Physicist Answers Your Question | The Spring Paradox Explained
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- Опубликовано: 6 сен 2024
- Is Physics Broken?! The Spring Paradox is an interesting one to solve.
Hey guys, so in this video I'm actually answering a question posed by one of you in a comment on one of my previous videos. Ahitagni Das, thank you for asking this question because it's a really interesting one to answer.
The idea is as follows: Let's say we have a spring sitting vertically on the ground, at its natural length. Then we place a block on top of the spring, which will cause the spring to compress by a certain amount. We want to try and calculate how much the spring compresses by, and we can do this in two different ways.
Firstly, we can consider balancing forces. The equilibrium position will be when the downward force on the block (i.e. its weight) will be exactly counteracted by the upward force exerted by the spring. This upward force is given by Hooke's Law, and we can use it to calculate that the equilibrium compression of the spring, x, is given by x = mg/k where m is the mass of the block, g is the gravitational field strength on Earth, and k is the spring constant.
We can also consider the Law of Conservation of Energy, and the supposedly logical thing to do is to say that the gravitational potential energy lost by the block during the compression (mgx) is equal to the elastic potential energy subsequently stored in the spring as it compresses (0.5kx^2). If we equate the loss in GPE to the gain in EPE then we find that x = 2mg/k. This is a factor of 2 different from the answer we got when considering forces!
So we get two different answers for the same scenario using two different (supposedly) logical arguments. In this video, I dig through the logic used in both cases and show where our arguments are incorrect. Don't worry, we do manage to resolve the spring paradox, and we can breathe a sigh of relief because physics is not quite broken.
Let me know what you think of the video guys, and if you enjoy it then please leave a thumbs up. Subscribe if you haven't already, and follow me on Instagram @parthvlogs for more concise physics content!
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And yeah you didn't mispronounce my name
Hi
You deserve way more views!
Hey parth bhaiya how you doing?
I really feel good when I watch your videos. I am a student of engineering and I want to pursue a career in research in future. Things are not going quite well lately. Few months ago I left my job as an engineer because I want to pursue masters and I wasn't having enough time to study for the entrance. My parents are constantly worrying about me. Though they are very supportive but often my relatives ask questions about my future and they get a bit worried. My exam also didn't went well cause I couldn't prepare well while doing the job ( after which I left) . I am again preparing for the entrance. I face questions regularly regarding my decision of leaving the job. But I am glad I am not doing something I never enjoyed. I really want to be a scientist someday. Just wanted to share. Thanks for reading.
Hey dude, I hope you're doing well in your life now. How's it going?
hey Parth you took my name , believe me I'm on top of the world, gooooooooood ahhhhhhhhhhhhhhhhhhhhhh I stilll can't believe it thanks a lot Parth for considering my doubt and being kind enough to make a viddy on it, thanks a lot
Good
I'm 17, aspiring to have a life devoted to some field in science like yourself. Hopefully will get there someday
Cool
Where u at after 2 years
This is a perfect example of solving paradoxes .Thanks
That was awesome! Pretty wild ride through the life of spring.
I've learned so many things through programming by trial and error like you're pointing out here. Realizing that you can only anticipate what's going to happen up to a certain point and then just trying it, is a skill. With programming I would run into this often, where I know that I'm not fully understanding the thing I want to model, but I also know that I have a significant portion of the logic sorted and that I'm simply not clever enough to carry the logic any further without seeing some experimental results. So I'd just run the thing and see where it breaks from what I need it to do, take that to confirm which parts of what I'd thought through were correct and what parts are wrong or missing, and suddenly the cognitive load was reduced and there was fresh clarity on what the next steps need to be.
This actually caused a lot of tension between me and my teachers in programming, physics and maths classes, because they were trying to get me to try to understand everything all at once before ever making a move, but by the time I got into their classes I'd already matured this practice of taking it as far as I reasonably could and then testing it to find the problems. I'd already developed a good sense of my own limits in thinking a problem through, so someone naively assuming that I didn't have this skill yet would frankly just become annoying. And this also led me to have lots of issues w/ students in science classes, because they'd constantly be asking me how I knew something worked the way I said it did, and my answer was always that I'd actually done the labor of working it out, which somehow never satisfied them.
Interesting problem.
Clear explanation.
There is a similar paradox of two capacitors in parallal.
I m not just learning concepts of physics here, also learning English Speaking 😂. Ur way of explaining is awesome sir....🙌🏻😁
Hey PARTH good to see your vodeo
This concept actually explains the difference between Static and impact force which is taught in Strength of materials in mechanical engineering.
Loved it. 😍😍
Mind blowing... keep it up
One could say F'K forces, but that takes energy :-) Crackin' video!
what a intiutional explanation ...am phyisicst student at iniversity and this blowed me up ...................just woow cintinue please
Well Done Parth Bhaiya
best wishes from India
Keep making
Very nice. Ty. People are really missing out, on this channel.
You are really good,Parth G.
