physics

Unrealistic radioactive decay

Hi,
today I am going to write about one of the problems that I had to solve for a physics seminar. The submissions for this series are already closed and you can look up the solutions so I know that I answered correctly to this very interesting problem.

Imagine you have two types of particles, A and B. They are radioactive, meaning they keep falling apart but in a very peculiar way, A decays into B and B decays into A. This doesn’t happen in a real world because the particles decay into something smaller, they break up, but this is a hypothetical scenario very simplified, we do not care about what is happening on the inside. The question is, what is the ratio of the particles at any point in time?

Since the answer itself and the calculation are not trivial I will mainly try to make some facts about this problem obvious and then show the answer.

There is one part that I didn’t mention in the setup. Radioactive particles do decay but there is a very important value that characterizes how fast. It is either T (half-life) which tells you in what time will half of particles decay (if there is enough of them it will give the right results) or in other words when the time T passes one particle has 50% chance to decay. It seems that also decay constant, which I like better, is used which is basically half-life except the larger the value is, the faster the particles will decay.

The problematic part of this exercise is that when part of the A particles decay they will increase the pile of B particles which means that more particles will decay into A and so on, this is a cycle. To get to an important point it is good to try some simple case of such decay.

Let’s say we have 200 of A particles and 100 of B and half of both will decay in 1 hour. In 1 hour:

A=200-100+50=150
B=100-50+100=150

Next hour:

A=150-75+75=150
B=150-75+75=150

It is obvious that from now on the amount won’t change. This little experiment revealed something obvious, there, first of all, no particles get lost, there is always the same amount present: A+B=constant and with a bit more experimenting it would become more apparent that there is an equilibrium between A and B meaning there is always some amount of A that when it decays it will equalize the amount that decayed from B, this equilibrium will shift depending on the length of half-life or the decay constant. From these thought experiments that reveal the behavior of this problem, we need to use some math that I will not get into here to get the result that you can try to play around with in Desmos.

Dragallur

 

How slow can slow motion get?

Hi,
ever been wondering how slow can slow motion get? If you hang for a longer time on YouTube eventually you might notice the channel The Slow Mo Guys or Smarter Every Day, both of them feature „quite often“ slow motion videos, meaning videos that have many frames per second (FPS). If you then slow the frames down you will get very slow video showing detail of whatever you are filming, whether it is flame tornado or AK-47 under water.

The slowest I ever watched is this one: https://www.youtube.com/watch?v=xbuvcQrAOSk

It has FPS of 343 915. That is a lot and in the video they are cracking glass container with high temperature difference. The video is so dark because in the short amount of time, not much light can get into the camera and that is often the limit for such high speed filming. You can also see that even though the video is so slow, the crack still propagates through the glass in surprising speed.

MovieBut this is not the limit, you can go much slower but it requires whole different technique. With 1 trillion FPS you can actually see light traveling through medium, it looks pretty impressive but how can it be done?

The scientists use a laser to lighten up what they want to take photo of. They take a 1 dimensional pictures, basically line of pixels[1], couple hundred times and then with a smart mirror they move along the object that they photograph. This technique is called femto-photography and the event on stage has to be performed many times before one gets the picture.

To put it in different words, you take a titanium-sapphire laser. Lighten up the object for a short time. Capture the photons that bounce back to you. Repeat over and over again and with some mathematical reconstruction techniques you got your result:

https://www.youtube.com/watch?v=qRV1em–gaM

Interestingly enough this kind of device is able to see around corners and has very high potential for use in many technical fields if we are able to make it work faster and in smaller devices.

Post based on TED talk.

Dragallur

[1]It is not really line of pixels as you can read in the next paragraph. You are getting back couple of photons and through the mathematical analysing you get the picture.

Gif source. http://web.media.mit.edu/~raskar/trillionfps/

 

Red Bull Stratos and its giantic balloon

Hi,
we all know that helium balloon raises up which makes it such a fun object, most things in every day life do not do that. This attribute can be used to raise objects or even humans quite high, but at one point you get a problem, the atmosphere is less and less dense.

Red Bull Stratos logo.svgRed Bull Stratos was a project involving helium filled balloon and a capsule with human (Felix Baumgartner). In the year 2012 it raised up to almost 40 kilometers and then the skydiver jumped down. He reached supersonic speeds (faster than sound: 1234 km/h).

