09
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    $\begingroup$ I believe it should be “before it is permanently deformed”. The material will deform very slightly even under lower force, but this deformation is elastic, and the material will resume its original shape once the force is removed. Above the threshold, the deformation becomes permanent. $\endgroup$ – Jan Hudec Dec 30 '19 at 20:44
  • $\begingroup$ Downvoted since you do not mention friction. For the correct answer see: physics.stackexchange.com/a/522360/5563 (this is not MY answer) $\endgroup$ – FrankH Dec 31 '19 at 21:17
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You got theoretical answers, here's an experimental one.

I was wondering if it is possible to drive a nail through, for example, concrete by dropping a light object on the head of the nail over many iterations.

That's how rotary hammer drills work. The motor actuates a piston which pressurizes an air cylinder which propels another piston (the hammer) until it hits a steel rod which whacks the back of the drill bit. The reason why it uses a pneumatic system is to reduce recoil and vibration. The wimpy version (hammer drill) is not pneumatic and uses a pair of toothed wheels rotating against each other to move the chuck back and forth, which is much less efficient and vibrates a heck of a lot more.

The interesting bit is that we know the impact energy of a rotary hammer, usually it will be between about 1 Joule and 30 Joules depending on the quality of the tool and how heavy it is.

1 Joule is pretty small. It isn't the fastest rotary hammer but it will make holes. Hammer drills have much lower impact energy, maybe a tenth of a Joule, and they also make holes (slowly and with lots of noise though).

So it is quite possible to drive things into concrete with repeated applications of a small amount of energy, but there are limits.

Also there are several big differences between a drill bit and a nail.

When the pneumatic hammer hits the back of the drill bit, it creates a pressure wave inside the steel which propagates along the length of the bit and delivers the energy into the tip, which pulverizes a tiny bit of work material with each hit. The bit itself moves very little front to back, as any energy expended in accelerating it back and forth is wasted. The only energy that makes a hole is energy delivered at the tip. This pressure wave propagation thingy is why you can have a one meter long drill and make a one meter deep hole with it. If the machine had to wiggle it back and forth it would take forever.

Once the nail has entered the material however, it is squeezed inside the hole, and in order to go deeper it has to overcome this friction on top of crushing material in front and compressing it in order to go through. So static friction is going to be your problem. Once the nail is in, even a bit, if you hit it with not enough force to overcome static friction, you will compress the metal a bit like a spring, then it will bounce back to its normal length, but it won't go in deeper at all.

You can do this experiment easily with a nail and a bit of wood: drive a nail through until the tip comes out on the other side of the plank. Now the only thing holding the nail is friction, and if you don't hit it hard enough to overcome friction, it won't move at all. You can even measure the static friction experimentally, using the favorite tool of any theoretical physicist:

enter image description here

So the reason why I bothered to explain about drills is that a drill bit evacuates material out of the hole, which solves the friction problem, but a nail does not do that. With enough patience, you could probably make a hole with a drill bit using really tiny impacts, as long as each impact removes at least one atom/molecule of material.

So, for a drill the limit would be how much energy it takes to break either covalent bonds or Van der Waals forces, depending on what holds the material together. For concrete, it will be covalent bonds inside the crystalline aggregates (ie, rocks) so that's pretty hard. I'd say ultrasonic drilling would be a good illustration of "lots of tiny shocks".

And for a nail the limit would be static friction.

That's why a nailgun for concrete uses one big explosive charge (it is quite spectacular) while the optimum strategy for drilling is lots of repeated impacts.

Bonus material:

The drill bit (or the nail) has to be harder than the work material. Drills for concrete use tungsten carbide tips. Concrete nails are made of hardened steel so that does the job for a single-use nail, but hardened steel is brittle, so they will chip, break, and send pointy razor sharp bits flying. Always wear eye and ear protection!

Also, ancient Egyptians machined granite with copper tools. That's not possible because copper is very soft. They did it by mixing in some fine sand (probably silicon carbide) which embedded into the copper tools and ground the granite. It was quite a labor intensive process.

