Which is faster * Brachistochrone Curve ❤️ C4D4U
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- Опубликовано: 1 янв 2022
- Which is faster? First write in the comments and then start the video.
For me the topic brachistochrone is still very new. But I am fascinated by what is behind it. If you haven't heard of it yet, you should take a closer look.
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google.com/search?q=brachisto...
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• Who is faster? Gravita...
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• Who is faster? Gravita...
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Relax and enjoy this video.
ASMR for my eyes. Some people make it happy and satisfied. It also has a calming effect.
ASMR = Autonomous sensory meridian response
MUSIC-MODE ;)
Why don't I enter the music title anymore.
Well, unfortunately some people not only copy my animations (because they have no ideas of their own) but even use exactly the same music.
These people may now search for it themselves ;)
I hope for your understanding. 
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Yellow
blue
Newton showed the curve of fastest descent was a cycloid.
Yellow
This is a great example of energy conversion and use.
At the very top each ball has identical potential energy (E=mgh as per basic high school science class). Normally when asking how long it takes for a ball to fall or go down a ramp factors like friction, rolling resistance and aerodynamic drag are ignored. We teach the same way with pulley systems and other machinery. What this shows is that in the real world these factors can't be ignored and I can give you a very real example of where this matters.
Anybody who has ever learned to fly knows that for any aircraft there is an optimal glide path and that it exists for all aircraft (powered and unpowered). For glider pilots its one of the most important factors to understand because it defines how they plan their flights and its involved in every decision they make. For powered pilots it incredibly important to cruising if you want to save fuel as its the most efficient way to fly. Its even more important of the engine (or engines) fail in flight. All powered pilots are trained to fly their plane like the red ball immediately if the engine fails. In all engine failure procedures the first item is to set (and trim) the plane for best L/D (lift/drag). It gives you more time to solve the problem and get on the ground safely.
Great video for demonstrating a very important physics and engineering subject.
The red ball will always win regardless of which track it's on, because red is fast.
Waaaaaagh
Red is always sus
@@codingvio7383 sussy baka
Well yellow would have win if that curve does go below the level in last 10 cm otherwise yellow flash never loses
Or maybe the angle closest to 45°
Is the fastest path
2things to consider:
1: Acceleration due to gravity
2: distance of path
Steady curve less drag maintains & gains speed from start to finish.
Ok Ashok Aj •
Exactly, kind of like what we see in throwing an arrow, around 45 degrees starting point is the key..
Yeah, size the experiment up in all dimensions and then do it again.
I am inclined to think the outcome will be different and will demonstrate that the curvature effect itself is not the thing we are observing.
There might be an advantage to a specific curve, but only when the travel times are short to begin with.
3. materials that were used
4. Temperature
5. Humidity
6. Height above sea level
I couldn't tell because the music brought me to tears every time I watched even with the volume down
Just wait til you play some Chariots of Fire in the background.
I'd like to see how much momentum it carries over a long distance.
Now this is big brain time.
Just make a bigger brachistochrone lol
@@Ugetora That's not what they mean.
@@Ugetora They mean who ends the race with most velocity.
Wouldn’t the results be the same ?
Since you already hace the brachistochrone curve model, you could simulate multiple ball on different spots on the curve and they should all get to the end at the same time. This would be such a cool part 2!
Very nice idea. I write it down and try my best. Thank you very much for your idea :)
wow thats actually quite a good idea
@@C4D4U you never even try the ideas
Isn't that the property of the tautochrone, not the brachistochrone? Same curve, but different end points
Smells like Vsauce
The red ball is on what is called the isochronous curve. It is the fastest path possible. It will always win over any other path. It has other cool properties as well.
my uncle had some cool properties too. until he got gambling addiction and lose almost all of it and his wife.
@@tenerife_sea lmao
I think the golden ball is cool too. If there is no barrier are the end. It would launch much further.
Other cool properties such as?
