Most Collisions Are Secretly in One Dimension
Вставка
- Опубліковано 10 тра 2024
- The first 200 people to brilliant.org/MinutePhysics/ get 20% off an annual Premium subscription to Brilliant.
This video is about elastic and inelastic collisions in 1D, 2D and 3D - and how the collision of conservation of energy with conservation of momentum, plus a secret direction, results in a completely predetermined behavior for most collisions.
REFERENCES
1D Collision Calculator:
hyperphysics.phy-astr.gsu.edu/...
Elastic collision of spheres Wolfram
demonstrations.wolfram.com/El...
Oblique collisions of two 2D spheres
iopscience.iop.org/article/10...
Ballistic Pendulum
hyperphysics.phy-astr.gsu.edu/...
Support MinutePhysics on Patreon! / minutephysics
Link to Patreon Supporters: www.minutephysics.com/supporters/
MinutePhysics is on twitter - @minutephysics
And facebook - / minutephysics
Minute Physics provides an energetic and entertaining view of old and new problems in physics -- all in a minute!
Created by Henry Reich - Наука та технологія
The equations you showed actually have two solutions, which makes sense, because the energy equation is quadratic. For a perfectly elastic collision, the other solution is that the objects just pass through each other unaffected, which of course also conserves momentum and kinetic energy.
this video was just clickbait man. Even confessed to it troughout the video.
@@maxluthor6800 in what way?
This kind of is what happens for wave collisions, though some weirdness might still happen while the two waves are inside each other.
There's still only one _physical_ solution, to a 2-body collision in that case though tbf; there's a mathematical second solution, but in physical terms for most objects it will involve a physical impossibility (eg two solid objects passing through each other without interacting)
@@Hannah_Em i guess that's why he said "in our universe"
Wow, 5 months with no video and then i stumble across this one minute after it goes live
Yeah me too I thought what kind of channel is this? And how did I get notification from this channel ... Did I even subscribe this channel?¿😂
@@kaijemofficial2726it's minutephysics lmao, what do you mean? 5 mil subscribers isn't nothing
@@DeLewrh He probably meant that it's been five [long] months since the last video that he forgotten that he had this channel on his notification bell or that this channel existed. So when he receive the notification for this channel he was momentarily confused. I don't think he's belittling the channel.
💀
If we are on youtube every second, can we really be surpirised about a coincidence like this?
As a somebody who deals with computer simulations of mechanical systems for living, I can assure that simulation of collisions is actually a really complicated topic. If you have a system of multiple interconnected bodies, i.e. you are dealing with multibody system dynamics (that is the scientific keyword here), you can no longer deal with mass and velocity only, but instead you are, usually, solving accelerations from a system of nonlinear differential equations that describe the dynamic force equilibrium of the system. Contacts are treated as external forces, which means you need to be able to solve both the magnitude and the direction of the force, which is not a trivial task when the shape of the object is complex. Also, for contacts to be actually any useful, you need to model the friction forces at the contact points, which is not exactly trivial either, since, among other reasons, many models fail to create any force at zero velocity. In total, this means any contact can need, depending on the models used, 4-8 individually tuned parameters to work.
Of course, if you are making a video game, things can get a lot simpler since accuracy doesn't really matter. But for an accurate simulation that you could use for engineering purposes, things are quite different.
As a somebody who used video game engines to simulate collisions for some simulator software, I can tell you things maybe get simpler - but they are definitely not simple. A lot of work goes into tuning simulation steps, and fake masses and so on, so that objects behave in a 'realistic' way and still not require a thousand simulation steps a second.
And remembering how difficult it is to simulate a rope still makes me wake up at night...
actually for engineering purposes things are often much easier than for games because you can do calculations offline. physics in games is realtime and both the collision detection system and the solver need to be fast enough in order to run in realtime and they also need to degrade gracefully when it just can't keep up.
for engineering you can often bruteforce very simple/reliable/slow methods that are simply not viable for realtime purposes.
