How to pile up stuff

Hi,
today I will write about block (in my case) or also book stacking problem. This is fascinating problem and I want you to try to take twenty cards or same blocks. Your quest is to stack them on top of each other but at the same time try to hang them over side of table as much as you can.


It should look something like this:

How much “overhang” can you theoreticly do? With twenty cards the overhand will be maximally 1.79886982857. You can only put one card on another of course.

What is this thing anyway?

Well there is nice physics and math involved behind!

Lets start with the proof why you can actually do this in the first place. Try to ask someone around “How much is it possible to overhang infinte amount of blocks?” most people will probably tell you that the answer is 1/2 which is kind of intuitive, but not true as you already know if you tried the experiment that I told you to do in the beginning.

It all has to do with the center of mass. This is the place that you are trying to balance at the edge of table. As soon as the center is moved behind the edge it will fall.

For first card it is easy, you can truly get overhang of only 1/2 of the width of your block.

For two objects you can get better, actually 3/4! The first block (highest) will stay the same, it will be exactly at half of the previous one to maximize the effect. For this the center of mass will be on the edge. What about the one under that? Well there comes the problem because it combines center of mass with the one above which means that it cannot stretch so far. It carries two times the mass, lets say 2M

First block goes like this: X*M where M is the mass and X is the distance it can stretch, it is 1/2. This must equal also for the second block which carries two so there are two “masses”.

X*2M=X*M (X is different value every time)

X*2M=1/2M (because as I said X for first block is 1/2)

2X=1/2 (divides by M)

X=1/4

the second block has to be one fourth of its width from the table.

For third one — X*3M=1/2M …. X=1/6

Fourth = 1/8

As you continue you will find that this goes in particular series called “harmonic series”.

1/2 + 1/4 + 1/6 + 1/8…[1]

This series sums up to infinity so you can theoreticly make any overhang you want!

For the overhang of 1 you need only four — 1/2+1/4+1/6+1/8=25/24=1.04166

For overhang two you need 31!
For three you need 227!
For four you need 1,674!
For five you need 12,367!
For six you need 91,381!
For ten you need 272,400,601!

As you can see it increases pretty rapidly. 

Now just enjoy me trying to get to the best possible overhang:

Dragallur

[1] Harmonic series are just 2x bigger: 1+ 1/2 + 1/4 + 1/6 + 1/8…

I used these pages as resources both for pictures and for information: 1) 2) (only first picture)

Book review 9) 10 Physicists who transformed our understanding of reality

Hi,
today I will do the review of 10 Physicists… bla bla. I started to read this book right after Christmas when I got it(but I read only one chapter finishing it last week). I actually wrote post about the first one in the list: Galileo Galilei.


Book: 10 Physicists who transformed our understanding of reality

Author: Rhodri Evans, Brian Clegg

Genre: Science, Physics

Pages: 258

Rating: 9.2/10


10 Physicists.. is a book that takes ten most important physicists in last 400 years and dissects their life and their impact.

Of course this list can not be very objective since you do not have any clear scale for something like this. I think most people would probably agree on the first four definitely:

  1. Isaac Newton
  2. Niels Bohr
  3. Galileo Galilei
  4. Albert Einstein

So sure, I would definitely from my perspective agree with those four though I was quite surprised that Bohr was rated so high. The problem is of course that most people will tend to remember Einstein and his theory of relativity but completely forget that Bohr did similar type of work but on quantum mechanics (plus many other things). Galileo may be surprising but when you consider his work on heliocentric system, well I would maybe swap him with Einstein though it is quite hard to compare people that lived in totally different times.

5.    James Clerk Maxwell
6.   Michael Faraday
7.   Marie Curie
8.   Richard Feynman
9.   Ernest Rutherford
10. Paul Dirac

In the first chapter the authors have quite good discussion about this list since they used some resources that already made similar ones. Maybe Schrödinger or Heisenberg should be there.. or Fermi?

Well we have to stuck with this one.

In my opinion the chapter that was done best was Marie Curie, I wrote about her in the last post and I must say that it was kind of thrilling, her work with pitchblende and the years that radioactivity was “adding” up in her and her husband’s body.

I guess that they could have done more work on Rutherford for example. Probably because he was so down in the list they did not want to give him so many pages but when I look back I do not remember much about him.