@@DamjanMilinkovic No matter where you put a ball in a Brachistochrone, it will always reach the end at the same time. Watch Vsauce video on Brachistochrone
Okay so this made the concept of brachistochrone curve clear!! If only gravitational force is considered, variational principle shows that time of fall is minimum only if trajectory is a brachistochrone curve! big thanks to the makers
This is a great question answered well. one thought, does it take into account any surface friction? what about rotational inertia?
The gold ball appeared to have suffered a slight disadvantage as it was the only ball to be forced to ascend a grade at the end.
Still would have come in behind the red one.
With some setups, the fastest curve (still a cycloid), can dip below the finish and ascend at the end.
how about it getting to jump at the end?
@George Washington -- You are a troll who's YT channel was created a year ago. You've faked some content and that effort makes you a nation state troll. Given the content, probably Russian!
@@Raptorman0909 Don’t reply, just report as spam.
shortest distance between two points is a straight line, but not the fastest :)
It's all about which one has the optimal value ;)
Once i put this statement on a science grouo in FB and replies i got gave me hard time... All Einstein's and Newton's in that group argued me that this statement is allegedly false and talked about 4th dimension and string theory to prove me wrong...
@@user-pl7tf9gv8e nice name and pfp
@@Pimp482 thank you fellow John Cena
@@GughaGSrinivasan which group was that? I barely find good science groups in fb. Mind suggesting me few of the good ones, thanx
The problem of finding the curve with this property was first proposed by Galileo Galilei, who however believed that the solution was a circular arc. Johann Bernoulli found the solution in 1696. However, the curve of the red ball in the video does not seem to be the brachistochrone, because it should be a cycloid with horizontal tangent at the end point and vertical tangent at the starting point (i.e. the starting point should be the cusp of the cycloid). In the video, one sees that the curve is not vertical at the starting point.
Yellow's track fits more with the theory, however the circle is a bit bigger
@@octobsession3061 Yeah, my first instinct was yellow/brown. But, then I noticed that it went below the plane and had extra distance that didn't help with average speed.
The brachistochone solution curve (a segment of a cycloid) between two fixed points generally won't end with a horizontal tangent.
But from one fixed point to a vertical wall a fixed distance away, where we can hit the wall at any height (y-value), then the solution curve is the cycloid with a horizontal tangent at the end.
But I do agree it should start with a vertical tangent.
What? Can you repeat that w/ explanations? You just gave me a whole days worth of studying looking up definitions and applying them to your statements. But thank you, it's nice to know there are people out there knowing why things work the way they do
What? Can you repeat that w/ explanations? You just gave me a whole days worth of studying looking up definitions and applying them to your statements. But thank you, it's nice to know there are people out there knowing why things work the way they do
This is very useful for music production automation
What this short video taught me is:
Don't be too tight nor too slack, you'll reach your goal quickly
That's... Actually very useful
It's almost as if this experiment was made to explain that
And for some reason I seem to have made a breakthrough
Damn
Hmm, I like it!
Wtf
Mind blown 😳👌
This video is also tell us that slacking is faster than just doing it immediately
Great job. Totally outsmarted myself and switched from correct to not.
thanks to your videos i first downloaded blender, now i render softbody and its so fun, thx so much
When it comes to these types of things. It's usually the mid point between extremes that wins. The same with finding the longest range for a cannon. 90 degrees, go no where, 0 degrees goes xx distance, and the 45 degree angle goes the farthest.
But it's not really the midpoint, because you could have a whole set of convex curves coming to the same point. In that sense, the diagonal line is more the middle one. This problem is obviously a lot more complicated than the cannon scenario - I'd say it's by sheer chance that your suggestion of the "middle way" as the solution actually turns out correct in this case, because of the way the problem was presented.
But if your cannon were firing from the top of Mt. Everest...
After looking at the paths I went with red because it has the smoothest curve where it is consistently traveling at a good speed the entire length of the ramp. Most of the other colors had too steep or too shallow of a ramp to start and end with like orange has to go back uphill to reach the end which slows it down
'orange' - wtf
@@TheSometimeAfter Mark must be colorblind, it's clearly purple..
