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.

Why do stars twinkle (and planets not)?

Hi,
I felt so embarassed that I finally had to find it out and now I am writing this short post about it. For few years, roughly, I am studying astronomy yet, I never knew why stars twinkle and planets not. I confess.


Stars twinkle because the light that reaches us goes through atmosphere and atmosphere is not very homogenous – smooth. Air refracts light and there is different temperature once in a while, humidity and so on, I think that lot of factors play the role. This causes the light of star to scatter a bit and creates the twinkling effect.

Planets do not do it. This is great because you can identify them extremely fast on the sky and you do not mistake them for some other bright star. Why? Their light still goes through atmosphere. Because they are not “point sources”. Stars are so far away that even with best telescopes we see them only as points. Planets with simple telescope on backyard already have shape. Some of their light scatters one direction, some the other and it basically cancels out creating nice image. This is also why it is better to go star-gazing in the winter, colder air does not create so much “noise” on the picture.

Dragallur

Jerks are even in physics

Hi,
the title is a pun. There are probably jerks yes, but what I want to talk about is physical unit[1] called jerk, it is named like this because jerk not only means, idiot or stupid, but also to move suddenly, because of surprise.


It will be nice, if we first recall that derivation describes the rate of change of something. For example, speed is the first derivative of position because speed describes the rate of change of position, the higher the speed the more position changes!

{\boldsymbol {v}}=\lim _{{\Delta t}\to 0}{\frac {\Delta {\boldsymbol {x}}}{\Delta t}}={\frac {d{\boldsymbol {x}}}{d{\mathit {t}}}}.

1st derivation of position “compared” to time

In the picture above you can see how speed is defined compared to position (x) and time (t). It is its derivative as I said before. Now of course you can define something, that describes how velocity changes over time. That is called acceleration.

\mathbf {a} ={\frac {d\mathbf {v} }{dt}}={\frac {d^{2}\mathbf {x} }{dt^{2}}}

Again, “d” simply means derivation and when it is “squared” it means that you need to derive it twice. Acceleration describes, how velocity changes over time.

This is all you might need for daily life. Of course though, scientists defined next derivations, the change of acceleration in time is called jerk. The change of jerk is called jounce the change of jounce is crackle, next follows pop and then possibly lock, drop, shot and put. The SI units of all of these time, position related things are similar. With each derivation you add one to exponent of time.

v=m/s¹
a=m/s²
j=m/s³

and so on..

Just to remind you, if you have lets say “pop”, which is 6th derivation, of 10 m/s^6 you will have a tremendous speed extremely fast. From this next equation it should be pretty clear:

{\displaystyle {\vec {r}}={\vec {r}}_{0}+{\vec {v}}_{0}\,t+{\frac {1}{2}}{\vec {a}}_{0}\,t^{2}+{\frac {1}{6}}{\vec {\jmath }}_{0}\,t^{3}+{\frac {1}{24}}{\vec {s}}_{0}\,t^{4}+{\frac {1}{120}}{\vec {c}}_{0}\,t^{5}+{\frac {1}{720}}{\vec {p}}\,t^{6}}

The power of the higher derivations is that the exponent does extreme changes in a moment. r is the position, v speed, a acceleration… p is pop and t is time.

This is probably not used much, if at all, even in engineering.. but hey, fun!

Dragallur

[1]It is not a unit. It is physical quantity or something like that. I do not really know how it is called in english.

1st day of school + Formula 1 strategy

Hi,
today was the first day of school. Lot of people were pretty “stressed” though since I will be leaving to Germany in 14 days it is not so important to me. Already tomorrow we are going to learn normally. Yeah back in the same lines and system ;). At least there are some changes in our school, new computer class and some renovated library or what. Anyway I was reviewing some stuff from last year physics and found this cool stuff about Formulas.


When racing car drives, it is curve that slows it down most. To minimize this effect they have special tires and the following tactics:

When you are driving in curve your tires keep you from flying off because of friction. They act as centripetal force too. Huge role plays the size of the curve or its radius. So when the drivers want to turn right they need to move to the edge of the road and then smoothly turn exactly around the other rim of the circuit:

Great illustration of how the Formula drivers deal with curves, they use the “racing line”.

