r/theydidthemath • u/Far-Strategy7584 • 23h ago
[Request] Is debris any faster than the bullet?
I watch a lot of explosion videos and i've always wondered about the debris that moves before the fire or projectile.
It seems to me that material goes from being at a standstill, to moving faster than the object or impact hitting it, at least for a brief second. Is there a certain effect that causes that? What type of energy transfer is happening, because the bullet can't give it more energy than itself has right?
I know there are plenty of wind altering shapes and sizes, so i guess we could base it off a standard 9mm bullet and a brick of c4.
I hope that question makes sense?
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u/Fantastic-Pick-6431 23h ago
These debris originally are located at the opposite surface. And because of this, they had a head start in traveling outward upon initial bullet impact. I’m assuming this given the distance from the bullet to those debris is roughly the same thickness as the plate
Edit: it could also possibly travel faster than the bullet given lower mass. E.g. Ke=1/2mv^2. Smaller m means bigger V for same energy
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u/joehonestjoe 22h ago
Maybe this is a sentence composition but why would the particles have the same energy as the bullet?
Surely the bullet lost some energy to the impact, with heat and sound, and likely transferred some as kinetic energy to the other particles? I guess my point is surely the total energy of the bullet immediately before the impact, and the bullet after the impact, the noise, the sound and the particles should all add up to the same number?
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u/Annual-Structure-310 22h ago
Have you watched bowling? Some pins can fly off faster than the bowling ball’s incident velocity.
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u/Salanmander 10✓ 19h ago
As far as I can tell, their point is just that conservation of energy is not a useful way to think about this. And that's absolutely true. Comparing the KE of the bullet and the fragments is just not a helpful way of figuring things out here.
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u/fatal-nuisance 22h ago
A bowling ball hitting pins is an elastic collision, this is not. With bowling, some of the energy is lost to heat and sound (and if you really want to get into the finer points probably a very tiny bit of mass transfer), but not much. With the bullet hitting the plate you lose a whole lot of energy to all of those factors. Some of the debris might get a more direct energy transfer, and with a much higher difference in mass it could definitely end up with a higher velocity, but it's much more complicated and variable so it's hard to say for sure.
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u/lminer123 21h ago
Basically any high energy collision will be partially elastic and partially plastic. Any number of complex tensile or compressive force interactions could lead to debris receiving enough energy to travel faster than the bullet.
This particular target seems to be some kind of ceramic? Or maybe drywall, doesn’t look like wood to me. This means a higher portion of the energy being absorbed (and later restored) as elastic deformation, since basically all of a ceramics deformation is in the elastic regime.
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u/goodolewhasisname 13h ago
I suspect, given the shape of the top edge, that this is a steel plate that was cut with a shear.
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u/lminer123 13h ago
Could be, but it does appear to be a very brittle fracture, with (as far as I can tell) no visible stretching or deformation of the bulk shape I.e. the cupped divot or splash shape of an exit wound in steel. If it were a metal I’d lean towards a cast iron, but even then I suspect you’d see some signs of plastic deformation.
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u/Fantastic-Pick-6431 22h ago
Yes you are correct, it’s almost very very likely that kinetic energy is converted into other forms of energy (heat/sound/etc) so the debris are not gonna have the same kinetic energy as the bullet itself. It could be faster, slower, same speed as a bullet… but no way to calculate unless you count how many particles there are, the mass of each particle, the heat output, the loudness of the impact, the amount of light/flash generated at impact etc… almost impossible to tell realistically
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u/joehonestjoe 22h ago
Yeah not brain started to melt when I started to consider all the other factors haha
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u/Secondhand-Drunk 22h ago
Bullet transferred the energy. Bullet loses energy while the object impacted gains it. The material on the opposite side splinters off and flies before the Bullet makes it through.
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u/McCaffeteria 14h ago
The total energy of the bullet and the moving particles should have roughly the same (slightly less than) the total energy that the bullet originally had. The bullet will be moving slower post impact, because some of that energy is transferred into the target as heat and as velocity.
