Is this a proper perpetuum mobile?

today I want to investigate one particular perpetuum mobile machine. First when I wanted to write this post I wanted to let it open ended since I did not know the solution for why it does not work but I have found it so here you go:

Physics is basically based on the fact that energy and mass are conserved. If you were able to put enough strong evidence against it, modern physics would basically collapse, this is the foundation.

Now perpetuum mobile is a machine that is trying to break this law, but not very succesfully since none was ever built. Perpetuum mobile is a machine that gives out more energy than it needs for running.

Performance is larger than power and effciency is larger than 100%. This is not possible though you can check your basic physics skills by debunking these machines.

One of the most common “perpetuum mobiles“. As it turns it is supposed to create torgue and rotate forever.

It has been while since I saw what is called “Brownian ratchet” and I was simply stucked. It is kind of different from other “perpetuum mobiles” since it uses what is called brownian motion to work.

Feynmann was one of the guys who popularised this machine and also showed it flaw.

In the box 1 you have small paddle wheel. Particles bump into it because of brownian motion, that is a motion of small particles that goes indifinetely (this is type of thermal fluctuation).

This paddle wheel can only turn in one direction because in the other box you have ratchet as you can see above. The paddle wheel turns one way lifting up something or simply doing work. Where is the problem?

I remember asking my teacher about this. She said that it would really be perpetuum mobile. I knew she is not a good one. Now I did not know but I was sure that there is some flaw in this and I found that there is but I did not find explanation.

Today I found wiki page about this “Brownian ratchet” and they basically say that if the pawl is the same temperature as the paddle it will also undergo the same brownian motion sometimes jumping up and down. The thing is that we can not forget that the thing is also extremely small. If it would be different temperature it would work but based on thermal difference which over time disappears.


Solution to 12 coins balance problem

in the last post I described this cool balance problem with 12 coins where one of them is false one (heavier or lighter than others). You are allowed to weight them 3 times to find out which one of them it is and if it lighter or heavier.

The hint that I gave you is to separate them on 3 groups of 4 coins. Otherwise it is not possible to solve it. For the first one there are two options as you weight 4 coins against 4 coins.

If the outcom is even it goes as follow:

  1. If nothing happens the 4 coins that you have not used must have the false one. Now this is quite tricky. You have probably come out to this part but you have to use all the facts that one weighting will get you as you will see. If something goes down, it is good to know it and vica versa.
    1. a) Now you know that the rest of the coins (4) have to have the false one since it was even. You take one away and put the three against 3 that you are sure about (you have 8 of those). If it is even you know that it is the last coin and you just weight it against one of those normal ones to see if it is lighet or heavier. If you find out that one of the three has to be false you will remember if they were heavier or ligher. Then you take two of them and weight them against each other. The one that did the same thing like in the last weighting is the false one. (If in the 3 vs 3 it was heavier you are searching for the heavier side again.) If they are even you know that it is the last one.
  2. Now it can also happen that one side from the first weighting is heavier than the other. All of the 8 coins are unknown but you can use the fact that one went down and the other up so you need to remember that fact. You also need the 4 coins that you know must be all ok. Put three of those on the “lighter” part. From the lighter part move three original to “heavier” part and from there away three.
    1. b) The easiest thing is when the heavier part is again heavier. Then it has to be one of the original coins from both side which are only 2. You weight one of them against any other coin to get the result.
    2. b) If the part that was heavy is lighter this time, one of the three coins that you moved from lighter to heavier last time must be the wrong one. It is also lighter as you know. Weight two of them against each other. If they balance it is the third one if they do not it is the lighter part.
    3. b) If they balance it must be one of the three coins that we removed completely. We use the procedure described in the last post to find the solution, it is heavy coin then.

Now that is for solution. It is not easy to come up with it and there are some even more difficult versions. Thanks for reading and thanks to Wikipedia for the solution.


12 coins balance problem

today, in this short post I want to show you this cool puzzle that I first encountered on my summer camp. The problem goes like this:

You have got 12 coins. One of them may be false one. You can not know by looking but you have a balance weights. You are allowed to use it 3 times and find out which one of the coins is heavier or lighter (you do not know and it might happen that none is).

I really recommend you to try it out. I almost had a solution though when I checked it I saw that I had mistake in one of the scenarios. Try it out for yourself and in next post I will reveal the solution.




