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Superheroes, Crazy Clocks and Selfish Bosses: Einstein’s Theory of Special Relativity (Introduction: Part 1)

Hi Guys!

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This post is finally out.

After 12 months since i started this post and more than a year since the idea of this post was conceived, it’s finally out. I’m extremely sorry about the errors and having to repost but i cannot teach the wrong thing.

I strongly believe that it’s better not to know anything than to know the wrong thing for a human can talk, a human can tell other people things which may eventually lead to :

1. Awkward situations when you try to prove your physics teacher wrong but he ends up proving you wrong.

2. Trying to impress girls with physics knowledge but getting destroyed by the nerd sitting next to you

3. Writing the wrong answer in a test resulting in unsightly scores.

All of the above situations should be avoided at all costs. So i have rewritten the post. I have also realised that this topic has much more than i thought it had in terms of content so i have decided to split it into 2 separate posts. (the word count for this post approaching the 3000 word mark steadily) This is to prevent the “Too-Long-Don’t-Read” or TLDR syndrome from arising in some of my readers ūüôā

This post is still pretty long but i hope you will enjoy it. Feel free to post in the comments any doubts you have and i will not hesitate to address them.

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This is the first part of another science concepts series. I will be introducing Special Relativity to you guys. This post is just to introduce you guys to the topic so don’t panic yet. Contrary to popular belief Special Relativity is actually very easy to learn.

Well here are some prerequisites if you are still feeling uncertain (like Heisenberg always was):

  1. Basic Arithmetic
  2. Basic Algebra Knowledge
  3. The ability to picture scenes in your mind
  4. An open mind to accept extremely counter-intuitive concepts
  5. A calculator, paper and pen/pencil
  6. A spaceship that can travel at speeds close to that of light (optional)

Yep that’s it! You can pick up the basics in a couple of minutes but i will going in some detail in this series.

I picked up this knowledge from my physics teachers so before I even begin my post, i would like to thank Mr Damian Boh for his support in my pursuit for scientific knowledge and as a friend. I would also like to thank Mr Jeffrey Goh and Ms Sonia How for giving me the opportunity to pursue further knowledge in the field of science and for being very supportive throughout this journey.

Okay so on to the the introduction.

In a previous post, I explained a little on reference frames.

If you haven’t read that post, go ahead and click the link to read it. Its pretty important in the understanding of this topic and i highly recommend that you read that post first (It takes only a couple of minutes).

So how are reference frames important in this topic?

As the name implies, Special Relativity relies on ‘Relativity’. An object’s relative velocity to another object. How does this all work? I shall explain the mechanics in a later post. As mentioned earlier, this post is just to give you a rough idea of how Special Relativity works.

Special Relativity works on the idea that time and space are variables and they alter themselves to keep 1 thing constant. The first letter of my name: c. The speed of light (in a vacuum of course but to keep this post nice and short I’m omitting all the ‘in a vacuum’s so yes). It relies on the fact that the speed of light is a universal constant and is constant to any observer regardless of his/her/it/whatever ‘s velocity and whatnot.

The idea can be represented by using a light-clock experiment but I’m going to use parabolic motion as an analogy first.

When you throw a ball upwards in a van, the ball, to you, goes up and then down, just as it would while you were standing on solid ground. However, to some guy who just happened to see you throwing the ball, he would observe that the ball was travelling in a parabola, aka a curvy symmetric shape. To picture this, you can type the function: y=-x^2 into your handy search engine, Google. The curve that results is a parabola.

The Parabola of the function y=-x^2
The Parabola of the function y=-x^2

Now from this example you can thus see that the same event can be viewed in different ways. All you have to do is replace the ball with a photon (particle of light) and you will roughly get the idea of what happens.

I know what all of you are saying, “But Clyde, light can’t go in a parabola like a ball!”

Well you’re right, it can’t so its time to end this post and forget about everything.

NOT!

We can explain this using an imaginary device. We’ll call it a “super-awesome-cool-type-thing-that-measures-accurate-time-and-is-generally-awesome-light-bouncing-time-changing-clock”

Alright. So this¬†“super-awesome-cool-type-thing-that-measures-accurate-time-and-is-generally-awesome-light-bouncing-time-changing-clock”, (We can shorten it to SACTTTMATAIGALBTCC but let’s just refer to it as a light clock for now) what does it do? Let me draw this awesome device.

The Light Clock

There. Pretty neat eh.

The way this light clock works is by bouncing a photon (our light particle) up and down the box. Every time the photon hits the ceiling of the box, the clock ticks once. Every time the photon hits the bottom of the box, the clock ticks against. This happens several million times in a second and by the frequency of ticks, we are able to determine the amount of time that has passed.

However, the above is how the light clock looks like when it is stationary. When it moves, something crazy happens.

The Light Clock when its moving

The light now moves DIAGONALLY!

And if you still haven’t realized, the light has to travel a longer distance due to it moving at an angle.

Alright. Now take that in for a second.

So what happens?

The interval between the ticks get longer. And now the clock is reading time wrongly.

Or is it?

Remember the thing about the speed of light being constant? Regardless of what velocity the observer is travelling at?