@@TheSometimeAfter people see colors differently. Everything affects the color the see, including the screen they watch this on. To me, it's brownish, but I can see why they said orange
@@Locormus2 they are talking about why they chose the red and not the one that ended up being the second place, not the blue ball
You need more explanation than that to convince me you pick red before watching the video.
Firstly- very nice rendering. Very smooth and the lighting effects are well done. Second- the Brachistochrone curve will be the shortest in a real-life test because physics. V-Sauce and Adam Savage made a one-day build that demonstrates this concept in real-time.
The brachistochrone curve isn't the fastest when the objective isn't the end of the track but the plate that's a bit further away. The further the plate is the worse the brachistochrone does since its velocity isn't pointing straight to the right but angled upwards.
The brown one is a close 2nd, however it also the only track that dips under and comes back up i.e. longer travel. Would be interesting to see what the outcome is if that track does not dip below.
It's a trade-off between gaining speed early in the path with a steep drop, then running through, but this requires to travel more distance due to the deviation from a straight line between the start and finish.
The exact path would also depend on the rotational inertia of tue ball.
This also happens in motor races, nascar especially because they mostly race on banked ovals, you'd see this on their road courses too and like the f1 tracks
@@brapa1190 Ah yes that's a good example. I was just watching Cleetus McFarland doing some banked dirt racing haha.
yes if the other ones where flatter in total and thus the path woule be longer in total the blue one would have outrun all of them, cause it gains speed the fastest,and thus for long flat track its average speed would be the highest.
Yeah, you could see the blue ball was faster than the red for maybe the first 90% of the course, but not sufficently fast to compensate for the extra distance that created that speed.
“Did Bernoulli sleep before finding the curves of quickest descent?"
- Peter Parker
Took me too long to finally find this comment
Surprisingly intuitive
why was i crying at the end this shit is emotional
I was still impressed with how close the purple one finished considering it’s path was much further than all of them. It’s spent half of its time falling straight down while all the rest were actually heading towards the finish line.
That ball is blue, not purple.
That ball is blue, not purple.
It gains energy really fast on the slope, which counters that distance to an extent.
the sound design, the music, all perfect!
Thank you very much for the very nice compliment but I must learn so much more about sound design.
I mean C is going to reach a higher top speed than D since the lane is almost vertical and has the least amount of friction. But it is also the one that will lose the most amount of speed compared to the other lanes. And the question was "which is the faster one" NOT "which one will reach the end point first". So technically the answer could be C depending on how you define the question!
Interpreting the question as which is the faster one by top speed, is not a reasonable interpretation of the scenario, faster is here clearly defined as the first to reach the end.
why try and act smart. we all know what the question was referring.
@@barrymore87 There is no justifiable reason for you to insult somebody over difference of opinion.
@@hypercubemaster2729 it's not a difference of opinion though.
it's clear what the video is about.
@@hypercubemaster2729 Calling that comment an insult is a stretch, he called him out, thats it.
This music makes me remember some sad memories while watching some ball race
I thought 5 would be fastest because it’s the shortest route. And I thought maybe I’m wrong and it’s 1 because that one would have the fastest acceleration at the start. Boy, was I wrong
Yep, it needs to be a balance of gravity and distance
Id say you were on the right path to the final answer
That's the beauty of physics!
Check out Michael Stevens' (Vsauce) video on D!NG (yt channel) on the Brachistochrone
If you've got a solid mathematics background, I encourage you to examine an introduction to the calculus of variations.
Similar principle to throwing a ball at 45 degrees for maximum distance
In physics and mathematics, a brachistochrone curve (from Ancient Greek βράχιστος χρόνος (brákhistos khrónos) 'shortest time'), or curve of fastest descent, is the one lying on the plane between a point A and a lower point B, where B is not directly below A, on which a bead slides frictionlessly under the influence of a uniform gravitational field to a given end point in the shortest time. The problem was posed by Johann Bernoulli in 1696.