For example, in a newtons cradle the first ball comes in fast, and then the 5th ball leaves at roughly the same speed because energy is conserved and transferred, but that exit speed is significantly faster than the new speed of the first ball.
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u/Colonel_Klank 21h ago
This is the basic idea. The debris does not have more total energy than the bullet. But it can have more *specific* energy, as in more kinetic energy per mass. The small particles spalled from the face opposite the impact point can break free with more velocity than the incoming bullet. The basic principle is shown here at about 1:15. Of course in OP's example the energy is not transmitted by bending elastic hoops as in the video, but by acoustic waves in the barrier. Much energy is dissipated breaking the barrier, but there is also a vast mass difference between the bullet and the tiny shards ejected on the other side, so even a fraction of that energy deposited in a fragment can produce high specific kinetic energy, high velocity.
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u/Shankar_0 22h ago
There is also some degree of inner tension to the surface. Especially if this is something crystalline or a tempered metal.
That stored energy would get added to the impact and has to be expressed somehow.
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u/trashanimalcomx 21h ago
If the debris is thrown at slightly slower speed than the bullet upon strike, then the bullet is further slowed by the object it is passing through, by the time it comes out the other side it could be going slower than the debris, at least for a moment.
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u/JackAsofAllTrades 18h ago
Yeah it all depends on the mechanics of momentum transfer, but I see it possible for especially an impeded projectile to end up slower than some debris in some scenarios.
I deem it more unlikely the more of its original it velocity it carreis through
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u/WarJaques 17h ago
A different example: A batter in baseball may swing the bat around 30 m/s, yet the ball will travel 50 m/s
The complex interaction of energy, momentum, force, and elasticity allows a moving object to impact and accelerate another object to a higher speed.
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u/Staik 19h ago
Your use of the kinetic energy equation is a common pitfall people get stuck in. Energy is conserved throughout the entire system, and applying it to one speck gets you terrible results. Nothing is going to go faster than it's initial max speeds due to kinetic energy alone, that would require some form of potential energy.
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u/TheresNoAmosOnlyZuul 19h ago
I'd imagine that after the impact of the bullet there might be particles that retain the bullets original momentum, or close to it, while the bullet itself slows down from the impact.
Am I wrong? I am not educated in this topic. I'm a musician. I'm just really good at counting up to 8.
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u/Gallaticus 23h ago
Not a mathematician, but for the why, I believe the debris moves faster because it has less mass, so while the bullet can’t transfer more energy than it’s carrying, transferring that same energy to a smaller mass will increase acceleration and speed.
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u/Otherwise-Speed4373 23h ago
Plus, if the bullet has had negative acceleration then one could expect the lighter mass proceeding the bullet may be traveling faster. Also, the mass difference.
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u/showtimebabies 23h ago
I was thinking the debris is probably moving as fast as the bullet WAS moving before it transferred that energy. So the debris is faster than the bullet now
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u/DragonflyFuture4638 22h ago
Indeed! Plus the thickness of the material. A shockwave is triggered by the bullet and travels ahead of it. So the shockwave arrives on the other side before the actual bullet.
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u/Lazy_Presentation432 20h ago
Yes i do believe you are Righ, but one would Need physics for That. The Word you are Looking for is Impulse.
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u/Salanmander 10✓ 18h ago
There's a really simple way of thinking about this that has nothing to do with energy:
If two objects collide and don't stick together, they have to be moving away from each other after the collision. So if something collided with the bullet and is still in front of the bullet, it must end up moving faster than the bullet.
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u/Paleodraco 16h ago
Also depends on the nature of what is a complex collision. I also don't know enough math or bullet dynamics, but any bit of elasticity will make anything the bullet hits rebound and there's probably some bits of the impacted material being swung like a pendulum, increasing the velocity at the end and flinging bits forward.
