How The Spring Paradox Actually Works
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- เผยแพร่เมื่อ 11 เม.ย. 2024
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*Steve Mould* ,
Answering questions which i never had
I guess that when the blu rope was connected the two springs were behaving like a single long spring with less force and more range, but when the blu string is not connecting them they are both pulling in parallel with double of the resistance and less range
in later part of the main video he says this is an analogy to traffic. in some situations, there would be less traffic if you remove a road.
@@alexm7023 Also electricity. This is literally how resistors work.
@@leileijiang337 both springs are carrying the weight on by themselves, plus the top spring has to carry the weight of the lower spring also. No wonder they're stretched...
it's like apple: create the problem, sell the solution
Fantastic explanation!
I never would have thought that springs and batteries have that much in common
Yes, same here
It's easier to comprehend when you think of it as the flow of energy and how it always wants to reach equilibrium in the simplest way possible.
It’s springs all the way down!
@@backwashjoe7864
String theory ❌
Spring theory ✅
Springs kinda are batteries, they are a stroe of elastic potential energy which can expel or be charged by kinetic enegy, still batteries just a different type of energy to electricity
The analogy to electrical circuits in series and in parallel really jumps out at me.
yes wow
It's not just an analogy, the terms 'series' and 'parallel' are commonly used for springs too!
Not only that, but such a circuit is used to switch motors between series and parallel on old streetcars (the ropes are switches and the springs are motors)
Was just about to mention this
Personally, it felt like a jumpscare to me cause it was unexpected and I instantly understood the analogy.
The really cool parallel you can do with this situation is considering the ropes as being roads and showing how eliminating the direct (and very crowded, naturally) road can improve the overall travel time. Not sure Steve showed that or another channel.
yeah thats on the main video
Roads don’t stretch and contract though 🤯
@@mikebond6328They do. When traffic moves more quickly, the travel time shortens. As more strain is placed on a road, traffic slows, increasing travel time. By directing all traffic through parts of both roads, you place twice as much weight on each road, mimicking the effect of two springs in series rather than in parallel.
@mikebond6328 The fun, and paradoxal, situation is, that often REMOVING roads lower travel time, while ADDING roads leads to more traffic jams and slower travel time overall. And yes, this had been proven IRL too: Seoul removed a main artery through their city, and overall travel time lowered.
@@annekekramer3835 Yep. That's because individual drivers cannot predict or consider the bigger picture, so the average driver will automatically go for the route that seems shortest, creating traffic jams.
I've heard this explained before, but didn't get it. With your explanation it made sense straight away!
Even after understanding why it's doing that, it still looks very wrong when I watch it one more time...
ya. just ignore the ropes
.
if he just showed 2 springs "in series and parallel"....... then it would be obvious
.
but the ropes confuse us
.
.
but the ropes make for one hell of a demonstration!!! (aka, learning experience for students.... which we all are, no matter our age)
This is exactly the same way resistors work, really. In series, two resistors share the same current, while in parallel, the current is split between the two resistors.
My mind also instantly went to circuits and resistors
more specifically, springs are similar to capacitors than resistors, but the thing with capacitors is that you can use a simple amount of math to mathematically turn them into "effectively resistors"
Braess paradox came to mind.
It's the exact same paradox. The ropes behave like highways with fixed travel time, and the springs behave like the roads where travel time depends on traffic.
Know of a video that talks about it?
It’s the same, yes
Once again, I've watched the full video, loved it, watched the short, and wished shorts never existed
Ahh, you're elite compared to me, a meagre shorts watcher. Thanks for coming here and asserting how much better than me you are.
@@MintRobin it just... it doesn't give you the full context. cramming the whole experiment into a minute means you have to cut so much.
@@nothayley Sorry that it takes you half an hour to understand this concept and that 1 minute is sufficient for me. I'll use the other 29 minutes to learn 29 other things.
Oh but you can use that extra 29 minutes to understand this even better than I understand it? We call that a diminishing return.
@@MintRobinyou’re very combative. Don’t take everything personally. Except this comment of course.
@@MintRobingrow up 14 year old tiktok dweller
I like how this a true paradox, really a case where intuition fails, and not just one guy misunderstanding something obvious.