I did not know about this paradox and after watching this video,I am going to have some fun with my friends.
Thank you....
Final thoughts are very elegantly put! Great videos. Very entertaining. Looking forward to more maxwell’s ones.
You ended the video by saying physics is broken in a lot of places . Could you make a list of where it is broken and do a short video on each break describing what the break is? That would be a great way to help move science forward - as many people keep those breaks in mind as they pursue science the chance of someone figuring out the resolution to the break (ie reveal our wrong thinking or new things we didn’t know) will be improved.
That was actually predictable for missing one energy component in the problem because the force intuatuions are really more general and bright to see . But it was fun at last and I realy enjoyed it.
Hey Parth! Love your videos. They are so very intriguing. Would love to see a little more of rigorous maths behind the topics you present and explain. Thumbs up anyway; keep the contents coming!
Hi Parth,
Your videos are amazing. I am a Structural Engineer and we use the energy equation to calculate a steel rod deformation. In our texts the steel rod will be shown as a spring with stiffness. So really a spring does not mean a spring that oscillates. It could be more stiffer and do not oscillate at all. like a steel rod loaded with a point force. But If I remember correctly we always use the load applied gradually and not suddenly. I don't think the energy will be lost by oscillations if the loading is applied suddenly on a steel rod. correct me if I am wrong.
If a load is applied suddenly to a steel rod, the energy would be lost by vibrations (the "thud"), which are, in a sense, microscopic oscillations.
This is a great paradox! I will def use it later this semester
This spring is resting on a surface that actually defines that how much damping force will applied on that spring harmonic motion by the resting surface i.e how quickly it will get stopped.
Hey Parth! Please make a video on the BROKEN physics(10:30)..btw love your videos❤☺️
Great video!
Hey Parth, hope you doin well, could you pls make a video on how to break the laws of physics ( if its even possible) love your content btw!
You call the first solution to the naive energy calculation "boring", but I can't help but notice that if you take the mean of the two solutions, you get the answer from the force calculation.
Dude, u just explained the velocity in an SHM without knowing it !! :)
sorry if I'm bothering you every time in comment(im super excited) I had another question, what happens to electronic movements at absolute 0 , do they still revolve or do they stick to the nucleus ? coz considering the fermi Dirac equation, the electron still exist at 0k but do they revolve and can you try explain the zero point energy tooo? thanks again and b-b-b-b-bye
They revolve in constant potential so no heat energy experienced
Actually temperature is either vibration of atoms or electrons.but when considered 0K condition electrons revolve but dont vibrate and energy of revolution is balanced with electromagnetic potential energy so no need for heat energy
You could have talked about why the potential energy of the system was exactly double.
Hello sir, please make a video on the group and phase velocity of the electromagnetic wave and whatare their physical meanings.
Very little energy is dissipated by air resistance at low velocities. Most of the energy is being obsorbed by the earth due to the nature of gravity being an upward acceleration by the earth. In other words, all the force being applied by the spring is being supplied by the earth. Hardly any is being applied by the box. Basically, all of the box's energy is kinetic. The real load is being done by the earth, and it absorbs the energy. Many factors go into that absorption due to the compressability and spreadability of the mass energies beneath the spring.
If the entire earth were made of a completely incompressible rod the width of the spring, then the spring would continue to bounce for a very long time. Instead, it is a large sphere made of highly compressible and shifting materials that are absorbing the energy over a wide area.
A paradox is entirely a fault in the calculation. There are no true paradoxes.
2 could be the constant for potential energy and force.
Man feel so guilty!!! I did the same thing at one point but I got the wrong answer... I just ignored it cause I was lazy to ask anyone... I think I should have asked.... Anyway, thank you bhaiyya for the explanation! Your videos are very good....
I actually had this problem about a year ago when first introduced to springs/SHM.
Great video
7:05 But why x=m•g/k? Shouldn't we solve for x taking into account the velocity?
which position is the equilibrium for the spring and block as well?
what will be the velocity of the block at the equilibrium of the spring?
what happens if i drop a block on a spring sitting on a floor at its natural length?
this could be a question for jee and it is quite easy for 11 grade students
Hey Parth can u share what application u use for editing and drawing for yr contents??
I like your videos alot...love from India❤️
The easy way to approach this is using the difference in gravitational potential energy between when the spring is relaxed and when it is compressed. This avoids all of the complications of the different varying forces and energies during the translation.
hey how many halo lights have you set up?
Can you please explain to us the Euler's formula?
yes, g = 0 to allow 2 x the mass to be stored for that upward thrust.
Nice one 😅
Damn! I wrote out a long comment and the internet ate it! Never mind. The essence was this:
I am wondering if you would consider doing a video showing the derivation of escape velocity from the Schwarzschild metric.
When I search the internet for the function of the escape velocity in the Schwarzschild metric for values of r>the Schwarzschild radius I find two different answers.