@@PavelKostromitinov Oh, I never claimed they were simple :) In some ways it is actually simpler to aim for physically accurate solution, since you can, at least in theory, rely on hard data when tuning the system. However, not all parameters are available and not all parameters have a physically clear meaning, so you will still end up tuning your system to make it behave in realistic manner.
And yes, ropes are nightmare material, even at around 1 millisecond step size where I am working...
@@Alexander_Sannikov Here is the catch: I am working with real-time applications. But you are correct, if you can brute force a solution offline, things get simplified, since you can use actual parameters and you can use more advanced integrators to get the accuracy needed.
Agree with this a lot. What this video is basically saying is: if you ignore everything that makes collisions complicated, they become simple, which is something rather vacuous.
The fact that collisions can get pretty complicated is the reason something like the LHC exists, because by colliding things you can see how the physics works by looking at the cross sections.
Great video but all those flashing texts are a bit annoying. I love to read the extra complexity you put in the notes but on a phone or smart TV it's almost impossible to pause at the exact right time. Please keep them in the screen (a bit) longer in the future
This.
This is probably the only minutephysics video I haven't up-voted. And it was borderline on getting a down-vote.
Yep. Even on PC it is hard :(
It is really annoying.. it seems like our fried is very shy of using the "incorrect" words and tries to cover his "imperfections" without giving out the slip... Still enjoy the video, but YES - ANNOYING! Either correct yourself properly or own the slips...
Not a bit, it was REALLY annoying
I thought it was just that my coffee wasn't working yet and dawn is not the time for physics.
Great video, and it’s so good to see you back! I’d never considered that fact that even when there’s energy loss, conservation of momentum and energy uniquely pin down the velocities. And I hadn’t heard of the secret axis of collision either, but it makes so much sense! Feels like these two points should be added to kinematics classes.
Also, what did you use to simulate all those collisions??
hi Looking Glass Universe
I have an BS in physics, and this point was included in my Classical Mechanics course. Picking the right coordinate system to describe your problem in can cut down the algebra work in half or better.
@@justinmullins1112 Picking the right coordinate system is taught in high school physics too. Take the case of a mass falling off a slope for example. That way we only have to break down gravity into the component parallel to the surface and the component perpendicular to it. But I don't think it's taught in the context of collisions because it's more complicated to work with.
@@Exachad At least in my locale, that's exactly right - 2-D collisions are for the most part glossed over and vastly simplified, with the full treatment left to university.
Part of it is probably also due to vectors being formally only taught at the last few months of HS, which means physics can't make any mention in-curriculum of projections, dot product, cross product (makes the magnetism calculational portion... *interesting* to teach), and vector maths in general is highly limited.
I love it when there's a sentence or two of text added on screen and it flashes for a bat of an eye so I have to rewind twice and then accept I need to pause on the third rewind.
So glad to see Minute Physics back! Thank you. And though I don't know how much more it takes to animate, I think that the animations are a great addition. I would ask that your *caveats and *clarifications be more than 1 frame, it is distracting trying to scrub to find the one frame that had something I wanted to read.
Try the "," and "." keys.
@@Deus_Auto TIL about the "," and "." keys. Thanks!
@@Deus_Auto A useful workaround but a workaround is not a solution.
@@mrdragon5142
Also when you open the transcript (the three dots next to save to playlist), then you can search for specific words or phrases with Ctrl + F, and it'll jump you to the exact minutes/seconds every time it's been said.
I remember having to figure exactly this out when making a physics simulation for coding practice. At first I had no idea how I was going to handle collisions in 2D, but then I realized I could simply look at the collision from the frame of reference of the two colliding objects (ie their total center of mass) and that simplifies things to one dimension.
Whoa I would’ve felt so smart coming up with that :O
But then you have to translate it back into 2D or 3D to get the correct x,y,z offsets so it's easier to just do the calculations in 2D or 3D which is how almost all simulations work
I'd love to see the same kind of video for rotating objects - spinning tops colliding, theoretical spinning spheres, maybe touch on spinning black holes....