Not a paradox that's hoe springs in parallel work 😂
That's... not a "true" paradox. There's no such thing as a "true" paradox. All "paradoxes" are in fact imperfections in human knowledge and perception. This is also literally just a case of something being unintuitive and hard for some to understand, but plenty of people find it obvious, so is it a "true" paradox for some people but not for others? No; all paradoxes are just unintuitive facts. I don't know what you mean by "one guy misunderstanding something obvious"; I've never heard of any well-known paradoxes like that. If you're talking about things like Zeno's paradox, where there's not """""actually""""" (I CANNOT put enough quotes around that ridiculous word being used here) anything paradoxical about someone walking a set distance, then that's just you not understanding what concept is being explored.
@@goreobsessed2308 seriously lmfao not only does this guy not understand that all paradoxes are illusory in nature, but THIS is what makes the cut for a "true paradox" for him? 😂 this is literally the exact kind of obvious concept he was talking about, and he's the "one guy misunderstanding" it lmfao. Of course, it's not THAT obvious, it is initially unintuitive, but he's the one that came in with the attitude that "these things are obvious and people just don't understand them." He was insulting a certain template of people; it's not my fault he fit the template lmao.
@@joshyoung1440the biggest irony here is that you're the one misunderstanding what a paradox is. Go read the Wikipedia page and come back before you continue to incorrectly correct someone.
@joshyoung1440 "this statement is false" that's a "true paradox" because it has no answer. Although your definition of true paradox is wrong. Look up the definition of paradox "a statement or proposition that, despite sound (or apparently sound) reasoning from acceptable premises, leads to a conclusion that seems senseless, logically unacceptable, or self-contradictory." Note that it says seems, paradoxes are based off human perception and something being unintuitive makes it by definition a paradox.
That just helped me understand resistors a little bit more.
wait, if i just "extremefy" it , make the green and red rop very very long at the beginning, that still satisfy the original state, but it will obviously be longer once the blue rop is cut, isnt it?
As long as the red and green ropes are the same length, and we are allowed to ignore the weight of the ropes, the results will be the same
@@play005517No, it's only a paradox when the extra slack in the long ropes is shorter than the difference between the length needed for two springs in parallel versus two in series to support the weight.
Yes. The "after" springs will be shorter than the before strings, that's it. The total will be that plus whatever the ropes are. If you make the ropes longer, the weight will end up lower.
@@play005517Erm, no. Say the springs extend to 5 inches each under the weight, the blue rope is an inch long, and the red and green ropes are, let's just say they're a mile long. When we cut the blue rope, the springs move in series and drop back to five inches total length, and then fall a mile downward until the rope goes taut.
@@8stormy5 you can just ignore the blue one because it won't be relevant after it's cut, and you can ignore both red and green because if you swap the position of the spring and the rope on any side (move green rope to the lower part, or move red rope to the upper part) you will see we can also ignore both red ans green ropes too, they become static rope suspending the two springs holding the weight.
So that's why as long as the green and red ropes are the same length, they won't mean anything to the force system.
Cool and as always a super explanation 😊.
I feel like now we have to make logic gates with ropes and springs
This is a brilliant explanation. Because I work with electronics the series vs parallel analogy is so spot on. Thanks!
What would happen if the red and green ropes are different lengths?
You could write a book on the physics of springs.
Number one bestseller among insomniacs.
Mom: "how was your day?"
- watched a 20 second video on repeat until I went mad
Your explanation is surely accurate in terms of the final state of the change. However, right after cutting the rope, there should be an extremely short period of time that the newly formed circle-like loop doesn’t have enough tension which will let the weight fall a little bit(like
REALLY LITTLE).
Yes, right!? But it really does seem like it goes up initially as well... every time I see this video or short, I think the question is about the first thing the weight does instead of where it ends up
In the main video he tries a second thing where he slowly lengthens the middle rope until it's slack (that instead of cutting it). The weight falls a bit, then rises.
I like these videos in short form because the people I want to show your full videos often lack the patience for those initially, but after just a few shorts they're typically ready for a full video.