Try to take first step of weighting 4 coins against 4 coins, it will help you😉


Private companies take the space industry by attack

today I want to talk about how private companies like SpaceX ,which I already talked about few times and Blue Origin for example, influence the space industry.

For many years there was NASA and only NASA. Now these days you could have noticed that SpaceX appeared, self-funded company with priority of making space cheap. Same interest has also Blue Origin, space company founded by Jeff Bezos, the owner and CEO of Amazon. (billionare as well as Elon Musk of SpaceX)

These two guys and others are aiming for cheap space which is something that NASA was never able to do. After Apollo 11 they wanted to start to use reusable rockets but it never went to perfection. The primary goal of 25 dollars per pound on the orbit of Earth, changed more into something like 25,000 dollars per one pound.

Now NASA wants to make Space Launch System and Orion capsule to get us to Mars. Noble goal it is. There is one “minor” problem. Look at NASA budget over years:

The peak is when we were trying to get to Moon

Right now NASA has about 0.5% of federal budget compared to 4.5 that got us to Moon. Estimates are that the whole Space Launch System (SLS), which is basically huge rocket, will cost in the matters of tens of billions of dollars (this is just development, see later for launch price)! (0.5% is something like 19 billions of dollars).

The thing is that there are other players, like SpaceX who can do this much easily. SLS will be using boosters RS-25 that are from 70s and throw them away after every launch while we have New Shepard of the company Blue Origin that has already been used 5 times over!

From what I have read from Phil Plait and others, SLS will probably be one huge fail. Already now it is behind schedule for its first unmanned launch, not talking about the approximation of mission to Mars (something like 2030-40) where as SpaceX is investing huge amount of money to Falcon Heavy that should be able to carry over time enough stuff to build a base on Mars. Falcon H. payload capacity is over one third of SLS though it should be able to fly several times for the same price as SLS. (I found that it would be able to make more than 5 flights for the same price on the Low Earth Orbit, thats some difference!)

The thing is that NASA is underfunded and right now it even spends money on something that may not ever be working while there are smaller players but with clear and cheaper mission.

Mind you that SpaceX is planning to design Interplanetary Transport System and Blue Origin’s New Armstrong (they are working on New Glenn right now which is one of these huge rockets anyway).

From what I have understood, the key in the future of space exploration is reusability.


Check out these pages for more info: 1) 2) 3) 4) 5) 6)

Btw. NASA does not plan to use SLS more than 3 time per year because otherwise they would have to build up huge facilities. Also the first version of SLS will have payload capacity of almost half the one that I counted in this post. They will have to change it a bit and add some things over time to get to the final capacity.

Binary system explained (part 2)

in the last post I wrote about converting from binary to decimal number. Today I will continue, if you want to read the basics about binary just check out the post. This is also linked to my post about counting to 1,023 on your fingers.

So lets say that we have number 137 and we want to convert it into binary.

You have seen in the previous post that there is some highest digit that has the value of 1 instead of 0 which means that it stores the information[1]. We need to find out this value.

Its easy, its the highest 2ª number smaller or equal to our original value (137).

Such a number is 128 which is 2^7 so it is going to be the 8th number since we use 2º too (and 2º is on the 1st place).
Now we subtract it having 137-128=9 (1xxxxxxx)

Now we repeat with 9. The number that is smaller or equal is 2³=8
9-8=1 and the next 1 that stores information is on the fourth position. (10001xxx)

1 is easy because 2º also equals to 1 and it is on the first place. So 137 looks like this in binary: 10001001.

Lets try 759:

759-512=247 (10th number is the first 1) =1xxxxxxxxx
247-128=119 (8th number is 1, stores the information) =101xxxxxxx119-64=55 (7th number is 1) =1011xxxxxx
55-32=23 (6th number is 1) =10111xxxxx
23-16=7 (5th number is 1) =101111xxxx
7-4=3 (3rd number is 1) =10111101xx
3-2 … 1-1 === 1011110111 (quite lucky with so many ones ;))

Hope this all makes sense, if it does not just write in the comments below.

Btw. thought you have infinitely many systems that you can use, binary is the simplest of them all. You can not store information in less symbols because with one symbol you would not be able to distinquish where one information ends and another begins. You need to use “space” or some number or something.


