foreign that you have a solid object say a bar of Steel this is quite solid I mean it's a it's a piece of metal 5 8 thick uh you know three foot long can't bend it with my hands certainly and it's sitting here on the table surprising absolutely nobody if I were to push on one end of the bar an observer watching the other end of the bar would be able to see it move right away can confirm it's hot move but what is right away to help think about this let's scale up the bar from just under a meter to about 300 000 kilometers or one light second wait what yes 300 000 kilometers foreign let's assume that the person at the near end of the bar is infinitely strong because now the bar weighs almost a half a million metric tons and we need to be able to get it moving so now the question is once you push on this end of the bar how long before the Observer at the other end of the bar sees their end of the bar move does it happen instantly because the metal bar is still a solid object does it take the length of the bar divided by the speed of light or one second because the speed of light is the fastest that objects can travel is it C the length of the bar divided by the speed of sound in the metal if the material properties are most important or D does the delay depend on how you hit the bar along with some Choice material properties foreign [Music] did you leave a comment with your guests for bonus points this is this is a really fun question because it completely depends on your choice of model and almost every physics model that we use is technically wrong but it's a general rule the more correct a physics model is the more painful it is to use and Implement in the real world one of the most common responses to my last video about the speed of electricity equated a Wire full of electrons to a water pipe full of water I didn't even realize I had props imagine that you have a water pipe like this and it's full of water if you put more water in one end of the pipe water has to come out of the other end of the pipe immediately because otherwise you've got a full pipe and you're packing more water into it than will fit so it feels like something's breaking there but when I did this with electrons I pumped electrons into one end of the wire from the battery and it was a good long while before the electrons came out the other end of the wire I could measure the delay so what gives to make a much more extreme version of this experiment I decided to skip the liquid and just go with a solid metal bar I mean this thing feels quite solid I can't I can't even come close to deforming it like this actually I think I might have whoops okay yeah it's really hard to deform but if I push on the end of this beam the other end moves too right away and I can use this to transmit Force long distances like pushing on this switch from across the table so now we need to ask how fast that happens when I start pushing on this end of the bar how long does it take for the rod to exert Force 91 centimeters away and flip the switch what we really need in order to start answering this question is a valid useful approximation for the physics that describe this bar the only accurate way to model the behavior of this bar given our current state-of-the-art understanding of physics is to create a quantum mechanical wave function for every subatomic particle in every atom of this entire bar and then probably add in the complicated things that we don't really know how they fit in like gravity and solve all of those equations simultaneously so imagine how many atoms there are in this bar are how many particles there are in each atom that many equations with you know a few unknowns each and uh solve them all at once easy right there's no way that you're ever ever ever even going to come close to solve that equation there's no computer that we could build that could model the behavior of a macroscopic chunk of metal like this sitting on a table there's just no way so how do we ever actually do physics if we can't do physics accurately well we approximate so at the other end of the spectrum from the really really complicated quantum mechanical description we have the rigid body approximation and Newton's loss of motion and then it's really easy to say this is one object this object has a mass I apply a certain amount of force which makes this object accelerate and we can even model the force of gravity as a single force on this object and we can model the friction against the table as a single force acting on this object and with math that is no more complicated than pen and paper math you can with great accuracy describe what's going to happen to this bar when I push it across the table and that's because all that quantum mechanical stuff just sort of averages out and doesn't matter in the final result but that approximation also says that the other end of the bar moves instantaneously when I push on this end of the bar and if you try to combine that with other pieces of physics like relativity and the fact that the speed of light shouldn't really allow that to happen it starts to be weird so let's do the experiment now is your last chance to update your guests is that delay zero seconds if it's an ideal solid object three nanoseconds if the speed of light is relevant 180 microseconds if the speed of sound is relevant or about three and a half milliseconds if the speed of the hammer and the yield strain of the steel are relevant okay so of course this is scaled down from the 300 000 kilometer long beam but 91 centimeters is a little easier to work with I have it sitting here on the table pushed up against a force sensor you can see that the the yellow tray sort of freaks out when I push it against this this backstop and on the other side here I have a wire clamped to it and this wire is actually attached to a battery or resistor and a hammer such that when I make contact with the wire there's actually a circuit completed here the moment that this Hammer actually touches the metal bar if I hit the metal bar here that's going to start our timer of sorts and then as soon as this pressure sensor detects that the bar is actually pushing into it as in the whole bar has moved a little bit and pushed into the pressure sensor that's going to stop our timer and we'll know exactly how