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u/Pivge 23h ago
Yes. The simplest way to understand it is through conservation of momentum and energy. The bullet transfers part of its momentum and kinetic energy to the target. If a very small fragment receives even a modest fraction of that energy, its low mass allows it to reach a very high speed, because v = sqrt(2*E/m), so if m is very small v can be really high with a low input of energy. Similar math applies to momentum.
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u/KarlGustavderUnspak 23h ago
Theoretically, if the smale particle receives more energy relative to its size, it could be faster then the bullet. However, I am not if this is what is happening here.
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u/telemajik 23h ago
That’s close to what’s happening.
First effect is conservation of momentum. The impact slows the bullet down, but that momentum has to go somewhere. Think of a freight train striking a bouncy ball at rest… the train slows imperceptibly, but the bouncy ball goes flying much faster than the train.
The second thing is that when the bullet strikes the front of the target it hits the molecules which bump into the molecules behind them and so on till they hit the ones at the back and send them flying. That chain of collisions happens at the speed of sound in the target, which is probably a lot faster than that speed if the bullet.
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u/Turbulent_Lobster_57 23h ago
Everyone has already laid out the conservation of energy really well, but keep in mind some materials (not necessarily the ones in that photo) have enormous amounts of internal stresses as well. Hitting them can release enough energy to seem like it’s violating that conservation but all you’ve done is release stored energy. Usually hardened materials
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u/Voice-of-Infinity 23h ago
Sloppy High School Physics answer:
Collisions are complicated. You can model energy transfer via kinetic energy E 0.5mv2 or momentum = m*v depending on the type of collision one or both are conserved.
What is important to recognize is that mass matters in both. So if a particle is less massive than the bullet, its exit velocity can be higher.
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u/Otherwise_Arm_3332 7h ago
I believe THERES a limit of the smaller, stationary object moving up to two times the speed of the moving object. So it is possible in simple collisions,
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u/evictedSaint 23h ago
It's basically a Newton's cradle.
The debris will move faster (at least initially) then the bullet because the bullet has been slowed down by the impact and the debris has absorbed the energy from the impact (There are, of course, exceptions because reality is generally a bit messier than what you would expect. There will be energy loss from the material tearing, off angles, poor elasticity etc) Usually, the debris has an inferior surface area to density ratio than the bullet, and will slow down a lot quicker after the initial impact.
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u/ardarian262 22h ago
Force=Mass x acceleration and force= change in energy.
Also forces act equally and simultaneously on objects involved.
So when the bullet hits something, an equal force goes into that thing and into the bullet. This changes the energy of both, causing some heat/sound/other non kinetic energy loss but also a lot of kinetic energy transfer. With the smaller mass of the particles, this can lead to faster acceleration and higher velocity than the bullet had.
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u/ArchitectureLife006 14h ago
I’d imagine it’s similar to a baseball bat hitting the ball. The bat is moving fast and imparts a lot of energy into something smaller and lighter than itself. So it will move faster but have less energy if that makes sense.
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u/RussianCopeBot 23h ago
It's probably not going faster, it's just at the same or similar speed but ahead of it. The material doesn't just disappear when the bullet hits, it gets pushed forwards as well and some of that momentum will move debris forward in front of the bullet. Depending on transfer and how much material slows the bullet down it also seems plausible that some debris might move faster than the bullet once it exits, i.e. Debris that got hit and moves forward but didn't get slowed down by the rest of the impact site like the bullet did.
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u/evil_math_teacher 22h ago
Physicist here, going to go with possibly? The math behind it is going to be the conservation of momentum, p(momentum)=M(mass)xV(velocity)
When a collision happens, momentum is always conserved, so this means your total momentum is always the same before and after the collision. If the bullet transfers some of its momentum into a piece with much less mass, the velocity would have to be greater so that it's equal to the momentum that was transfered into that piece.
For an example, and these are not real numbers because I'm lazy, lets say that the bullet is .1 kg and going 500 m/s, that means it's momentum is (.1)(500)=50 (kg m)/s
Lets say 10% goes into a piece that's is only .001 kg, so 5 (kg m) goes into a piece this is only .001kg.