Binary system explained (part 1)

in the last post I showed cool trick, how to use your fingers to calculate to 1,023. It was based on binary system but I did not explain it much there. Here I will go through the conversion from binary to decimal system, that we normally use, and back.

So all of these digits systems work with some number of symbols, 10 in decimal system for example. These digits means some number and when you run out of them you will just add another digit, for decimal system you have of course 0,1,2,3,4,5,6,7,8,9 and after 9 you have to start repeating previous symbols. Now if you think about it you could actually use this various ways, for example we write 10 but it could also be 00.

Binary system has 2 symbols only. 0 and 1. This means that you will have to use much more digits if you want to symbolise big number. Basically if you add one to number you display one higher symbol and you never skip any of them so there is given amount of numbers you can store in x number of digits. Because there are 10 symbols in decimal system you can display 100 different numbers (different combinations of these symbols) in two digits. From 0,1,2,3… to 97,98,99. This is 10² where the exponent is number of digits you have. For binary system the base will be two because you can store only two symbols in one digit. In two digits you can store 2² numbers.

This is good to know if we want to transfer from one system to the other, lets say that we have number in binary:


We want to change this number into decimal so that we understand it.
Every digit here stands for one of those exponents first digit (from the right) stands for 2º which is one and it either stores the number one or it does not. Since it is 0 and 0 is usually reffered to as empty, the first digit, again from the right, does not store any information[1].

2nd is for 2¹ and there is 1 which means that the information is there and we know that our final number (n) equals to the rest of the numbers plus 2.

We continue and there is no number on the next place but on the 3rd 2³ we have one which means that we remember this which equals 8. The next is 16 and the last one is even higher: 128. We now add all of them together to get 154 if I count right.

It is good to notice that with this system you can create any number you like because always this applies:



Because the post is quite long right now I will continue in the next post. I do not know when this will be because I am going on a trip this weekend and some days after but after I return there will definitely be new stuff😉


[1]Same as zero in our system! If you have number: 00456 its just 456 of course that it is something different than 45600 where it moves the place where the numbers are but still it does not count to the final number!

How to! 7) Count to 1,023 on your fingers

as promised, weekend post is here! Ok, so I learned this cool thing when I was on seminar in Hamburg. First I thought that someone is pointing middle finger at me for fun (you will see the reason soon) but it was actually counting method. Though you have only 10 fingers you can use them to produce all numbers from zero to 1,023 which is cool.

If you pay close attention and you know something about computers you know that the number 1,023 is very special. It is 1,024 but one smaller (1,024 is actually the special number).

The thing is that 2^10 is 1,024. And in computers you work in binary system with only 0 or 1  ….    on or off and you get the number of combinations that you can arrange binary system if you put 2 to the power of digits you have. On fingers you can not arrange 1,024, you will see why[1]:


Turn you palms towards you. Since in Europe we write from left we will start with left thumb (palms still towards you). Now make fists.. that is number 0

Rise your thumb, that is 1. (1000000000)
Put only your index finger up, that is 2. (010000000)Put your thumb and index finger up, that is 3. (1100000000)  –> the number of digits shows the number of fingers you have.

So basically if you have number lets say 17. You want to transef it into binary. You will do this by subtracting the highest 2^x power which is equal or less to the number itself.

The 2^x numbers go like this: 1,2,4,8,16,32,64,128,256,512,1024…

In the case of 17 you will subtract 16 which is 5th number in the row. 5th finger on your palm is your left pinkie so you will put it up. Then you are left with 1 which you again subtract by the highest 2^x number which is equal or less and this time it is 1. 1 is first number and left thumb on your hands.

If you want 349 you have to subtract 256 (9th number – right index finger)
You are left with 93-64 (7th number – right ring finger)27-16 (5th number – left pinkie)
9-8 (4th number – left ring finger)
1-1 (1st number – left thumb)

Now train a little bit and impress your friends😉 The key is to remember the first nine numbers and at what positions they are. Also you can show others just counting one by one. Just do not turn your hands towards them, numbers 4,5,128,640 and other could be dangerous😀


[1]The reason why you can not count to 1,024 is of course that you are starting with 0 not 1 so your right thumb stands for 2^9 and not 2^10. You can produce another binary digit with your tongue😉

Still here, but in Germany

ok so I did not post for few days and I have an explanation😉. I started my exchange year in Germany. Actually right now I am third day in my host-family and second day in school.