This way the centripetal force that you need is lower.

Dragallur

In the video below you can find sooner or later example of such tactics:

Traveling faster than sound: shockwaves

Hi,
today I want to shortly explain phenomena called “shockwave”.


You may have heard this word already used in the context of supersonic traveling. That is exactly it. Shockwave is the event, whether it is visible or not, that comes when you reach and/or cross the local speed of sound.

I say local because speed of sound changes with temperature, air density and humidity but for normal purposes it is roughly 343.2 meters per second.

When you are slower than the speed of sound the waves made by your movement do not

Circles to illustrate shockwave.

ever hit each other (without obstacle). This you can see on the left first picture. As you move through fluid [1] you create those “circles/ripples” around you and they are closer to each other in the direction you travel.

 

When you speed up to the speed of sound you will create this shockwave because suddenly all of those circles are hitting

everything at the same time which means that the hit is pretty hard. What you see usually is something similar to the picture on the right. This is just the condensed water in the squashed air.

I have read that it is quite dangerous to fly exactly at the speed of sound. It is not very efficient at least because the drag increases 2-3 times compared to supersonic speeds.

With sonic speed you can calculate two numbers. The first one is Mach number which is calculated as your speed divided by speed of sound. This means that Mach 1 is exactly the speed of sound. There is also something called the Mach angle which exists only in supersonic speeds. You can see it labeled as theta in the picture above. The smaller the angle is the faster you travel and the equation goes like this:

sin θ = c/v

Shockwave can also be created in space, though here that speed of sound is way higher (9,000 m/s), I already mentioned this in another post.

For more illustration you can check the video below that I made in GeoGebra:

Dragallur

Read more: 1) 2)

[1]Watch out, fluid means both liquid and gas!

Levers are amazing!

Hi,
today I want to shine light upon one of the simplest machines that there ever were. Those are levers, so intuitive that you will see even small kids use them.

SPOILER alert:

They are amazing in crushing your fingers.


I kind of connect this word with the game Neverwinter Nights where it was used for the handles on walls that opened doors and so on, I had to use translator to make sure it was right because it did not feel so.

With this “door thing” it could come up to your mind that levers are kind of long rods of wood or iron. It is quite useful to have them like that.

Take for example something very close, door handle is an amazing illustration of how levers should look like! It is long quite enough for you to open the door.. now try to take

Epic door handle

just the closest part to your door, the one perpendicular to the plane of door. Sure it is much harder, probably even impossible for you to open them. This is because the further away you are applying force from axis of rotation the easier it is to rotate the whole thing.


Lets assume you have one Czech locomotive of class 363.

V čele orient expresu.

This is old Czech locomotive… there is ENGLISH wiki page about it!

Lets say that you are able to stabilise it and you have unlimitely strong rod of something that is also weightless. Also you have something that works as axis of rotation and it is also undestructible.Levers are amazing!

Everything is put like above. Lets say that you weight 70 kilograms (if less than you have sack of sand with you, if more than you touch the ground with your feet).

How far away do you need to be if you were able to put the locomotive 1 centimeter from the axis?

Well, we have to calculate it precisely because if you sit too close you are going to be thrown across a long distance!

What you want for balance is that the final moment of force is equal to 0. Both you and the locomotive has this moment which means that:

M(locomotive)=M(You)

You calculate the moment here pretty easily, there have to be to things in the equation and those are very intuitive. If you push on door handle very hard (force) it is easier. If the door handle is longer it is also easier (r for distance).