In my physics class we talked mostly about the balloon because of what I mentioned in the first paragraph. 40 kilometers is very high and the pressure there is only about 0.497325257421 Pa which is basically vacuum since the atmospheric pressure is 100 000 Pa. (I used the barometric equation)

Because of this, the balloon can not rise so high in thinner air even though the helium is lighter than air. There is so little of it that it does not provide the necessary lift and the balloon has to be huge. In this case it had 9 144 000 cubic meters! Thats a huge thing. The problem of course was that it was not lifting up only one human but the capsule with all equipment weighted 1315 kilograms and the material of the balloon had 1681 kilograms[0].

The whole project was kind of supposed to be for science and finding out how body reacts to high speeds and for further development of pressurized suits[1]. At the same time there was a lot of helium used which was then of course lost. Beware because helium is on the list of endangered elements!

Dragallur

Btw. You can check out my Patreon site here!

[0]The helium also has to be lifting itself.

[1]At about 18 kilometers the pressure is so low that the water in human body starts to evaporate (not all because blood is enclosed but for example saliva). I wrote about that in this other post. To survive you need to be in a suit.

Logo source: By Source, Fair use, https://en.wikipedia.org/w/index.php?curid=37329038

These telescopes are huge (E-ELT, OWL, VLT)

Hi,
today I will write more about telescopes. In a previous post I already mentioned why radio telescopes like Arecibo are so huge, its because of the long wavelength. Today though I will concentrate on another type of telescopes and those are the ones that sit on Earth and collect information from visible light (those are called optical telescopes).

Comparison of various telescopes. Note OWL, the big circle in the background and even bigger white Arecibo.

I already mentioned Hubble telescope and James Webb Telescope (JWT) that is planned for launch next year. Those are in space so they have quite limited size. Down here we can build bigger ones. Right now in building phase is the E-ELT (European Extremely Large Telescope). Its primary mirror will have 39 meters [1] making it the largest optical telescope. It has to be so big because otherwise it could not match the ones in space. This is because we have our lovely atmosphere in the way and it makes harder for telescopes to distinquish small objects (though these days we have software that is able to account for that).

VLT aka Very Large Telescope is already working optical/infra-red telescope. It consists of 4 telescopes each of them with primary mirror of 8.2 meters in diameter. They can work together to make images of angular resolution 0.001 arcsecond. In one post I said that we are not able to take an image of star other than just point like source of light but apparently that is not true so I apologize for it:

First Direct Photo of Alien Planet Finally Confirmed

First confirmed image of an exoplanet. The ones that we can see are bigger than Jupiter and usually quite far away from their star. Credit: Gemini Observatory

VLT is second, right behind Hubble in the amount of scientific papers that its work produced (in the field of visible light/infrared telescopes).

There are many other telscopes that I might mention in the future like Thirty Meter Telescope but I will end it with OWL – Overwhelmingly Large Telescope. It was supposed to be the largest telescope ever, with primary mirror of 100 meters! The price was estimated to be about 1.5 billion euro and because of that it was decided that its not worth it. If we do not kill ourselves we might see giants like those in the future though I have no idea how the scientists, or whoever does it, will name them (UGHT – Unimaginably Giantic Huge Telescope).

Dragallur

[1]Just as JWT, the mirror is made from smaller segments. In the case of E-ELT it is because the mirror would be too heavy and we do not have the technology to build it and in the case of JWT it is because you have to somehow get it into orbit.

Comparison of telescopes: By Cmglee – Own workiThe source code of this SVG is valid., CC BY-SA 3.0, https://commons.wikimedia.org/w/index.php?curid=33613161

Vacuum decay and Trump

Hi,
today I want to do a fun post inspired by a meme that I saw some weeks ago on Theoretical Physics Memes. Well here it is:

https://qph.ec.quoracdn.net/main-qimg-0be932f563bde21614fc7bfbcff409d9

If you dont understand the joke, its alright, I will explain. If you do understand the joke you can continue reading for the sake of… reading?

Disclaimer: I have not been using disclaimers before but the truth is I am no physicist so I do not claim to actually comprehend this stuff.

So vacuum decay or also false vacuum is the idea that you could die any second. (See I am no physicist)

Basically fields (meaning electromagnetic and other types) want to get into the lowest energy state possible. Also electrons rather like lower energy states to be more stable so, if they have more than they “need”, they will radiate it away in form of photons. Now it is assumed that these fields are either in stable position (lowest energy level) or they might be in metastable position[1], which means that there is energy barrier between the metastable level and stable, if it is “reached over” and the field drops into lower stable or again metastable level it will release energy.