The brachistochrone curve is the same shape as the tautochrone curve; both are cycloids. However, the portion of the cycloid used for each of the two varies. More specifically, the brachistochrone can use up to a complete rotation of the cycloid (at the limit when A and B are at the same level), but always starts at a cusp. In contrast, the tautochrone problem can use only up to the first half rotation, and always ends at the horizontal. The problem can be solved using tools from the calculus of variations and optimal control.
The curve is independent of both the mass of the test body and the local strength of gravity. Only a parameter is chosen so that the curve fits the starting point A and the ending point B. If the body is given an initial velocity at A, or if friction is taken into account, then the curve that minimizes time differs from the tautochrone curve.
He was a man of principle, that Bernoulli :)
Most viable comment thus far. People love to "sound" smart and it's irritating.
@@eyeHATEuall85 Annoying for sure. It was probably just copied and pasted from Wikipedia.
But what did you mean by *viable comment?
I think Sir Issac Newton solved this problem and sent the solution anonymously but Bernoulii recognized that elegant solution could only from the great Newton and supposed to have said I recognize the lion by his paws. I assume that story relates to this problem. I read it ling back, so I could be wrong. I am always fascinated by the genius of Isaac Newton, he is the only person in history who can be recognized as both thr all time greatest mathematician and physicist.
I just want to say, the only word in your post that I understood was "curve."
This explains the best way on how to dive in battle royale games
I guessed red, It made the most sense to me. Considering the length of the path and the potential for most acceleration.
While reading about it, I noticed that experimental limits exist -- on a horizontal path the ball won't move. On a right triangle path, straight down then horizontal, it will fall and then stop; it has not developed any horizontal motion. On a linear descending path, the velocity will increase linearly but the distance traveled will be parabolic (time-squared).
Consequently it can be visualized that an EARLY increase in velocity with a gradually reducing gradient works best. So at Time zero, you want it vertical, and at the end of the path horizontal since you are no longer interested in acceleration; you want to have "used up" all of the acceleration force.
I totally agree!
Oakily dokey Yo
No, the velocity don't increase linearly... you write a bunch of crap.
@@l.lawliet164 "No, the velocity don't increase linearly"
An object dropped straight down subject to the force of gravity and discounting the effect of air resistance will increase velocity by 9.81 meters per second, for each second it accelerates by that force. The increase in velocity is linear, the distance traaveled will be the integral of that velocity and if graphed will be parabolic.
On a slope, the accelerating force is reduced according to the angle from vertical; at 45 degrees it becomes one half the square root of 2 (approximately 0.707) times the force of gravity. the increase in velocity will be linear with time.
I invite you to show me the error of my thinking but you'll need to use something more specific than "crap".
@@thomasmaughan4798 Well if you discount the air resistance you are a fool! Air resistance affect the process more and more as speed up. The second point you are wrong is the ball number 2 only finish second because it has a level down that have to go up, in comparision to others, wich desacelerate the ball! The thing is the more inclinated the best as long as the ball doesn't hit the path wich desacelerate the ball a lot. There is no big brain time here, the best inclination without unevenness and path hit.
For you rocket nerds out there, this "most efficient" speed between two points concept, applied in reverse, is essentially the concept behind a rocket's "gravity turn" to enter low-earth orbit.
So they do a turn when coming down to not have all the momentum keep accumulating? Is that the same as how applying force to a falling object sideways changed momentum? Maybe the second question doesn’t make sense, IDK, but the first question does
@@amosdraak3536 To your first question, no. The gravity turn is used on launch, not descent. On launch, the engines gimbal slightly to lean the rocket over. After that, the engines straighten out and gravity does the work to keep leaning the rocket over slowly so that it achieves "sideways" orbital velocity as efficiently as possible.
@@glennpearson9348
Thank you. I watched this video looking to learn a thing or two, and read the comments for additional info. I appreciate it and I’ll go watch a rocket video to see it in action.
Thanks.
I just watched the video upside down to give the balls the appearance of "lanching up", it makes sense what you said. Ive done the gravity turn in kerbal space program, cool to see it applied here in reverse.