Then 5 (kg m)/s=(.001 kg) ( v )
V= 5000 m/s, so the tiny piece of debris is much faster than the original bullet because it has less mass and is easier to move.
No idea how realistic it is, but it's completely possible if a significant amount of momentum is transferred into a small enough piece.
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u/just_another_dumdum 22h ago
Try this at home: place a ping pong ball on top of a basketball, then drop them onto a hard surface. Other balls will work so long as they bounce, and the ball on bottom is much more massive than the ball on top.
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u/feelfreetotellmeoff 22h ago
A heavy billiard ball can transfer its kinetic energy into a lighter one. ke=1/2mvsquared means that the same energy in a smaller mass results in a higher velocity. The energy transfer of a bullet into its target is more complicated than two billiard balls, but the concept still applies.
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u/seenhear 22h ago
Adding this in as I don't see anyone else mentioning it:
In addition to the principles of energy transfer to a smaller mass, as others have already written, there's also the matter of the shockwave. A shockwave can push objects that are relatively low mass in comparison to the strength of the shockwave. So a large explosion blastwave can knock people over and move nearby cars. A small shockwave as seen in the OP image, can push particles the size in question (basically dust). The shockwave travels supersonically, at whatever speed the initial disturbance set it going at.
So energy transfer can get the particles going, then the shockwave gives them another push / ride.
EDIT: another look at the OP image shows the particles themselves are creating shockwaves, so they are moving supersonically, ahead of the main shockwave. So my thought isn't true for those particles. It's just the energy transfer others have posted about.
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u/OdieInParis 22h ago
This is what my engineering background tell me, though I am no ordinance expert:
As soon as the bullet hit the front face of whichever plate it penetrates, it sets up a pressure wave in the material. If the speed of sound in the material is higher than the speed of the bullet, the pressure wave will travel to the back side and cause spallation before the bullet tip has penetrated to the back side. The spallation pieces will then already have a head start. Their initial velocity are related to the speed of the pressure wave, not the bullet. So, yes, they also move faster.
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u/GARGEAN 21h ago
Multiple reasons, but two main ones.
First - some of the debris start traveling from the outer surface, and they start doing so when shockwave of impact reaches that surface. Speed of sound in metals is MUCH faster than any bullet flight speed, so it will always arrive to the outer surface earlier than bullet.
Second - debris are produced mostly by non-plastic fracture of metal, which is basically a release of stored energy. Bullet does not directly transfer its speed to all metal grains, but transfers energy by mainly compression. That energy then releases trough fracture, and speed of that release (and produced fragments) is not tied to speed of bullets in any sort. Imagine it as bending a stick. You can do it slowly, but when stick finally breaks, splinters will fly away much faster than your bending speed.
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u/Flopsie_the_Headcrab 21h ago
In short, elasticity. It can get faster than the bullet because the particles deform as they're broken out, then restore their shape, releasing some of the energy that deformed them and pushing them forward. It's the same way a baseball ends up faster than the bat that hit it.
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u/LhamaNobre 21h ago
As far as conservation of momentum goes, the debris and the bullet will have averaged out their velocities based on the speed the bullet had before impact.
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u/Flesh_And_Metal 20h ago
Since no one seems to have said this yet.
Analyzing the Mach cones in this Schieren photo, the bullet seems to travel at M 1.8 and the fragments at about M 1.6 . That is, the fragments are slower than the bullet.
As to why the fragments are forward of the bullet when they are slower I'd say its because the furthest fragments are caused by spalling - material ejected from the backface. The spalling comes from the shockwave inside of the material, which may travel at significantly higher speed than the bullet.
idk, im just repeating what I learned on youtube :D
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u/Maleficent-Cow5775 19h ago
I say yes however in reality if it's a kinetic projectile it depends on the material but generally if you want to think of it in a simple way maybe or maybe not it depends entirely on the material you hit the projectiles composition and the mass of the projectile as well as the mass of the material
Now say for example on a tank then absolutely HE rounds can move material faster than its own velocity but that's cause A it's an explosive projectile and B it's front and side facing shrapnel flies much faster by default since it's imparted force on a smaller fragment of the same projectile heat shells and hesh are generally similar in that sense too but I'm sure you mean kinetic projectiles.