If we were in false vacuum[2] we would just need to reach over the hill to get to true one.

Since particles arise from these fields some new types would appear and Universe in this place would look a bit different inside. The reason why this is connected to the discovery of Higgs Boson is that the mass that it has indicates that we may live in false vacuum, if our physics is right than we could die any moment since the false vacuum is expanding almost at the speed of light.. means we can not know if it is coming on us or not, which also means that you do not need to worry really.

Now you understand the joke though if you are Trump supporter than you do not find it very funny in which case I pity you because it is great joke 😉 [3]

Dragallur

Pic. source: By User:Stannered – Adapted from en:Image:Falsevacuum.png, CC BY 2.5, https://commons.wikimedia.org/w/index.php?curid=1711800

Post source mostly.

[1]They can also be in unstable position but not for long.
[2]The name false vacuum has nothing to do with the vacuum of space.
[3]Proper explanation: it is so bad that Trump is elected, I hope that Universe will end soon, oh hmm.. what is the probability of it happening?

Precession

Hi,
in the last post about Polaris I mentioned precession as the effect that causes change of North and South stars. I did not really explain what is happening there so I decided to make a short post only on that topic.

There are two other good examples of objects that precess alongside Earth. Take gyroscope for example:

On the left you can see gyroscope. It consists of spinning wheel (orange/yellow) and a pin on which it stands. When you speed the gyroscope up it will be able to stand as you can see on the animation. This is basically what Earth looks like and what it does in matter of 26,000 years.

There is a thing called torque in physics. If you hold a pole on one side and something is hanging on the other side it will be very hard to lift it up. You will have to use both of your hands and one will push down and the other up to counter the torque that the objects has, that is a force causing it to rotate around one of your hands.

If you spin the thing though it will suddenly be easy to lift the thing, why? Because of angular momentum and conservation of angular momentum. If you spin on your chair and stretch your arms and legs you will slow down but if you do the opposite you will speed up. No force is acting on you only conservation of angular momentum takes place. Angular momentum is calculated as the amount of mass spread in distance from axis of rotation. If it is further away it does not need to be so fast as then the mass is closer to the axis.

When you speed the object up the angular momentum will stay conserved so you do not need to provide the torque anymore, in other words it is going to be easy to lift the thing up. If you try to change the angle in which it spins it will feel weird and it wont like it.

Even than gravity is still pushing down. If you add the vectors of the forces together, you will find out that the object will rotate –> precess. The slower it is the bigger the angle in which it precesses. If the force would be applied only on one spot all the time then it would not precess. Take a round sheet of cardboard and rotate it on tip of pencil. If you blow on the spot close to you the thing will tilt left from your point of view. Gravity though will try to tip the thing over always on the side that is lower and thus it will continously change and rotate – precess. If Earth had no tilt there would be no precession.

Dragallur

Book review 12) Thing Explainer

Hi,

Cover of the book Thing Explainer

Randall Munroe is a great guy. Creator of XKCD (totally free nerd comics) and the author of What If which you can also read on the internet maybe only some parts… Now one day about two weeks ago I noticed in our school library that they bought his “new” book Thing Explainer. I wanted to buy it earlier but I found out that it costs like almost two new books and was quite discouraged (and I did not have the money anyway). So for some reason the people in the library bought it and I have read it in few days.

Book: Thing Explainer

Author: Randall Munroe

Genre: Science

Pages: dunno

Rating: 10/10

Thing Explainer is a book that explaines complicated stuff in simple words, simple means ten hundred most used words. Great idea I admit. Randall says that when he was younger he purposefully used complicated words so that nobody thought about him, that he did not know them, but in this book he does not need to care about it.

Inside you can find explanations of: Saturn V (Up Goer Five), Keyhole (Shape Checker), Periodic table, Sun, Washing maschine, Car and many many more. There are I think two or three double pages which extend the books already giantic size to double and the page about Skyscraper (Sky toucher) is of the format A2

1000 words is not much. Most technical terms do not exist and even if you know them IRL (in real life) you may find yourself wondering what some things mean. “Fire water” took me some time indeed. Or helium is “kind of air that makes your voice funny”.

Basically there is no objection from me, hopefully the author will write 2nd part since there is lot of stuff outhere that still needs to be covered!