I doubt there'd be much rebound when it comes to colliding blackholes (for the singularities themselves, at least), but it's a really interesting topic that you can find a really neat explanation of using TODAY'S SPONSOR: BRILLIANT
@@LagAttacktoSlay what happened to your dream of making gaming content?
-Matter didn’t create anti matter
-Anti matter didn’t create matter
(Both of them were present at the time of big bang)
-Both of them didn’t create themselves.
-Both of them came from an unimaginable source, that unimaginable source created matter and antimatter (everything) thats why it is known as “the creator” of everything.
------:::::::::::::::::::::::::::::::::-----
- that unimaginable source/creator has created sin and virtue which are opposite to each other,
- logic says every action has its own reaction, so the reaction of sin is different than the reaction of virtue,
- the creator has created prophets to let us know about each and every detail of sin and virtue, also about their reactions,
Thank you :)
'Most 3D collisions are really quite simple, but don't worry, because you can make them really complicated by over-simplifying to 2D'.
@@LagAttacktoSlay blackhole singularities don't follow exclusion principles ( and behave partially as dark matter in that regards. Although in my personal opinion singularities are more likely high energy waves of non gravitationaly unified strings but unified in electromagnetic, weak nuclear and strong nuclear forces, furthermore, the dimentionality of these non gravitationaly unified strings is zero ( which means they are pure energy which still interacts with Higgs boson and Higgs fields ) ). Blackholes still warp space-time via gravitational waves (Higgs fields) though.
This is one of the first video by minute physics where I actually know and understand what they are talking about
Newtonian Mechanics lol
Good for *us* lmao
🤣
I'd never thought of it this way. One of the first things we were taught in High School (AP) Physics when it came to collisions was that you always separate the vectors into their components, but it never occurred to me that essentially we were computing a 1-dimensional collision.
Because you'll have to convert it back into 2D or 3D for it to be relevant to any experiment or simulation
@@Ziplock9000 But that's a much easier task.
It’s one dimensional along that arbitrary axis… which you can describe as a vector, which is more convenient for understanding
@@willmungas8964 For understanding maybe, but not for computer simulations which always use separate x,y,z.
It's all really simple, but also complicated. You know, science.
Incredible animation this time! Great work!
This is a fantastic way of introducing and understanding vectors imo
Awesome, loved the explanation and the animation!
This is the secret to physics: It's not hard, just pretty damn tedious
Fr lol
Sounds more like mathematics, expecially for people with ADHD.
Not when you have computers
He's lying. It's super hard.
It's all of it. Some things are easy, most things are hard. Some are trivial, some are tedious and a lot are extremly tedious. Even simple things like a pendulum get really tedious once you do physical pendulum, air resistance (and any onther resistance), laminar and turbulent flow, flow separation, air pressure, air humidity, coriolis force, propagation of uncertainty, vibrations and flexing. I probably missed some.
You should make part 2 for this video which will explain rotations. I really love Newtonian mechanics!
Glad to see minute physics again!
And this time I understand more of this concept because I'm actually learning it in college now! So that's really neat ✨
I was internally screaming "what about rotations!" the entire video, but then I sighed in relief when I saw the note at the end.
Great vid! Just a little remark: Those side notes flash by way too fast. I don’t want to stop the video, scroll back to the exact frame it was shown.
My physics teacher showed us a way to calculate collisions by switching to the center of mass's frame of reference, which a) turns the problem into a 1D collision and b) is really easy to solve then convert back to the lab frame.
That is a great trick. It turns the giant quadratic equation that would lose half the students, into an equation where it is easily isolate the unknown variable with simple algebraic steps. It also gives us the result that for elastic collisions, the two objects simply reverse direction in the center of mass reference frame. I feel it even gives you more insight as to what is really happening, as well.
Bro, you should have made this 5 years ago when I was studying collisions in Physics. This definitely would have helped.
Great video! Question: does this not just follow trivially from a change of basis vectors? Or am I misunderstanding the result!
Yes, moving to another reference frame is just a change of basis in 4 dimensions
Very cool video on the basics of kinematics of collisions. Love it!