@@jordandrake9822 Pretty cool stuff, isn't it? I loved orbital mechanics when I was in college. Probably my favorite non-engineering class.
Please, can you remake the same experiment but without the wall after the slopes ? I'd like to see which ball has the highest momentum, that would be very interesting. Great video !
can a slower ball have more momentum?
@@rickblaster-xu5ie momentum is mass x velocity. To have a slower ball with higher momentum would mean it would have higher mass to compensate and then some extra mass on top.
So if they have the same mass, then the one with the highest speed at the end wins. The optimal shape for this at the end of the track would be a super light gradient at first with a huge slope at the end with a nice curve to send the ball in the direction you want to measure the linear velocity for. If this doesn't matter then straight down momentum would be highest for a straight drop down after a nearly horizontal movement (slightly down so it would move to the right).
This being said, of all the balls here the yellow ball here seems to have the highest end speed -- and thus highest momentum at the time of finishing the ramps (if all same mass).
They all have the same momentum (mass times velocity) since they all have the same mass and the final velocity is only dependent on the initial height. This is an ideal experiment without friction, therefore there is conservation of energy. Potential gravitational energy at the starting point is all transformed in kinetic energy (mass times (velocity squared)).
I think that if friction was involved the result would be the same. Air resistance is dependent on the shape (that is identical for all the balls) and on velocity in each moment. I would assume that the overall energy lost to air resistance is the same for all the balls but I might be wrong.
The rolling resistance would be higher for the longer paths (paths get longer from 5 to 1). In most cases of hard balls on hard surfaces, the rolling resistance would be negligible.
Ball 2 arrived instants after ball 3, having ball 2 a longer path, the rolling resistance would further delay it.
Come on guys, it's obvious he meant velocity, because he want to see how far they go, thinking that different paths would end up faster.
Exactly. Ignoring friction, all balls will have the same speed at the end of their tracks, since the drop height is the same. Potential energy converted to kinetic energy.
The ball hitting the wall first has the highest ratio of (average speed)/(track length).
Btw. changing the mass of the balls has no impact on the results in this case.
What destroys the blue ball is the long HORIZONTAL distance with no acceleration. What destroys the brown ball is going low and then having to get up later (waste of energy and time). Then we are left with Green, white and red. For those the sooner they fall at first, more speed they get from gravity, building more speed for them. Great experiment! ♥♥♥
I thought it was going to be gold, but I didn’t realize before the release that its track went below the horizontal line. Otherwise I would have guessed red.
I thought it was common knowledge that anything red will always go faster lol
I literally went through the same
Same here! Lol. Had I been a little more observant, I would have then gone with my second choice (red). Even so, I did not expect the blue ball to finish before the green.
Same
Same
It wasn’t about velocities, but CHANGES in their velocities that made the biggest influences (decreases) in speed
Keep calm einstein
@@ashleyhyne7027 What are you talking about? The point of the curves is that the various angles produce a different acceleration per distance traveled. "The speed of the velocity" is a contradictory statement, those are two different terms.
@@ashleyhyne7027 You know that only works for spoken conversation only, right?
@@ashleyhyne7027 why not leave the physics to people who actually know what they're talking about?
Whatever language sucks but it appears to me that Chris made a great comment it reads all right to me
My guess was Gold, but I didn't see that little uphill portion that, watching it in slow mode, totally killed it's chance for a lead, but it was CLOSE regardless.
Ikr. I feel like it got cheated
I would like to see this done again, but round the curve on the blue track more towards the bottom and make the gold track not go below the end point like it does.
I'd like to see track lengths as well.
Blue looks like it's taking longer buts it's traveling far more distance over all.
My guess was yellow! I had thought the more time gaining downward momentum would speed it up more to take the horizontal gap. The steepest was too much vertical and I knew wouldn't translate into horizontal as well. I was a bit surprised to see it come second, but it was very close!