long it takes for motion or Force to get from this end of the bar to that end of the bar so without further ado zero out the cursors here we go first of all there is a delay which is interesting in and of itself it means that this metal bar is not an ideal rigid body that you would use in like freshman physics because this end of the bar can move when this end of the bar isn't moving so this end of the bar starts to move when this blue Trace goes from low to high right here and then you can see that the yellow Trace is pretty much flat and then all of a sudden it spikes way up and that Spike up is when the bar starts to push into the backstop at the far end and if I actually measure that out very first bit of signal is at a hundred and wow it is exactly 180 microseconds which I believe is the answer that I put at the beginning of the video script that couldn't be more perfect so what's the speed of sound in the bar so you can see that the hammer itself only actually makes contact for about 150 160 microseconds and then that current falls off again but the yellow line is what we care about in terms of the actual Force at the far end of the bar and if I zoom in on on the yellow line I'll make the Blue Line go away here we're basically plotting the force that the bar exerts on that pressure sensor versus time and as we go along we're going along we're going along there's no force on it whatsoever and then here at about uh uh what is this like 190 microseconds or so it starts to tick up and we get this positive force that says the sensor is being really completely compressed and that's when the bar has actually started to move and it's pushing into the sensor now you'll notice that I measured from over here because this little negative blip is an artifact of how Those sensors actually measure and when you're only compressing part of the sensor rather than the whole thing it actually goes negative for a minute I think it has to do with the capacitance I'll talk about that at the end but regardless uh this is starting to feel a force exactly 180 microseconds after the initial impulse with the hammer so this is sort of like the speed of motion in the bar and the velocity of this bar is in homogeneous the whole thing is not actually a solid object so information about the velocity of this bar is not transmitted instantaneously to all of the atoms in the bar at the same time so why was I so excited to run this experiment and how did I predict what the answer was going to be at least a close enough prediction that I knew that I'd be able to physically measure the answer uh given this setup before going out and buying a whole bunch of Steel and buying a bunch of pressure transducers I wanted to know what was possible and thankfully I have had way too much practice at trying to find uh useful and not too inaccurate physics models for various situations in this case because I wanted to do this with something like a bar of Steel the first thing that came to my mind as a material scientist was the atomic structure of Steel now steel is primarily made of iron atoms and those iron atoms are arranged in a structure a crystalline structure called body centered cubic all of the atoms in this structure have a nucleus that we really don't care about because we're not doing nuclear reactions and they have electrons which we do care about but only some of them a good number of the electrons are free to travel throughout the meta they may move you know millimeters or centimeters away from their original atoms if you could even Define they had an original atom the rest of the electrons actually most of the electrons in a metal like this are trapped they're stuck at or in between adjacent Atomic nuclei and those electrons sort of act as the glue that hold the whole structure together if you pull these nuclei apart with their cloud of electrons in between they get pulled back together but if you compress them they are pushed back apart there's a force that always restores the bond length to some equilibrium value the common approximation here the model that most people use is that these electrons act like Springs so this is a more accurate BCC model this is it's hilarious to hold one of these in my hands I don't know about uh physicists but to a material scientist this is exactly how I picture you know elastic deformation in a material it's just a whole bunch of atoms connected by Springs and the whole material sort of Jiggles around plastic deformation uh where the material is permanently deformed is a whole nother ball of wax I actually have a separate video on that if you're curious but elastic deformation looks like this so when I hit one end of a spring model like this I'm applying a force to the atoms right here but it's clear that the other end of the material isn't going to respond instantly there's a wave that has to pass through the material a wave of compressed bonds or in other words a wave of pressure or in yet other words a wave of sound at the risk or maybe at the dream of this sounding like a three blue one Brown video I want to take a minute and appreciate how important of a connection this is we don't even care what material we're dealing with and we were able to link the behavior of this rather abstract question that is not by any means a simple question two a macroscopic quantity that you can go look up in a textbook atoms are not balls connected by Springs we've thrown away everything about the nucleus we've thrown away all of the information about a lot of the atoms the free to move atoms in this piece of metal and we've really really dramatically simplified the interaction of all the electrons that are left if you want to get one end of that material moving by pushing on the other end then a compressive wave of scrunched bonds has to pass through that material just because it's made of bonded atoms and because the speed of sound the speed of a compressive wave traveling through material is something that's very well studied and well documented I just got to this point in my head and went to go look it up went how fast can sounds travel through the three foot piece of Steel that I can go buy at Lowe's and figured out that it was about 200 microseconds and that I would be able to measure that with the scope and then I started