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  • $\begingroup$ with a drill, you don't theoretically need any impact at all, since it keeps scratching the surface. As long as you apply some tiny amount of pressure, constant or otherwise, and keep the drill (not the bit) from rotating (i.e. preventing the bit from getting stuck), and as long as the drill bit doesn't wear off much faster than the wall you're going into, you'll have a hole eventually. $\endgroup$ – Zak Dec 31 '19 at 19:38
  • $\begingroup$ Sure, that's how you make holes in brittle materials like tiles, with diamond core drill. But OP wanted to hammer on it, not rotate it. $\endgroup$ – peufeu Dec 31 '19 at 20:21
  • $\begingroup$ Drill bits for concrete also normally have a head which is a lot wider than the shank. Much of the material can remain in the hole swirling around instead of being evacuated, though some of it does makes it way out. $\endgroup$ – UuDdLrLrSs Jan 1 at 12:12
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Macroscopic: Driving a nail forward amounts to non-elastic deformation of the material. Generally, (almost) every material has some limit of force that causes only elastic deformation and you have to exert a greater force in order to make it deform non-elastically.

Then again, the above is an approximation. No deformation is ideally elastic even if the material is engineered to be highly elastic (that's why springs break after some use).

So, keep hitting.

One can think that there is a minimal energy needed to crack a single chemical bond. Even then, a thermal movement of the particles may supply the exact amount of energy to your bond minus the amount you apply by hammering so in general you make the "thermal decomposition" at the place of the tiny hammer hits more probable than elsewhere. That means, keep hitting - even with an energy less than a single chemical bond you can advance after enough hits. A great number of hits, actually.

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  • $\begingroup$ "A great number of hits" - well, I guess there is some threshold below which you can keep hammering until the end of the universe without finishing driving the nail... $\endgroup$ – cmaster - reinstate monica Dec 31 '19 at 14:50
  • $\begingroup$ @cmaster-reinstatemonica - nah, if you keep at it long enough, the protons in the material will decay and make the job easier ;-) $\endgroup$ – Kevin Dec 31 '19 at 18:17
  • $\begingroup$ Downvoted since you do not mention friction. For the correct answer see: physics.stackexchange.com/a/522360/5563 (this is not MY answer) $\endgroup$ – FrankH Dec 31 '19 at 21:16
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    $\begingroup$ @FrankH the answer you linked to is WAY more deep than mine, but I still don't see where I am wrong. For the purpouses of my (very oversimplified) model, friction is just a matter of non-elastic deformation of both the nail and the concrete block. $\endgroup$ – fraxinus Jan 1 at 18:00
  • $\begingroup$ @Kevin we still don't know if the protons really decay. But if they do, they will really make the task easier. $\endgroup$ – fraxinus Jan 1 at 18:07
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While others have answered the questions here is a simple matter:

The strength of the nail must be far greater than the material into which it is being driven. The force applied to the nail must exceed the molecular cohesion and overcome the friction of material in contract with the nail.

The modulus of elasticity of the business end of the nail must be far greater than the plastic deformation limits of the material into which it is being driven that it continue to maintain its shape and strength.

There is an optimum shape to the nail point according to the material into which it is being driven. The sharpness angle of the point will determine the efficiency of the force required to penetrate the material.

So long as the force applied to the nail surface area exceeds molecular bond strength over the length of the nail, it should work as long as the nail used has higher elastic deformation than the plastic deformation limit of the material into which it is driven. The item used to drive the nail ought to be stronger than the nail or it will not complete the job.

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The following is not totally what was asked about (unless you have an eg Iron or Aluminum surface) but is relevant enough to be useful:

Ferrous metals have "fatigue limits" - many* others do not.
This means that there is a limit below which you can deflect a ferrous"beam" repeatedly and never cause fatigue failure - it acts as a "spring" without destructively absorbing the deflection energy. Above this limit damage occurs which will lead to ultimate failure.

Aluminum, as probably the most commonly encountered example, has no lower fatigue limit. Any practical deflection** will result in some permanent damage and contribute to ultimate failure.

So eg a suitably corrosion resistant load bearing hook can be designed such that it will still be able to support a load below it's design limit after 2000 years of continuous use. An Aluminum hook can be designed to last 2000 years with N load applications at some maximum limit but it is progressively failing at each load application.

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*I said "many" rather than all as there may be others I am unaware of that behave similarly to iron. Iron and Aluminum are "good enough" examples in this context.

**"Any practical deflection" -> There may be an atomic scale limit. For real world applications there is no lower limit.

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Assumptions:

  • The nail is weightless
  • It's relatively stiff but still elastic
  • The hammer, or whatever you use to drive the nail is completely stiff, or at least much stiffer than the nail.
  • The nail is strong enough to be driven through the concrete, i.e. if the force pushing the nail increases, the concrete will deform/break rather than the nail.