Some sites say that escape velocity in Newtonian physics and General Relativity are the same. I.e. Ve = SQRT(2GM/r)
I think this paper, www.ccsenet.org/journal/index.php/apr/article/download/48996/26316, for example says that, their results being at formula "10" for Newtonian and formula "26" for GR, I'm struggling to understand the maths, well, OK, I don't understand a lot of it, but I think that is what they are saying).
But others give an extra term: Ve = c SQRT( (2GM/rc^2) - (2GM/rc^2)^2) or Ve = SQRT( (2GM/r) - (2GM/r)^2) (these two options are equivalent, the first expresses Ve as a fraction of c, the second cares about the units you are using).
See for example physics.stackexchange.com/questions/33916/what-is-the-escape-velocity-of-a-black-hole where "jinawee" says "I don't buy your derivation"
This alternative option appears to be either wrong, or only applicable where r >> 2 x the Schwarzschild radius (because using that formula, if r < 2 x the Schwarzschild radius then Ve starts to decrease as r gets smaller).
Can I interest you in the challenge to make the derivation of Ve(r) in GR understandable in a video? Even if you agree with the answer that it is the same as Newtonian physics, proving that to be true is beyond most of us.
Physicists are like real-world wizards. I mean, they study and teach the truest, purest nature of reality. That's hot.
Your vids are excellent for to help me relax, if u no what I mean😉
So can we say in short that kinetic energy is not conserved in inelastic collision....??
Thatwhy we can't use conservation of energy.
1:06 .. why do you assume that the upward force is linearly proportional?
Bcz thats how an ideal simple spring is its spring force is directly proportional to spring length of contraction with constant K called spring constant
If this mass measures exactly 299,792.458 km long and it can accelerate to exactly 299,792.458 km per second, what happens to this mass? Is the front and rear of the mass during the acceleration remain as one unit or will be different units?
Thank you bro this was killing me yesterday
Love u Sir from Bangladesh
I had same question.
about energy required to lift a mass.
When u lift any object from some height to heigher height u need to apply more force than that mass.
So by force multiplied by distance for mass and external force is different.
It seems we put more energy to lift the mass.
What gives?
I can't speak English, I just love physics 💞
Physics is great!
I actually realised that as u r taking two different heights there must be a kinetic energy involved
Wow
I worked on a similar problem where I tried to graph the kinetic, gravitational potential and spring potential energy vs time. And they should add up to a constant but it didnt for me and I could never figure out why. Was wondering if anyone could explain.
Whats the problem.
They will add up to be constant try it again
Is math related to science?
We all think we know what happens when we swivel a massless flashlight (torch for my Brit friends) by 1º instantly. If there is an object 1 foot away from the source of the light, to us it appears that the light instantly shifted from one place to the other. So what really happens to the light beam at a distance of 1 light year? How does it behave? How long does it take for the beam to move from is starting point at 1 ly to its ending point at 1 ly if, for example, the 1º angle at the source is achieved in 0 seconds? The answer should be obvious.
Obvious answer consider a machine gun shooting bullets at a target from 100kilometers and suddenly shooter moves gun in 10° angle does the target suddenly stops getting bullets hit and bullets strt hitting another place(obviously no) the bulltes travelling in air are still in the same direction only new bullets after angle change are shifted so it will take the time of bullet from gun to target for the target to actually know that gun changed its direction its like giving ur friend a long rope eyes close and u suddenly move rope to a side ur friend wont even know that u moved until the wave in rope reach him and then he will feelt hat u moved even though u moved so fast it took speed of wave to affect the target
Same way at 1light year light will still continue coming for while year and then suddenly next new light rays will shift to far away galaxies. It will take 1year for end target to experience that source has changed the direction
Next video:quantum entanglement
Where does the k come from?
Parth V?
Lmao it froze at like 4 seconds in and I was waiting for him to say something for a good 15 seconds before I realized
That's a Vsauce intro right there. I approve
Hey Vsauce, Michael here😏
Hey man plz tour ur room
Hey, what are the possible jobs for a physics student other than a university professor?
the beard has grown
Lol
@@ParthGChannel :D-
10:32 I bet what you want to say was "at the quantum scale".
2:30 absolutely incorrect ... the energy gained is not conserved as there will be thermal radiation.
Well, the crux of the clip is to explain why that assumption was wrong in the first place - energy dissipate
@@johanngerell Maybe I was too quick to the draw?
In ideal case we dont consider thermal energy obviously it would be heck more complicated
@@anandsuralkar2947 Is that or is not that a cop out? .... just curious :-)
Are you from India ?
He surely is Indian but of course not from India .
If the spring truly had zero mass....then why doesn't the math say that the spring is simply pulverized into near nothingness? I mean, I know physics deals with things that are imaginary, but if we're talking real world bricks and springs, you'd think the math would show a destroyed spring instead of anything else.
can u make a parody video as vsauce? I think that'd be lit
You look like an IITian
Lol
Are you Indian?
Please stop clapping so many times