Here is in the same style Einstein and Theory of Relativit explained.
Here is Up Goer Five.

This video is from Minute Physics about getting to space:

Dragallur

Do we see in 3 dimensions?

Hi,
its been quite long time since I wrote about dimensions. Just a quick recap since people do not click on links much: 0th dimension is point, 1st dimensions is line, 2nd dimension is plane and 3rd dimension is space. We are talking about spatial dimensions, another thing is atime dimension, but that is not important here.

So I got into this argument if humans see in 3 dimensions or not, I got no clear conclusion though so I am just going to discuss it here. We live in 3 spatial dimensions, proof, cubes exist. How do we see though? We can see cubes but I would argue that we see in 3rd dimension.

  1. Retina does not capture depth, it is 2 dimensional detector so we simply can not have a 3 dimensional vision.
  2. We have two eyes though, lot of people seem to like to point this out. With second eye you have what is called a stereoscopic vision.. the second eye has little bit different point of view and when brain combines it stuff gets depth. This does not mean that we see in 3D though. Still it is just two 2 dimensional pictures put together. Brain interprets this picture as 3 dimensional and based on experience judges distance. Also colors and shades can help us with that.

    File:3D stereoscopic projection icositetrachoron.PNG

    This is stereoscopic picture, disalign your eyes and match the pictures so you see 3 of them.

  3. You can draw anything you see on piece of paper and it will be exact representation of what you see, all angles same and so on. This I think would be impossible if you actually wanted to transfer 3D image to 2D plane because by definition 3D space is made up of infinite 2D planes put on top of each other. Same as you can not take infinite picture and store it in 1D line.
  4. If we could see in 3D we would see all angles as they actually are. If you look into corner you do not see 90° angles though because you remember the way that walls work you know that they are there.

Thats about the arguments I have, hope you enjoyed reading,

Dragallur

Sunset elevator

Hi,
today I will write about one particular physics problem that I was solving during weekend. It was pretty hard, but quite interesting set-up. (It is originally from Czech physics seminar called Fykos)

You and your boyfriend/girlfriend are sitting on a beach watching sunset. Luckily you are prepared to extend the romantic moment with elevator that will drive upwards. How fast does it need to drive for you two to be able to watch sunset continously?

Normally sunset related problems are about plane or car driving and how fast does it need to be for you to watch sunset all the time. That is freakin’ easy because you just need to drive at the speed that the Earth turns in your place. For Prague this is roughly 300m/s which is about the speed of sound.

This problem is way more unique. I do not know if my solution is correct since the people from seminar did not release solutions yet.

Basically you are standing on top of circle that is rotating at 300 m/s or also 0.00417°/s. You are soon leaving place from which you could see the sunset so you need to go up. The problem is that you are not actually going directly upwards to this place but as Earth turns your elevator rises in a line perpendicular to tangent of Earth at your paricular location, check out this desmos graph which helped me a lot to understand it (my creation): https://www.desmos.com/calculator/oftnm48s3b

Here is a picture though it is better to go on the original link which is very interactive:

(Check out complete end of post for explanation of picture) What does it mean for you in practice? In one hour you will be going almost 100 m/s. After 6 hours you will certainly be dead because the acceleration will kill you. At this point Earth would still be bigger on the sky though you would already be 500,000 kilometers away. After another three minutes from what I have considered last time you would be almost 3 million kilometers away and Sun and Earth would be the same size, at this point you would also ride in 1/3 of speed of light. But this journey still continues. After another 13 seconds you would go faster than the speed of light with acceleration of 14 km/s. There is not much time left but lets see.. 10 million kilometers would be reached by next 9 seconds. 5 seconds later you would go in freakin 10 million kilometers per second if it would be possible. One second before the journey would end you would reach 0.5 of AU. Soon after you would divide by zero which is dangerous[1]. After exactly 21600 seconds which is 1 quarter of day your elevator is perpendicular to this horizon, which sucks.

I bet your girlfriend/boyfriend would not be so happy about this trip though the first few hours would be amazing.

Dragallur

Explanation: black circle is Earth. Green line is elevator that with you turns left, after 21600 it will go 90 degrees. Red dot is the spot where you need to be in order to see sunset. Blue line is the original horizon.

[1]Do not be discouraged by only 0.5 AU. In the next mili and microseconds you would whizz through whole Milky Way and Observable universe as you would reach infinite speed.