Wowwww. It was such a long time minutephysics uploaded a video! Even though minutephysics have more science that other people can bear, it’s still great!
Firstly, this was a fantastic video and I really appreciate the effort put in. Im going to watch more videos from this channel for sure.
I do think that the *captions should be visible for longer though. Unless I'm not aware of a method that makes it easier to pause within a particularly small time interval, I really think they should be up for longer 😅 it's more than likely because I'm dyslexic and can't read quick enough but I doubt I am alone.
Thanks for the great video!
'.' and ',' keys can increment by individual frames on desktop youtube
The animation looked awesome. Does anyone know what software is being used for these?
great to have you back ! you rock dude! :P
You missed a great opportunity to explain that, in fact, there are 2 solutions for the conservation of momentum equation. One is what you presented. The other one is to keep both velocities the same as they were before the collision. It's not physically possible, but it's a valid solution for the formula.
If you were to implement the other formula in a collision simulator, this is what you'd get: ua-cam.com/video/SqpIcsN0FTI/v-deo.html
It is possible. In fact the system was precisely in that other solution before the collision. Notice that the equation only mention velocities, not positions. At the moment of collision the system simply jumps from one solution into the other.
All the collisions at the end were so satisfying to watch
And again, I need to watch your movie twice. First time I'm just totally locked in to the awesome bass backing track
Great to see a new video from you!
We have been trying to realistically simulate collisions with computers for more than 30 years now, and we still have to use hacks, like virtual thickening of surfaces, smoothing out surfaces and their motions etc. When you measure time in discrete intervals collisions are a lot more complicated. In order to know where the "hidden axis" is, you need to know the exact moment of collision, which is near-impossible in a system where time is discrete and of limited resolution.
What about colloision of matter and antimatter?
please make a video on superposition principle..
The animations were so cool! :) Do it again!
I learned this in dynamics but it's cool to hear from a different perspective
Dimensions are (in other words) directions, time can also be considered a direction ('arrow of time' for example). So a way to interpret this video is a single dimension plus a time component.
Yay! You're back! What were you doing, Henry?
I think you put it brilliantly my friend. Scattering and subsequent spin variations I find less important. I know people want to know exactly what is going on with all the composite particles of the collision, but the predetermined mechanism is clearly there and the spin variations are likely do to mass clumps
Back in high school I was very weirdly obsessed with physics engines for games, can't believe how much time I spent on these equations. Thinking about them still makes me feel giddy. Then I had advanced dynamics as a post-grad, life changing most fascinating shit I ever studied. Also the most difficult.
Many years ago I came up with idea, that there's no such a thing as "random".
That's the concept that allow us to comprehend thing we don't understand.
If we could have a power to define every single possible variable of any event,
we could tell the outcome of that event.
That's certainly what Einstein believed. "God does not play dice". Current interpretations of quantum physics may say differently, but who knows what the truth is once (if) we have a full understanding of the quantum world.
I have to agree that I'm uncomfortable with the idea of a universe that is fundamentally random, and therefore in some way non-causal.
@@Brad-gc9cq no, no. Even a spooky actions at a distance, could be explained somehow. We didn't get there, probably never will. There's a lot a things we don't understand, so maybe there's a chance to understand quantum entanglement someday.
its been a while since ive looked at one of your videos. I still remember back when i was watching you channel, CGP grey, and Vsauce.
It's cute that you have those single frame footnotes, but it's only a distraction when not stopping to read them and a nuisance when you have to interrupt the flow of the video every 10 seconds or so. And it's pain on mobile.
Maybe scoot them over to captions?
I have fallen in love with this kind of Physical thinking. The work of David Hestenes "Geometric Calculus" works to formulate all physics with the dynamical vectors as the basis. It makes these realizations much more apparent. 10/10 recommend
Macroscopic collisions also have friction, but still, the sum normal + friction points in a single direction. We do need to allow for rotational energy in that case. Long-ranged interactions with energy loss/gain; however, can be asymmetric.
Sir, you just inspired me to make a collision simulation.