As mentioned in a previous comment that was the only path that had an ascending slope. Path 2 actually dipped below path one. Some of us cry foul, unfair but interesting non the less.
I was surprised at how close they still were to each other. I figured that the blue ball would be the worst by a large margin.
Guessing is the wrong answer!
I chose that too
Thank you for answering a question I never knew I wanted an answer for!
No tengo la mas mínima idea de física, lo cierto es que este video me distrajo un monton y me puso a analizar. Me encantó 👍
Nice video, thanks :)
Always a curve of acceleration has advantage over straight (that's why blue won over green. But too much will make the way longer. Thats why white won over blue. Brown wins over white because the first rule. And then, red won because was the perfect balance between acceleration (provided by the curve) but keeping the curve with the minimum distance possible.
Maximun acceleration with minimum curve possible.
Red beats brown because brown has an incline at the end of it finished on a straight like the rest it wins
What this tells me is that a balanced approach is the best approach generally.
easy on the racism
@@jub8891 huh?
@@jub8891 only one who seems to be racist here is the one who brought up race..
it's amazing how much momentum the red ball manages to get during it's travel down the curve. Look at how long it stays glued to the barrier (dissipating energy) after winning the race before finally falling to the ground.
Reminds of the old Boys Scout days with the PineCar racing tournaments...I was trying to tell everyone that there is a “catch” to it!
Balance is key my young padawan 🙏
The way spider-man swings so he can pick up as much speed as possible. On point that it’s the red ball too!
2-3-4-5-1 would be my guess based on gut feeling. edit: I missed the fact that 2 dipped under the "sea level" from the original picture and had to climb uphill final moments and I was expecting there to be more of a reverse spin/impact from the sharp angle turn of ball number one.
Likewise I didn't see the dip. Trick question!
Same here as soon as I saw it I was pissed at myself. I guessed 2-3-4-1-5 though
i think 2 would have won if it didn't dip below.
Same. 2 was actually the fastest based on speed, as it had more distance to travel vs 3, which is why it just barely hits the target 2nd. If the dip levelled off with the others it would have won.
@@CanadianLoveKnot I'd like to see the experiment redone with number two leveling out at the same point as the others instead of dipping lower, and see if that would turn out true.
The parabolic curve is the curve will provide the lowest interval of time to reach the target. Remember the final linear speeds for all (considering no rotation and friction losses) are the same.
So cool! 🤩Maybe we should make roads in Brachistochrone curves 🤔
This is a very cool science experiment. I love it. Thank you.
Paths 2, 3 and 4 (increasing radials) can help understand the optimal speed a racing car follows in a constant radius corner, of course excluding the gravitational force shown here.
The gravitational force is everything here. It has nothing to do with race car lines.
Yes it does. You know nothing. Replace gravity with the throttle of the car, and racing lines definitely apply here
@@kaustavkapur5532 Nope. The equations are different.
this is the same thing that happens when spiderman swings his web, he indeed thinked of the fastest way to save people, what a hero
boy i would love one of these and start taking bets from first time players only
You know you're getting old when a concept that a VSauce video went in-depth on isn't well known anymore. :(
VSauce rocks
Hello, nice video! Just a tip. This is about which ball arrives first at the end of the path, not which ball first hits a target at a distance from the end of the path. This is because their trajectory is different after leaving the course and this affects their arrival time at the finish line according to the angle they are at, which can increase or shorten the distance.
This could have affected the result if the distance had been a little longer.
But I think the result is correct, the Brachistochrone Curve is a Cycloid curve.
@B S, so in an auto race the car that crosses the finish line first isn't necessarily the winner, It's the car that gets there before he?
@@M60gunner1971 no. Is the car who finish in less time. The kee is the time, not the distance
hate burst your bubble but it IS about which one hits the target first. Its HIS experiment not yours. When you design it - then you get to set the 'What it is about' condition.
@@armastat lol hate to make you look like an idiot, but this experiment is about Brachistochrone Curve as you can see *in the title* . Which means "what is it about" is already been set by people who introduced this experiment. So it's not this youtuber's experiments, it's Johann Bernoulli's experiment.