In order for the nail to move forward, it needs to be pushed with a sufficient force. If you were using a heavy hammer, this is how that would work: You accelerate the hammer towards the nail, i.e. store kinetic energy in the hammer head. That kinetic energy is then transferred to the nail, thus pushing the nail into the material. The material pushes back, so the nail will compress a little.

The easiest way to visualise that is by imagining the nail as a (fairly stiff) spring: The hammer hits one end, compresses the spring from the "head" end, and on the "foot" end of the spring, we can measure a force that rapidly increases while the hammer is being slowed down, peaks when the hammer has been stopped, and then reduces again while it bounces back.

To decide whether the nail progresses at all, we need to look at the peak force during the bounce. If this is below the threshold for the concrete, we're not getting anywhere. If it is above, then as soon as the threshold is reached, the "foot" end of the nail will start to move into the concrete, thus doing useful work. This means some of the kinetic enrgy from the hammer will be used to enlarge the whole rather than just bounce the hammer back. This also means that the theoretical peak force won't actually be reached because the concrete gives way before it gets there.

So, what decides how high that peak force is, i.e. whether we reach the threshold required to drive the nail forward? Going back to the spring analogy: The peak force depends on how far the spring is compressed, and that in turn depends on two factors.

Factor 1: The stiffness of the nail

Think of hitting a trampoline with a hammer, to drive it into the ground: The hammer slows down very gently while the nail compresses very far. if you plotted force over time, it would take a long time to stop the hammer, and the forces would be very low. With a very stiff nail (think of a thick, straight metal rod), there's almost no compression, and the hammer is stopped abruptly, so the peak force is huge. This is why nails are usually straight metal rods, and why people prefer bouncing around on trampolines :)

Note: A critical look at the assumptions above shows that really we should be talking about the combined stiffness of the material/nail/hammer combination. Any elastic deformation makes reduces the peak load on the nail, as anyone knows who's tried to drive a nail into a thin, free-hanging plank of wood. -- I'll ignore this for now since the question was about nails in concrete.

Factor 2: The momentum of the hammer

Momentum is mass times speed. So if you double the mass of the hammer (while keeping the springiness of the nail constant), it will slow down the hammer at half the rate, meaning it will compress the nail twice as far, thus giving you twice the peak force. If you double the speed of a hammer, it will need twice as much slowing-down before it stops, so it would also compress the nail twice as much.

So, could a very light hammer work?

In very general terms: The peak force is proportional to nail stiffness times hammer mass times hammer speed. So to find out if the nail can be driven, you could start with the weakest hammer blow that would still drive the nail just a tiny little bit, and in proportion to how much lighter it gets, you have to either move it accordinly faster or stiffen the nail proportionally. In practical terms, steel nails don't get much stiffer unless you make them thicker, but that would increase the driving force they require. Maybe a different material could help, but there are no huge gains to be made, even with very expensive materials. This leaves the "hammer" speed. For every halving of the mass, you'd have to double the speed. This means "dropping" small objects wouldn't work unless you drop them very far, and their speed is not limited by aerodynamic drag. Hitting the nail with fast-moving small objects could work, of course.

In slightly more realistic terms

"hitting it with small, fast-moving objects" ... if you've ever used youtube, you'll have noticed slowmo videos of stuff being hit by bullets. And what they tell you is that some of the assumptions at the start of this post don't really hold up once you reach certain speeds:

  • The bullet/hammer itself can deform, thus absorbing some of the momentum
  • the head of the nail has some mass. At too high bullet speeds, it might not be able to start moving down fast enough (to hand the momentum on to the rest of the nail) and might rather just deform/break itself before the impact is really felt at the foot.

You could mitigate the last problem by having a very lightweight stiff material (carbon fibre? ceramcis?) for the nail, with maybe some sort of impact protection at the head, but now we're getting a little bit crazy. On top of this, the stiffest nail in the world won't help you if it then turns out that the material you're driving through is suddenly less stiff than your new improved nail, and becomes able to absorb the momentum from the bullet by elastic deformation, while using the supernaturally robust nail to evenly distribute the impact across the contact area with the nail ... In that case, you should maybe just fire the nail directly at the material, but then you'd have to get it all the way in with a single blow, which needs extra momentum...

Conclusion

There is a lower threshold for how much momentum a blow needs, based on the elasticity of the system (nail, material, hammer/bullet), in order to make any progress. You can compensate for a lighter hammer by moving faster, but there's a limit to that where the impact can destroy the nail. You can also do a little bit by stiffening the nail/hammer/material but that's not going to get you very far without having to go to very impractical lengths.