(in my beloved C++/SFML of course)
This is the first video I saw and I subscribed
🔥🔥
I wish you would talk more about numbers of variables (V) and numbers of equations (E) for multiparticle systems and confirming or disproving that V=E. Because I worked on this problem, trying to calculate in general, and I could never get V to equal E. I always had V > E. So every collision problem I had with more than 2 particles and in 3 dimensions was underdetermined.
Also @minutephysics, I have to ask if the title card object colors are a nod to Portal 2's goo that either increases speed or makes things bouncy.
Very cool! But how do you find the secret direction for a given 2d collision?
Seems like a pretty standard eigenvalue problem.
What did you used for the collisions ?
Great explanation brother.
For those who like to think in terms of symmetries, in 3D, if you combine translations, rotations, and frame changes (boosts), there are 10 symmetries that are imposed-i.e. ten equations to be satisfied. The variables of a 2->2 scattering problem are the four incoming and outgoing momenta, which account for 4*3=12 variables. So in total the collision depends on only _two_ variables, which you can take to be the incoming energy and relative momentum.
that ending was very satisfying to watch
How is it different from any other physical interaction with a deterministic perspective ?
Wow, bringing out the Variational Mechanics hammer I see ~ totally, like, "If the only independent variable in this problem is time, then, the problem is 1 dimensional, b/c there is 1 time dimension!"
@@ajeetgary2706 ahah exactly
That was a really fun insight!
@1:48 Is there a way to definitively calculate this "secret direction" you mention - assuming objects of weird shapes/sizes and frictions? I'm curious whether this is the kind of thing where sufficiently-unusual shapes/friction would require computer modeling and/or real world observation to figure out, or if there's any formulas that can be worked out by hand to solve any given instance?
That reminds me of when I got rear-ended by a Toyota Tundra.
My Dodge Stratus was the stationary object at the light, the Toyota tundra was traveling at about 50mph and did not apply the brakes.
My car slid forward about 10 ft.
The Tundra collided with us again, sliding us forward another 10 ft and folding the trunk lid through the back window.
The Tundra collided with us a third time and buried itself to my back tires, finally bringing this abbreviated Newton's Cradle to a screeching halt.
The driver offered me any amount of money to let him leave the scene of the accident. I asked you've been drinking, haven't you?
He admitted as much, and his breathalyzer results were just barely over the legal limit.
There were five other vacant lanes he could have swerved into if his excuse of, oh the brakes weren't working, were valid.
Welcome back man
Great work 🥳Thank you 💜
A video on elastic collisions would be the perfect time to talk about newtons pendulum
I suspect that in reality there is probably a great deal about the science in your videos that I don't understand because, you know, maths. But ignorance is bliss and I still enjoy them and look forward to them because I always learn something.
I'm glad to see you back! By a crazy coincidence, I stumbled upon your channel yesterday and was surprised to discover you haven't posted on social media for 5 months. Your content was missing a lot ❤️
This would have been a great complement to my first kinematics class in high school.
❤❤❤❤minute physics is love... I commented about your absence on your recent community post yesterday, and here you r today
"In our universe, the equations have a unique solution"
surely there couldn't even hypothetically be a universe where the logical deductions involved were invalid?
minute physics, millisecond notes.
This basic physics but presented with beauty !
Is object deformation completely contained in the energy lost part of the equation?
Yes
Yes
Any energy lost due to the process of deforming the objects will just be heat, and it won't affect the motion of the center of mass (beyond slowing it down due to said lost energy). But when taking rotation into account, it can make things more complicated.
Does this hold only if at the moment of collision there is one contact point. I guess even if there are multiple contacts then by super position you can treat them separately.
Which physics engine did you use for your animations?
Henry, I think u want to explain that during a collision in 2d, one of the vector components of velocity (x or y) remains the same, while the other changes( y or x resp.). So it's just the perspective in 3d space that u look a 2d collision from
No. There is a plane in which their eventual velocity after a collision will reside, but it is exceedingly unlikely for said plane to be axis aligned.