investigating another cool thing is that for a Sharp impulse like this once the hammer is no longer applying Force to the bar the bar is on average moving with its final momentum but different parts of the bar are moving at different speeds relative to each other there are vibrations that travel up and down the bar getting damped out eliminating extra kinetic energy is heat without changing the momentum and therefore speed of the entire bar on average this project came about because I used the same balls on Springs mental model for electrons than a wire and this equivalence came up while I was thinking about comments on my last video I love it when the same models can apply to completely different physics and the underlying mathematical Machinery can be recycled now as to the actual physical test why the mess I initially wanted to just set a piezoelectric sensor at both ends of the rod so the rod was sandwiched between them and hit the stack compressing them both at once it's cleaner to explain and any delay of the sensor would be replicated on both sides so it felt like a great Simple Solution unfortunately it was also really bad because every time I hit the sensor I'd get this weird negative signal before the disc actually compressed also and more important the time delay was widely varying my first thought was that the sensors weren't completely pushed up against the bar so I actually super glued them to the ends of the bar but that weirdly enough didn't fix either problem the measurements were still all over the place and I ended up lasering out a couple of little acrylic discs in sandwiching the Piezo sensors between them now the entire disc was securely squished sort of at once the weird negative pre-signal was a lot smaller but the time delay is still all over the place after the second day of this trying different bars and different sensor arrangements and whatnot I finally gave up and then had a literal shower thought the next morning that the first sensor was probably squishing inconsistently and therefore causing an inconsistent delay between the hammer and the bar so I took it out but I needed a new way to get the start time and decided that since the bar was metal and the hammer was metal I might as well just clip a battery across them and wait for the electrons to flow and uh although it made for a very messy looking table it worked after messing with some variations on the Piezo placement experimenting with some really cloogy foil and tape capacitor sensors and running out of battery Clips I had a consistent result but it was the wrong result and I struggled with this for a while it's like I'm getting the same answer every time what could be wrong well maybe it's the squish of the sensor maybe it's just slower than I thought so I tried a bunch of different length bars I've got a three foot bar a two foot bar and a one foot bar so I put all of these in the exact same setup and they plotted a perfect line down to zero and because the intercept of that line was approximately zero I think it was like negative three microseconds that told me that I didn't have any sensor Squish and that the delay was actually proportional to the length of the bar but it still wasn't the correct delay I was getting something in the vicinity of 5 000 meters per second for the speed of sound but the velocity that I was looking up the compressive longitudinal wave speed through steel was something like six thousand meters per second and 20 percent was too much I did not want to be 20 off for an experiment like this where I should be able to eliminate almost everything because it's like bench top my first instinct was that it was just a weird formulation of Steel and I looked the speed of sound does vary in steel Alloys but that wasn't the final answer the issue is that these bars are very small as in the diameter is very small relative to the wavelength of the sound waves passing through the bars in general the speed of sound if you look at the Springs attached to weights model is proportional to the strength of the spring and the size of the mass that is at each point along the chain if you make all the masses heavier then the wave propagates more slowly if you make all the Springs stronger then the sound wave propagates more rapidly when you extend these Concepts to an actual chunk of material like one of these steel bars we can't look at the mass of every atom and the spring constant of Every Spring we have to sort of average these across the material and for an average spring constant you take the Young's modulus which is basically how squishy is it and for the average weight of the atoms you take the density the average mass per volume and when you combine those together you can calculate the speed of sound but there's an important extra parameter in there the poisson ratio which basically says when you squish the bar end to end it actually gets a little bit wider because it those atoms have to go somewhere and as it turns out that has a strong impact on the velocity that a sound wave travels through a material but for a really thin bar like this it actually doesn't matter because your transmission of the sound wave is completely one-dimensional the fact that it spreads out just doesn't have an impact so you get this simpler formula where you basically just have the speed of sound proportional to the square root of the density and the poisson ratio and when you do that math for steel you get the exact same answer that I did with this oscilloscope which made me very happy once I figured it out so I was getting the right answer I just didn't think I was getting the right answer and it made me question my methods also you can just go look up this one-dimensional speed of sound it turns out it has a name it's the extensional speed of sound as opposed to the longitudinal speed which would have been correct if I instead had a giant cube of Steel that was a three-dimensional object as opposed to these thin cylinders that were basically one-dimensional so that is why solid objects aren't actually solid objects and also why simple demonstrations can sometimes turn into complicated messes with electrodes clipped onto hammers but all of that included I hope that you enjoyed this video and I'll see you next time thanks for watching foreign [Music]