Otherwise I can dearly recommend this one if you do not know much about these people.

Newton who spent about the same amount of time on physics as on teology.
Bohr who was dismissed by king since he was correcting what he said.
Galileo with his: throwing stuff from Pisa tower.
Einstein who never got over the quantum theory and its probabilities.
Maxwell who finally made the theory that unified electrism and magnetism.
Faraday with his famous lectures that were attended sometimes attended by more than 1600 people.
Curie:

This had to be

Feynman playing his bongos:

That is whole new style

Rutherford and his new model of atom (as always for atom models, proved wrong).
Dirac with his serious social problems but pretty cool mathematical skills.

Dragallur

Optics: 6) Experiment that changed our thinking

Hi,
today I will again write about optics but I have to return at the very beginning of 19th century when Thomas Young proved that light is behaving like a wave.


So there was this problem.

Newton thought that light has to be lot of particles, he called them corpuscles.

At the same time Huygens thought that light is behaving like a wave.


Then came this smart guy called Young. He conducted easy experiment to prove this.

The experiment is based on phenomena called interference of light. Imagine two people calling. When they both call at the same time. The called person is more likely to hear the call because they amplify the sound together. Now imagine that they want the person to hear some word that they are repeating again and again, such a word could be: RETURN!

When they call both at the same time it will make mega RETURN! And you can be sure that the person will hear it. But if one of them is slower by just a fraction of the time that it takes to say the word, whole message is destroyed:

1st person:   |return!|
–>  RETURN!
2nd person: |return!|
1st person:   |return!|
–> retuRneturn
2nd person:         |return!|
From the second example you can clearly see that if it is just a little windy the message may end up some thing like: “ertueruterut” and that is something you do not want. So light behaves in the same way. If both lasers are calling “red” at the same time you will get mega red (amplyfied red, with higher amplitude). If not well, you know what happens!

But analogies can take as only so far. There is one more problem. In my example if one person would call: “return” and the other “go away” the message should be destroyed. But with light, nothing happens, the words (colors) do not interact at all (in this way) because to interact the frequency has to be the same, this is called coherence of light.


So how did he use the interference of light to prove that light behaves like a wave? In his experiment imagine having a dark room with one small hole that leads to another two holes like this:

As the light passes through both slits it creates interesting pattern that is unique for waves.

If light would be particle you would see two lines on the right. But instead what happened was that at some places the amplitude was increased, as both sources (both slits) were calling (shining) at the same time or they were just moved by one word (one top of wave).[1] So some of the light is in consctructive interference (peaks on the black line) and some parts of the wave is in destructive (bottoms of the black line). This creates lighter parts and darker parts:

The double-slit experiment

And finally animation:

The light passing through both slits, green part is destructive, blue, red and yellow constructive.

Dragallur

If you are not still sure about this, watch the video below:

[1]By this I mean that one person starts calling: “return return return” and the second joins for the second return so they are moved by one period.

 

 

 

Receding planets

Hi,
today I will continue with short post because I have a lot of work to do for my 15 page essay.


When you are watching planets they travel along some predictable paths which from the view of whole Solar System are ellipses. If you measure where they are on the sky you must do it relative to something. Usually you will use stars that is because ground is too far away and it would be inaccurate (too far away in degrees).

So you measure the planet’s position every day and then strange thing happens, the planet goes back and weeks later it returns back to its original pathway, what happened?

This movement is called retrograde – backwards motion. Of course nothing like that happens simply because there is nothing to cause it.
It would take about this force to actually stop Mars in one second: 15,453,822,450,000,000,000,000,000.

T is Earth, P is planet which we observe, A is the projection on celestial sphere.

The picture above should explain you what happened here. The thing is that we orbit faster than Mars. The picture that we see A1-A5 is the projection on the background, also called celestial sphere.

The same thing happens when you are driving on highway and there is truck ahead of you. As you catch up, the truck moves relatively to objects that are very far away. At one point as you drive around the truck you may not even see them and then suddenly the truck seems to be behind the far away stuff that you watched but the truck was moving the same way all the time.

This was a huge problem for astronomers. First they made various epicycles on epicycles to explain this strange movement and it took Copernicus to show that it is just an optical illusion.

Dragallur