You're thinking of billiard physics, not at all what is being talked about here.
ah, a "back to basics" minute physics video. It's why I subscribed in the first place!
Can you explain this 1d collision with that old 'wood shooting' video veritasium did?
Seems to my simple mind that there is no secret 1d collision between the 2 shots.
Since any collision of a "particle" with another ends up being contact between a single point of each particle or (ridic imho) that particles are points.
A thought about actual exchanges in real world and the real nature of being a singularity.
Imagine a hollow metal sphere a meter in diameter. If we put a charge on this sphere where exactly is that charge? It is distributed over the entire sphere. And once charged, regardless of where on the sphere I touch I will ground out the entire sphere. So as soon as there is a deeply connected sphere, regardless of size, we begin to have a strange probabilistic distribution of all events.
Thoughts. Great videos. 🖖
Even if the sphere is a very real solid object
The amount of split-second footnotes showing up seemingly every second of this video really makes this video feel like a drug ad. "It's simple!" followed by a minute of disclaimers.
Was thinking about this the other day- two photons colliding, and realised that without something weird and 2D happening, there's not actually a meaningful distinction between colliding and phasing through.
Crazy right!! That's because there's not a meaningful distinction between the two photons ~ you and your friend throw a photon at each other like straight-on and they overlap in space during their journey and then you catch them: when you ask your friend "is this your photon? or is this mine that bounced back off of yours?" the question has no meaningful answer b/c you never gave a meaning to which photon is which besides it's initial location; "which photon is which" isn't like a falsifiable meaningful sciencey thing
Ever since UA-cam added playback speed adjustment, I've had to check to make sure I was at "normal" too many times.
I know the channel is called “minutephysics”, but could you make more 10-15 minute videos? I feel like this just scratches the surface.
It's simpler to solve equations separating them by axis than it would be to do them as a whole, this applies to any equation that deals with dimensions as the result is the sum of the contribution of each axis/dimension. This is a very common topic in science so no wonder ppl are calling it clickbait.
Super interesting. Does this all mean that brownian motion is deterministic, or the extrapolation is not valid? I am genuinely curious.
I would be curious to know if this continues to apply in theoretical 4D space
Why wouldn't it? He didn't address a difference between 2D and 3D, so you could easily assume.
Sure, it's applies to collisions of point like objects in any dimension.
NIce. A genuine question triggered by your very first example at 0:48. When one object hits a stationary and both have the same mass, the first one stops, the second one moves on at the same speed as first one. Conservation. But .. so it would be if, for example, the first one continued at 1/3 the speed and the second at 2/3, or any other matching set. And with the m and m.20 example next, why not the m stops fully (rather than rebounds) and the second goes at 1/20th which would be more in keeping with the first example, eg the moving mass imparts all its momentum to the mass it hits.
Correct me if I'm wrong but are the examples here just perfectly elastic?
We have the case where one of the objects become embedded in the other, which Im surprised isn't even mentioned
YES! I waited for this
1:17, I get it you can cancel the "1/2" in terms regarding kinetic energy. But shouldn't the lost energy term be doubled?
Ngl I first thought this was an old video until I saw "19 mins ago". Great animations.
These days videos are sparse...it's always a pleasant surprise when I get the minute physics new video notification
How did you animate things..? Which software..?
How does this extend to 3D collisions and how does this simplify calculations/simulations in a computer?
This had to be one of the funnest videos to make with the animations.
Is the contact point between 2 spheres different than a sphere and a flat surface?
i already kinda knew this, because i've atempted to make a colision detection system in programming as a game dev
Love your channel!
Excellent video!!
That part at the end. I love it. Omg
I don't know what your personal situation is, but if I get a vote, it's for more minutephysics videos! You have one of the best channels on UA-cam.
But doesn’t this only work for spheres? If you hit the edge of something long then it will start spinning and stuff will be more complicated right?
How did you accurately turn the drawings into objects that collide?
I love having to stop the video every time additional text is shown for a fraction of a second
I have the creeping suspicion that you do not, in fact, love having to stop the video.