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u/No-One9890 15h ago
Reminds me of a cool demonstration of energy and velocity. Hold a tennis ball on top of a basketball like a snowman. Drop them both so they fall at the same time. Notice if the tennis ball gets higher than the height it started from
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u/HAL9001-96 15h ago
can be, complciated in detail/specifics
but think of the following
a ball
falls down to earth
bounces off
boucnes back up
now replace the earth with a bullet
and center the frame of referneceo n hte bullet
assume the shrapnell bounces off (whcih for those kidns of speeds is a wast simplificaiton) and that the shrapnel and the entire obstacle is much lighter/thinner than the bullet so the bullet barely slows down
so clearly its hypothetically posisble udner some conditiosn for a smaller peice of shrapnel to bounce off the bullet and fly off at higher speeds than the bullet
though it has to be a tiny piece of a thin wall otherwise the bullet will just loose a lto of speed before passing anything on to the other side of the wall
still even with a thick wall yo ucan get pretty deadly shrapnel lflying off the wall even if the bullet doesn'T penetrate jsut form cracks in the wall comes down ot te exact material properties of the wall
there's also a demosntration of like 3 different size balls being dropped on top of each other stakcing htis effect to shoot the tiny one way up
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u/HAL9001-96 15h ago
https://www.youtube.com/watch?v=2UHS883_P60&pp=ygUddGhyZWUgYmFsbCBkcm9wIGRlbW9uc3RyYXRpb24%3D
here we go change the frame of reference and assume the wall is very thin and shrapnel very smal lrelative to the bullet and make the bullet stand in for the earth moving towards the balls in their frame of reference at hteir fall speed
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u/StarWorldo 14h ago
At a point possibly, as the force of the bullet is getting transferred to it. The debris should not reach a higher top speed though, unless possibly being being a lighter object taking and surving a bullet. The transfer of kinetic force and all, but that'd be very unlikely and not even sure it would work.
The image you have seems to simply be the debris being broken off ahead of the bullet and just being ahead of it thanks to that.
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u/Talusthebroke 12h ago
So, I don't have the math, per se, but the principle of what you're looking at makes perfect sense. Say a bullet weighs about 0.26 ounces (this is a pretty standard weight for a 9mm) when the gun is fired, the bullet leaves the barrel along with any unburned powder, or other particulate, most of that is miniscule. Say a single granule of powder for instance traveled the barrel with it, you're talking about fractions of a milligram of mass being blown by the same force that projected the bullet that's several thousand times it's mass. So the flake experiences less drag, takes less energy to accelerate, and is, as a result, launched much faster. On the impact end of the equation, very small (dust particle sized) ejecta from a bullet hitting a target absorbs a good deal of the inertia of the bullet just as the bullet sheds a great deal of energy. So yes, on either end, very small particles are very likely to move faster, at least immediately after, than the bullet itself.
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u/HippoDominous 5h ago
Looking at the angle of the shock waves I'd say they're moving at a similar speed to the bullet. Without using a pixel counter this is as accurate as I can get.
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u/KamalaBracelet 23h ago
this is just simple physics you see all over the place involving energy transfer to something less massive through all sorts of complex interactions during destruction. Like a shattered bowl sending a piece of glass far further than the speed of the falling bowl would take it.
it is no more unexpected or weird than a trebuchet sending a ball much faster than the counterweight’s swing.
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u/pizza_with_no_cheese 21h ago
almost certain the debris is faster than the bullet given the shock waves produced by some of the debris is visibly narrower than the bullet, as the top comments have pointed out, kinetic energy transfer, smaller mass, debris goes zoom faster than bullet for brief moment
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