@@smallone2351 And here comes the late to the party word Nazi who barks and nibbles around the edges of a conversation rather than engage in fun and satisfying normal human interaction. If you want to be noticed trying going outside.
I voted for red ball, and sheesh it went fast, also the slow motion had me on edge, it was amazing!
It would be nice if you give short explanation in such videos
Btw good video👍🙂
The REAL challenge is to determine the absolutely optimal shape of the incline to achieve fastest run. To complicate things, the rotational speed at the end also contributes to total run time since rotation absorbs some of the energy.
You can find this mathematically by using Hamilton's action integral.
Of course. Why didn't I think of that?
Aw thanks except My math skills are so fucking basic I have no idea how to divide fractions
Was that in the play?
Hamilton is the name of my hamster
@@DAMfoxygrampa you can find your hamsters action integral
This is a concept we had to learn in plumbing school
What were their time differences? And the curvature? Just curious about it
*Same and I wonder about the balls mass too!*
A velocity graph can explain a lot here because my suspicion is only the green ball got a linear acceleration, blue got a strong one until reaching the horizontal path so its acceleration becomes zero. The faster ball can probably show the smoothest graph and the integral of its are can evaluate the maximum value
Never show this to a motorcyclist. This makes his mind go haywire. Wonderful!
I'm dirt biker, :)
No it doesn't, a motorcycle has kinetic energy
Hey, superb visualisation. What did you use to render this ?
Damnnnnnnn I guess the Yellow ball lol cool video
The problem with the gold and blue ball at the bottom of the track velocity was interrupted by the flat surface on the bottom which Disturbed the momentum therefore the red ball was curvy without being disturbed plus it was closest to the bottom and it had a better curve for velocity and speed
hi, thanks for the video! I want to ask what kind of renderer was used? Octane, redshift or something else? after all, not such a complex animation, but so much time to render! And I understand that this video was no longer made in Cinema 4d ?!
Thank you.
R.S I like the quality and texture
I used redshift. The render time is so long because I rendered a lot more. The close view was shortened very much. The original goes over the whole time. I may upload this to my other channel sometime.
Btw: Thanks for the nice compliment :)
I didn't realize this was an animation. Very nice work.
I hold my hands up I guessed green as it was the shortest distance. Back to school for me.
thank God (actuallt, thank the smart people) for the internet...what I'd do without this video
I want to see a face-off where red & gold are the two extremes, & the other lanes are in between. I feel like a sharper descent that doesn’t go below the floor plane & then up again would beat the red ball.
why???
This is a nice problem in variational calculus, that of finding the curve that minimizes the time of travel. You can also use the variational calculus to compute the path of a light ray in traversing a path that goes through differing optical media. When you do the minimization integral you have derived Snell's law for refraction, the bending of light. The same principle applies to the refraction of sound waves in travelling through ocean layers, of great use to submariners.
@jim, this can be explained using a flexible meter stick a string and some household lubricant.
@@M60gunner1971 I just use a hot-wheels track and a few race cars.
@@armastat those were the day, my dad was pissed one day he got home that I made a track that ran through the house. It was fun while it lasted :)
It's also the same equation used in electrostatic for the flux density boundary condition of dielectric materials.
That's how Newton did it, so I've read anyways.
I remember this problem from my first day of calculus of variations.
Fun to watch. But the music that is the best
I've watched enough Vsauce to know that red will win
Yes, you are right.
Vsauce is very cool :)
@@C4D4U i watch vsauce too :)
That green ball seemed to have a curve up not a straight line. That would severely hurt it's time. Might have beaten blue
interesting to see red strike that perfect balance between speeding up at not slowing down
I had no clue which one would be quickest before watching it
Moral of the story: "There should always be a balance in life, it should neither be too rough nor be too ease"
That's what she said.
I feel like blue's result could be better if its curve was a little bit more smooth
Anyway, good work!