I did not mention, of course, that this becomes a lot easier if the material you're driving the nail through is very soft, which lowers the momentum threshold, and reduces the load which the nail must be able to bear. So driving a steel needle into some balsa wood might well be possible by droping pennies onto it, although you'd need really good aim :)

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  • $\begingroup$ Downvoted since you do not mention friction. For the correct answer see: physics.stackexchange.com/a/522360/5563 (this is not MY answer) $\endgroup$ – FrankH Dec 31 '19 at 21:16
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    $\begingroup$ @FrankH: Wow, way to nitpick! Friction may gradually increase (depending on nail/material pair) as you keep driving, but in order for that to happen, you need to even make a hole first, which is what my reply talks about. If you haven't got enough momentum, you don't even get to that point. You'll just have a nail on a smooth surface, and you keep tapping it... $\endgroup$ – Zak Dec 31 '19 at 21:28
  • $\begingroup$ I did not mean to nitpick, sorry about that. I did not take the question to be asking about the limit where the mass of the hammer goes to zero. I think your answer does show that for any given hammer speed there is a minimum mass needed to make progress. This is good. However, the answer I linked clearly showed that once the nail made enough progress such that the shaft of the nail is now having static friction with the concrete, the minimum force (and hence hammer mass) will increase significantly to the amount needed to overcome that static friction. $\endgroup$ – FrankH Jan 1 at 0:28
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    $\begingroup$ still, whether you explicitly list friction or not, there will be some amount of force that needs to be delivered to the business end of the nail, be that to overcome friction or to actually tear that concrete apart (both, of course, if the nail has already gone some way). My practical experience is that with an inelastic material like concrete, the grip of a nail can be pretty low. Works much better in something like wood, which pushes back against the nail. One of the reasons why putting nails in ceramic is not recommended :) $\endgroup$ – Zak Jan 1 at 19:46
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Hammer is almost always able to transfer phonons, (this threshold is significantly lower than chemical bond energy).

To drill a chunk of concrete, put it in a thermally sealed container and use a non-conductive nail with a higher melting temperature.

Hit a nail, until heat dissipated in concrete melts it.

Disadvantages:

  • material requirements, concrete changes properties on solidification
  • time, to heat up an object of any significant size with small impacts may take millions of years
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Ultimately, yes, you do need a certain minimum force. The best way to understand this is to think about what happens at the molecular scale.

"Driving in a nail" requires some of the material to be split apart and pushed aside. To do that, you have to break either intra- or inter-molecular bonds (which, depending on the kind of material you're trying to press the nail into may be any mixture of covalent, ionic, or dispersion ["van der Waals"] bonds). Hence, your question in the end amounts to "can an arbitrarily small force break a molecular bond?"

And the answer to that is no. A bond is nothing more than force exerted between atoms or molecules that attracts them together, and to break it, you have to counteract that force, which means applying at bare minimum an equal and opposite force. If you apply less force than this, the bond will stretch, but not break, because the attracting force will still win.

On the macro scale, stretching, but not breaking, the bonds is essentially elastic deformation. Breaking some bonds bot only a few, so as to allow internal parts of the material to slide around while not pulling away entirely, is plastic deformation (a permanent change of shape but still retaining continuity). Cleavage, or fracture, of material (where the material separates into two or more separate pieces) is when the bonds are broken completely.

Penetration of the material implies localized cleavage to create the hole, followed by plastic deformation of the surrounding material to widen it, and hence there must be enough force available at and around the tip to break all relevant bonds. If, instead, you tap the nail very, very lightly, there will only be elastic deformation: in effect, the material, no matter how hard it may seem, will simply flex up and down like a trampoline. You might not be able to see that with your eye for "hard" materials like wood or concrete, but that is still what is going on. You can super-light tap it as many times as you like, but the material will just keep flexing - even if you tapped it so many times that the total energy you expended in the tapping equalled that which could drive it in were it applied all at once.

In more general terms, both energy and power - that is, the rate of energy delivery - count when asking about damage. It's why that you can sit in the sunlight during daytime for, say, 100 seconds, and over that time maybe about 100 kilojoules will hit it (assuming you present $1\ \mathrm{m^2}$ to the Sun and you get near the full Solar constant so roughly $1\ \mathrm{kW/m^2}$ of radiant flux), but if you received that same 100 kilojoules in 1 second ($100\ \mathrm{kW/m^2}$, which is comparable to the open maw of a blast furnace or very close to a fire storm, I'd think), you'd suffer extreme - likely deadly - burns. The same principle applies with mechanical energy as well, as here.

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