Somehow this helped me understand both sping physics and electric circuits better than any of the classes I've taken that taught those ever did
For me it makes more sense to point out that in the first configuration the top spring holds the weight of the bottom spring and the plumb.
The series-parallel analogy makes me think there could be incorrect inferences made from it.
the correct inference would be that springs are similar to capacitors, and since springs in a mechanical system are mathematically identical to capacitors in an electrical system (with the obvious exceptions of, like, needing to take extra steps to account for friction/air resistance/electrical arcing/etc) you can mathematically solve one to solve the other
Mould living up to his name by growing knowledge in our heads
Instructions unclear, bomb exploded
Best explanation I seen till now. 👍Thanks!
This gets me every time 😂 I believe I understand what's happening but I would watch a longer video expanding on this and maybe showing similar tricks or real world applications.
This is why it’s sometimes possible to remove a highway and speed up average commute time.
Ok here’s my analysis given my physics degree…
Hooke’s Law described a linear force interaction for springs (which is surprisingly accurate for short stretched distances for the spring). When a weight is hung from the spring, Newton’s second law is simple
k*Δy-m*g=0
The first force written is Hookes law, a spring constant (force provided by a spring given a certain compression/tension distance) and the second is just the mass of the weight times the acceleration of gravity.
Basically, the value of k is large for very stiff things like the paracord and is smaller for the springs. Since the tension force is what keeps the weight hanging above the ground, all we care about is the value of k being used. So, when the springs are no longer the only source of tension, the average value of k for the whole system increases, meaning Δy decreases.
Pretty sure this is also the thinking that goes into making roads better.
Probably the best quick science channel, ever!
I love this vid - it's explains the scale phenomenon - where you can stack scales atop each other and they all register the full amount of mass placed atop. Whereas if you put 2 scales side by side and a foot on each - each scale only registers half the mass.
you can also do this mathematically
initially the springs are in series and hence their effective spring constant is k1k2/(k1+k2)
in the final state they are in parallel and their effective spring constant is k1+k2
the force of the spring system in each case is equal and equal in magnitude to the weight of the mass
k1k2/(k1+k2) * x1 = (k1+k2)x2
x1/x2 = (k1+k2)^2/k1k2 = 2+k1/k2+k2/k1
since k1 and k2 are always positive, the ratio of the initial and final elongations is always greater than 1. hence the springs will always pull the mass up after cutting the middle rope
and if both the springs are identical, the reduction in the net elongation will be just by 75%
also note, this identical spring case will give the least reduction in percentage of elongation out of any case which you can prove by calculus or the AM>= GM inequality.
This reminds me of capacitors and resistors in series and parallel...
@@anthonymudge9768Agree. Also wave propagation through a variable series of media
GCSE physics @@anthonymudge9768
Strange to see that strings in series/parallel is the reverse calculation for resistors in series/parallel. Super weird to see a calculation I thought is only used with electric circuit calculations used elsewhere with similar conditions.
@@signedzulu7637 It's because the differential equations governing the movement of mass in a sprung system correspond to those governing the movement of charge in an electrical circuit. It should not be too surprising that the solutions (made up from damped harmonics) are so similar.
Interesting just like when you remove a short from a circuit
I watched the full video a few months ago and came out with no idea what happened. Shortform content forces you to explain concisely.
Made perfect fookin sense in just the last 10 seconds, bro makes the best shorts
The best part is not having to change the christmas light when the rope goes out
And if you do this experiment with 4 or more springs, you unlock the secret to time travel, and know exactly how to tune a flux capacitor.
Ropes works as two nodes.
I don't know why this is useful but I have a feeling someday it will be
Excellent explanation sir!
It's cool that the rope prevents the lowest energy state from bring achieved, which is the weight being higher up to have the spring be less compressed, by pulling the spring with weight attached upwards.
this is actually a really really cool demonstration!!
Awsome arrangement!
this man makes me feel like a toddler learning from educational tv again
A great visualization to help comprehend how resistors in parallel create a lower overall resistance for a circuit.
Awesome, I love this one. Next challenge: build a computer using springs and ropes!
The springs are both experiencing the same tension when the blue rope joins them, since they both bear nearly the same load. They will both extend by an amount caused by the same tension. When the blue rope is cut, the springs are now sharing the load, so the tension in each is now reduced so that the total of the individual loads is equal to what it was in each spring before the blue rope was cut. Less tension in each spring means less extension in each, so the mass rests higher than before.