Thinking about physics I did some pretty fun experiments with my host-brother though I have still lot to learn especially because it was electromagnetism which is not really my thing. I will have first class of physics the day after tomorrow but we have only 1.5 hours per week.

Today I had math in the local school. I will see how it goes because it seems that the class is really behind of what we were able to do in Czech Republic. I say able because it seemed to me that they had lack of some basics but they did successions.

Posts wont be posted very often I guess. I have lot of things to do but I will try to write something on the weekend. This also means that I wont be able to read your posts, if you want you can link me to some in the comments, that way I will take a look at it😉


Quick point about equations and graphs

mliae asked me to make some simpler post so she understands this post. So here it comes, she said that it was long since she used equations:

Well equation is something like this:


That is quite clear. Of course you can have very complicated equation with many “unknowns” which are usually noted as letters, x for example. All thats easy and it says that something (x) is equal to one, it has the value of 1.

We can manipulate these equations if we abide one rule: both sides (from left and right of equal sign) have to be manipulated. If we add one we have to do it on both sides:

x+1=1+1     —>    x+1=2

Easy. We can substitute in equations if we work with more:


2(b+42)+3=x    (“a” was substitued by b+42 because that is what it equals to.)

Now in the post that is our concern we used this equation:

To get here we have to use graph but I did not stop on that very much so I will go through it again.

Points on graph have two coordinates. This is because graph has 2 dimensions. These coordinates are usually called x and y and they are noted like this:


x says how much the point is to the left or right and y says how up or down (or closer/ further)

We had two points there on the graph:

Now we will take the blue point as stacionary of course but since we are working in general and not with specific numbers, it should not matter.

So black point has coordinates x and y (x;y)

Since we want it to be general we will left it like this except the y. This is because we are going to derive functions and in those y=f(x) which means that y coordinate of the point is f(x). That is the notation that is used. We are working with the function f that gave coordinate y to our black point.


The h should be clear from last time. It is the distance from the black point. Then when you insert this into the “slope” equation which I talked about here, you will get what you want.


Feel free to ask for more clarification.

Rosetta and OSIRIS-REx

today, as promised I will look upon two missions that has to do a lot with small stuff flying around the Solar System.

Now I said stuff because Rosetta is a mission for comet and OSIRIS is mission for asteroid.

Rosetta is a mission that was launched back in 2004 by ESA which is European organization. It went for the comet 67P or also called Churyumov-Gerasimenko which kinda looks like duck:

Comet 67P on 19 September 2014 NavCam mosaic.jpg

Ok, fine, it does not but look here.. from this photo I would say that it is cat with huge tumor on back.

It went with Philae which is a lander module. It took 10 years to get there. It visited two other asteroids and went around Mars.

After some small changes it went to orbit around the comet even though it has escape velocity of 1 m/s.

Then it deployed Philae in 2014 but harpoons that should have eased the landing did not deploy and the site was much harder than it looked like before (the site was chosen because there was supposed to be “soft” regolith). It bounced twice and almost float away completely. It had battery for 2 days which were of course not enough to conduct all experiments and it could not recharge because it was under some cliff. Nobody knew where it was and we could not identify pictures that it took.

Philae found

It puts me in awe to know that this picture is from a comet. (Philae sits in the right middle of the picture in shadow.)

Luckily Rosetta still orbiting the comet finally found it and put them all in context. The mission ends in 30th September and Rosetta will too crush on the surface.

close up of Philae

The picture of Philae

Now that is for some asteroid exploration back in time.

Three days back, 8th September OSIRIS-REx, an asteroid study and sample return mission was launched.OSIRIS-REx Mission Logo December 2013.svg

The last part is pretty huge, yes USA is for the first time going to return samples from an asteroid to Earth (Utah is the landing site).

It launched on the often used Atlas V and the whole mission for asteorid called Bennu will take 7 years. OSIRIS will stay on its surface for whole 505 days! (Look how planned this whole thing is!)

There are lot of instruments on its board which I wont go through all. There are many cameras because OSIRIS will first orbit the asteroid and scan its surface to find a good place to land.

It has special leg that will try to take samples using gas of nitrogen. It can take up to 2 kilograms and enough nitrogen for three tries.