M=F*r

This type of locomotive weights 87 tons. Now we can calculate the moment (F=m*g):

M=87 000*10*0.01=8 700 N*m

You moment of force must be the same and you know your weight (times gravity acceleration) so there is last thing the distance.

r=M/F
r=8 700/700
r=12.4285714286 meters

Wow, only if you are 12.5 meters from the train you can easily rest down! The problem here is that usually in this type of physics we consider that all of mass of one object is compressed on one place called center of mass. This is the problem because in reality whole locomotive simply wont be 1 centimeter away from the center. Cool anyway 😉


I mentioned at the start that levers are good in crushing fingers.. and they are. Take for example door that is 0.8 meter long and somebody pushes it with the force of 5 Newtons which is like lifting 500 grams. If your finger is 2 centimeters from the door it is literary going to be crushed with the force of 200 N which is like putting 20 kilogram thing on your pinkie.

Dragallur

 

Meteor, Meteorite, Meteoroid?

Hi,
as the title points out I will write today about meteors, meteorites, meteoroids and asteroids. I have to say that before I searched it was not sure which one is which.


Lets start with asteroid.

Asteroid

These things are the largest. You probably know few of them because the biggest are also called minor planets or dwarf planets. There are quite lot of them, the biggest one inside of the orbit of Neptune is Ceres, that is the dwarf planet with these cool bright spots. There are quite few types based on what are they composed of. There are carbonate, silicate and metallic asteroids for example.

Lot of them are also in the Kuiper belt.

Meteoroid

This one is a bit tricky. It is smaller asteroid, sometimes just a dust. The important thing is that as well as asteroid it has to be flying in outer space to be itself. Of course there are millions and millions of these objects. Usually they are considered to be smaller than one meter. When such object enters the atmosphere it can be fast as 20 km/s!

Meteor

Meteor is more often known as “shooting/falling star”. It is just the event when meteoroid enters the atmosphere and heats quickly since as I said it is pretty fast. In some time of the year Earth goes through dust that was left by comets. Those are called meteor showers. When meteor shines bright enough, more than any planet in the night sky, it is considered fireball, which was for example Chelyabinsk meteor.

Meteorite

Meteorite is object that survives the path through atmosphere and impacts Earth (or other object, Mars or Moon for example). Of course quite often these things shatter a lot. People are than trying to find the debris. Also some are quite dangerous and can easily kill person even if they are very small. The largest one piece has stunning 60 tonnes.

Dragallur

Impact on roof 

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

How radioactivity was studied

Hi,
today I want to write about radioactivity. It is rather new concept which is not very surprising as the process of radioactive decay is not very visible and the effects (on health for example) are not so clearly connected since they usually have long time span. Probably largest work done on this topic was by Marie Curie and her husband Pierre.

This is how radium dials looked like, cute!


Curie was from Poland. She had kind of difficult childhood since women were persecuted at that time in the east and it was hard for her to find place to study. Later on, she was able to move to Paris with her sister. There she met Pierre with whom she had two kids.

The first time she encountered with radioactivity was when she measured pitchblende [1] and uranium and how much radioactivity they  were “giving off”.

She expected that pure uranium would be much stronger but this was not what happened, what she found was exact opposite. Later on, thanks to this she found out two new elements: Polonium and Radium.


At this time it was not yet known that you can get pretty easily cancer by being close to radioactive stuff. Curie and Pierre were buying tens of kilograms of pitchblende to do their research and prove those two new elements since lot of other scientists were kind of sceptic about it.

In November of 1898 they extracted compound that was 900x more radioactive than uranium, you can see where this was going.

In 1902 it was announced that one decigram of radium chloride was succesfully isolated.

Four years later Pierre died when wheel of carriege run over his skull, this was because of the effects of radioactivity, at this point he was not really able to use his hands, they were pretty much destroyed by the pitchblende and his whole health was in very bad state.

In 20′ it started to be more and more clear that there is something wrong with the stuff. There was actuall factory that painted dials with radium (not pure of course), this is because it glows nicely and everyone liked it. The brushes that were used for this had to be kept sharp and this was done by lips. For this work about 4,000 people were hired, the so called “Radium Girls” was a group of women that also painted for fun their nails, face and teeth, noone knows how many sacrifices this caused.

Dragallur

[1] Pitchblende is mineral that is radioactive since there is uranium and other heavy elements. Lot of miners in extreme conditions died because they were mining it.