Hi, yes! I thought so too. Possible loss of energy because of knocking at the steep bend , and hence loss of velocity 🤔
I feel like it should jump a little when it reaches the flat part
@hohladych, blues curve should have been the opposite of what we saw. This exercise isn't worthy of plunder. My disappointment is profound.
I agree. Blue ball needs softer curve so high velocity not lost…
I was right. Nice one. Good old physics, never fails.
*Only* the physics OG‘s already knew which ball was gonna win 🤯😏
I knew the red ball was going to win because of the thumbnail -- red was further ahead
That's pretty fucking vague...regardless of what ball would win
"only smart people know this...number 5 will shock you"
I watched a VSauce video
Hi, nice tutorial. One question: What software do you use to make the animations? Greetings
His channel name is C4D4U, he obviously uses Cinema 4D.
Lol, I seriously thought that it's a fancy way of writing "CAD 4 U".
So I thought that all this was 3d printed and done in real life. My bad
Fastest is not the one which reaches first to the end because the path length and trajectory are not same.
Newton’s second law, we can deduce the equation after differentiation
V = gt, at any given time i.e., t constant velocity is directly proportional to g.
Now this g varies for each curve from gcos45 to max g, the max g is of the vertical curve, hence its velocity at any point will be maximum compared to others.
Commendable!!!
Thinking to go back to my school to understand this😛
But if we throw an object at 45 degree it will cover more distance as compared to other.
Does this work here???
As I see pink reaches first
Nice Raytracing demo.
I think of it like traffic everyone rushing only to end up in the same spot almost at the same time
Awesome!!!😁
Thank you :)
I figured the red would be first because it had gravity to work with and the lane it was in had a natural curve that was not awkwardly angles in any way, I figured blue or green would be the last ones to reach the end. Green because while the lane was perfectly straight, it had a constant amount of friction with little help from gravity to pull it down. I figured blue because with the angle of the lane it was in, gravity would have done all the work and the blue ball would have bounced
I'm going to say the Redwall. It has enough of a drop off to get the ball moving, but not too much angle so it will move fluidly.
Awesome reflections on the marbles. :)
Thank you very much :)
seems a little unfair on the purple having to travel the longest distance on a 0 gradient, even if it came 2nd last. what if the flat was sloped downwards too?
Yeah: I thought it would come on 1st: it came 4th! 😳
If you follow that logic and apply it to every segment of the curve, and continue adjusting until you achieve the curve with the fastest time, you get the brachistochrone. See Jim Nesta's comment about calculus of variations.
Also unfair that the one who got 2 hat to travel down and the up again.
Yeah and it was unfair to the brown one too , it had to go uphill! 😎
There is no ‘unfair’. It’s an experiment to find out the optimal curve to achieve optimal velocity across equal gravity. I’m not a mathematician that’s just my take. Not only do we see what works but we also see what doesn’t.
I lost my bet as I thought for sure the ball that traveled straight down would be the winner.
I’m open to being educated on this as I find it interesting.
i was RIGHT, though i got a lil angry when the gold one almost beat the reddish pink
Cool :)
Very interesting indeed.
This is art
If the Gold's track does not dip below the horizon line near the end, it might have beaten the Red
I didn't notice that. I did choose the Gold one to win and I am certain it would have if it wasn't for the fact that it had to rise up to the end after the dip below the base.
@@MrStringybark I also didn't notice the dip and I agree with both of you that it would have been first. Time for a rematch.
Nope none of this matters it is calculated by physics that between two points brochistochrone curve has the least time no matter what you change except the ball(distanace height curvature) it will always be fastest
@@babykanwar2100 As a life-long member of the Flat Earth Society the fact that you used physics proves you are wrong.
@@babykanwar2100 What? I see words but they didn't say anything useful. Is there an English translation?
Для полноты картины необходимо написать тут математическую функцию наиболее ускоряющего трамплина.
Me: i have to study and do something about it
RUclips: wanna find out which ball is the fastest ball?
Me: I'm in
We are studying thus exact topic at college today, So IDK why my RUclips knows and recommend me this video.