newtonian physics

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

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

Why golden trash bins do not help (modern equipment in schools)

Hi,
(few days back) I am sitting in a classroom, slightly bored by the teacher saying what I heard the day back. After few minutes I am being offered to do experiments alone. I agree with the hope that it is going to be more fulfilling. Instead of getting full access to the laboratory[1] I sadly accept white box, aka trash bin.

https://www.fdgate.com/photo-2/high-school-physical-optical-experiments-box-experiment-box-lens-optical-instrument-physics-experiment-equitment-m-0915.jpg

This is kind of similar, the fact that it is chinese[2] kind of fits the situation since my german is not so good yet.

Such a box contains “scientific” equipment for the study of electro-magnetism. This consists of few cabels, power source, resistors, capacitors, all properly laid on green boards. Function generator, some frequency and amplitude thing, two coils, magnet and some stuff to hold it together. This is probably almost perfect list of things that costs the school hunderds of dollars. I took it with the manual that contained roughly 15 experiments and decided to do one of them. I put components together as it said, found out the thing it said I am supposed to find out, it gave me the formulas to calculate it.. that is all.

So now the rant against these boxes (thrash bins as my host-brother pointed out).
The problem is that such a box with set up equipment and set up experiments does not enhance any creativity in students. Especially building circuits could be one of the cool things where you try what happens when you connect this and that. That is probably the biggest problem, you can just follow some manual and not understand what is going on. Also these components are totally dependant on each other and you can use only this box alone, there is no room for expansion or only limited. Not speaking about the cost, there is another trash bin like this for 800 euro. It had wagon, line on which the wagon could drive, two movement sensors and some things to hold it together and so on. We used it during physics class to demonstrate Newton’s 2nd law (F=ma). It took so much time to set it up, to measure it all to 3 decimal places. Actually it took 90 minutes and we did not get even to the formulation of the law. People were bored and I bet that if you asked half of them what was this whole about they would not have a clue.

This is modern equipment.. and it is useless. If they bought separate components boards to built circuits on, they even have those in the school but they are not used anymore. These days teachers probably think that they can not get better with chalk and a board.

Dragallur

[1] I do not think it would be a good idea to let me there alone though I go there anyway every monday with my host-brother.

[2] I do not know if it is chinese.

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.

Is this a proper perpetuum mobile?

Hi,
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.

Dragallur

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

Mach cone

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

 

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:

11 blogs should theoretically stack about 1.5 width.
Almost there! 4 stack on roughly 1 width!

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)