Very well explained. I was baffled beyond belief but I understand it perfectly now.
Bros really onto it.
I understand from these shorts much better than the full video
For the first time I’m stumped
I’ve gotta look more into this because this seems very interesting
which part are you stumped about?
Well that was a very fun lesson! Thank you sir.
Wonderful explanation sir ❤
Wow, just like in my electronic circuits class.
Very nice demonstration ❤
I'm an industrial mechanic, intuition told me that the weight would go up. I was thinking "yeah it should" but didn't know why. Well explained sir.
crazy thing is, this is also related to traffic.
Well, the blue rope can also be seen as an energy storage device, as it prevents the springs from reaching their resting position. The moment he cuts the blue rope the energy is released and the weight falls down and the springs try to return to their original shape, this would happen with springs of different strengths in both of the examples he gave.
That is actually amazing
My little mind was blown😂 Had to watch it several times to understand!
this one's awesome, confusing at first but easy to understand the explanation
Ah nice, the explanation really clicked for me with this one
Could've just said that when the blue rope is connecting them, the weight at the bottom is pulling both springs open, when you cut the blue rope, the springs close back up until the other two ropes (which were slack) become taught enough to stop them.
Or, cutting the blue rope takes the weight off that point of tension, springs close, ropes tighten, springs stop again.
This is amazing. How somebody just got to this idea!
This is a beautiful tool!
It makes sense once you understand why. Strings are like non-stretchy extensions of the springs.
For some reason my mind just didn’t even consider the fact that they wouldn’t still be connected in series until he explained it.
The same happens at some construction sites, if a congested part gets closed due to construction the traffic diverts and the overall travel time gets faster
Braess paradox.
Under the right conditions, deliberately _removing_ a connection can make overall traffic flow _better_.
I love this demo
This is an head breaking exercise
Great visual demonstration of why that walkway collapsed in Kansas City. Objects in series will always be under more stress than those in parallel.
This is also a visualisation of why adding more roads sometimes creates more traffic and increase distance for cars
Well explained
Sometimes my head hurts. But I don’t hold it against Steve. He’s alright.
Reminds me of the reason for why the Hyatt Regency walkway collapsed. Parallel forces vs. forces in series.
It's interesting that in the original configuration, it's almost creating an optical illusion. The blue is tight because it's pulling the springs together. But because it's almost straight up and down, it looks like we're seeing the springs in series. Which makes it counterintuitive when we try to imagine what's going to happen when the blue is cut.
The springs ARE in series with the blue rope...
Thank you!
There is also a trafic analogy here as well
Yes... yes... strength in numbers and such. Cheers
I can't believe you can just transition from series to parallel like that. I have the feeling you may be able to do the same thing with an electric circuit, by making the "blue rope" a switch.
At first I thought I got it but I think I’ll have to watch it again
This reminds me of the pulley system.
thanku mate❤
I wasn't paying attention at first and thought you cut the green rope and nearly lost my mind
I’d call it more of an illusion than a paradox. Neat!
This is a normal physical action, which is to distribute the load alternately when the load is sequential. This also applies to electricity when distributing loads.
Expertly explained!
I just hope AQA doesn’t get any ideas for their A-level physics paper 1 next year
Reminds me of that popular resistance circuit 😅
I'm more interested in what happens if you pull the weight down past the point of where the red and green ropes have no more slack.
Does the blue rope rotate 180 degrees?
I like sneaky unintuitive problems like this
Physics never fails to amaze me
Steve Mould is the best.
Traffic has something like this too...
I love when simple mechanics become counter intuitive.
Brilliant demonstration of hooke’s law, keep up this awesome content! ❤
This would be an excellent physics lab for high school physics.
Wow very cool thank you!
So basically lifting something with one arm that's twice as long isn't as easy as lifting something with two arms the normal size.
Apronto patent my design of an elevator where mischievous elements cut the critical element, and the passengers on the ground floor end up going to the first floor.
The situation would become quickly more complex if the red an green rope would have slightly different lenghts.