Now its time to refer back to my post on reference frames

If you read my post, you would understand that the conflict between Galilean Relativity and Maxwell’s equations on electrodynamics has been resolved with Maxwell’s equations coming out ‘triumphant’ in some sense. So light does move at a constant velocity regardless of the velocity of the observer. Meaning if I were travelling at the speed of light (which is impossible and I will explain why in a later post) light would still move at the same speed as it would to someone standing completely still.

Perhaps I need to introduce some concrete numbers to make this clearer.

Say Flash (from DC) decided to challenge Nick Fury (from Marvel) to a race.nick flash 1

But of course Nick Fury has other stuff to do than to challenge some crazy dude in some race. So he decides to take a seat and chill.¬†(If anyone gets the 21 reference then here’s a fistbump)

nick flash 2

But Flash is still in this and starts running. Like real quick. Like 250,000,000 ms^-1 quick. (Nick is busy with his Avenger stuff)

nick flash 3f

5 Seconds later, Superman (from DC) flies in and decides he’s had enough of this Flash¬†guy. He stands beside Fury and starts firing his laser towards Flash.

nick flash 4

But Flash¬†thinks that he won’t get killed because he’s running so flippin’ fast.

But poor Flash¬†didn’t read my blog.

Flash thought that since he was travelling at 250,000,000 ms^-1m, the light would slowly approach him at 50,000,000 ms^-1. And with his 5 second headstart (which made him 1,250,000,000 m away from Nick Fury and Superman) the light would only reach him after 25 seconds, giving him some time to run away.

nick flash 5

But that obviously did not happen

4.2 seconds later, Flash gets fried. Although he was travelling at 250,000,000 ms^-1, the light was travelling at 300,000,000 ms^-1 to him, clearing the 1250,000,000 m distance in that short span of 4.2 seconds. Though Nick Fury was sitting down, he watched the light travel towards Flash at 300,000,000 ms^-1.

nick flash 6

This is probably very puzzling to you.

You might be thinking that the light got faster, since Flash saw the light moving at 300,000,000 ms^-1, the light should have been travelling at 250,000,000+300,000,000 ms^-1= 550,000,000 ms^-1

But Fury saw the light moving at 300,000,000 ms^-1.

“Where did all that extra speed go to?” You are probably asking yourself now

Let’s go back to that clock.

Since Maxwell was right, the above should happen. (If all those super heroes did exist and decided to do all that weird stuff.)

Let’s say Flash and Nick Fury¬†were each carrying one of our light clocks.

nick flash 7

Since light travels at the same speed to Flash as to everyone else, his clock ticks along just fine.

nick flash 8

But if Nick Fury were to listen to Flash’s clock ticking and compare it to his own clock, since light travels at the same speed to Nick Fury as to Flash, Nick would hear Flash’s clock ticking much slower as compared to his own.

nick flash 9

Why? Because the light travels diagonally to Nick and travels a longer distance. Nick would see the light travel a much longer distance, thus making the clock tick slower, but to Flash the light still bounces up and down, ticking at the same rate as if it were stationary.

Do you see what just happened?

TIME SLOWED DOWN.

But wait.

Let’s take a step back from here. Let’s go back to reference frames. After all, relativity is all about reference frames.

The above is only portrayed in Nick’s perspective. What about in Flash’s perspective?

flash nick 11

Flash would see Nick’s time slow down too. Why?

In Flash’s reference frame, he can take himself to be stationary and Nick Fury to be moving backwards at 250,000,000 ms^-1

This is due to the fact that there is no absolute reference frame. Be it Nick running or Flash running, there is no difference.

To explain this, let’s go back to Nick Fury.

Now say Nick takes one of his S.H.E.I.L.D Helicarriers out for a spin.

So while Nick is having fun flying his huge flying craft across the globe, he gets tired and takes a nap.

nick-tony-2
Nick Fury sleeps with his eyes open. At least I think so…

Tony Stark decides to play a little joke on Nick by shutting all the windows. Perhaps he spent a little more time studying physics and knows how to confuse other people.

Ncik Tony 1

Nick then wakes up, realising that he can’t see what’s happening outside.

Ncik Tony 1

Now here’s the big question: Did the Helicarrier land or is it still in mid air?

And here’s the big answer: You can’t know.

The problem with this problem is that in Einstein’s theory of special relativity, it is impossible to tell if you are travelling at constant speed or if you are stationary for any experiment conducted in 2 different inertial reference frames will yield the same result.

This means that every reference frame is equally valid and equally correct regardless of the observation it makes.

So the question of who is right ultimately shouldn’t be a question, because both are equally right!

Whose time slowed down? That ain’t even a proper question mate!

If you really want to know what the clocks would say, the clock Flash is carrying would say 5 seconds and Nick’s clock would have said 9 instead. (These values are rounded down. I will discuss the mathematics at a later date.)

Flash’s time is passing by slower than Nick’s.

But that’s only half the story.

Say Flash ran next to Nick Fury. Nick would see an ultra thin Flash, almost like a Flash that had been squashed flat like a paper.

nick flash 10

Why? Because time slowing down isn’t good enough to account for light moving at the same speed.

I can hear all of you going “Huh?” right now.

Why does time slow down when you move faster?

It changes to allow light to move at the same speed to you as to some other guy sitting on the ground.

Let’s go back to the super heroes.

Earlier we mentioned that Light should in fact have been moving at 550,000,000 ms^-1 when it in fact was only moving at 300,000,000 ms^-1. Now i shall tell you where all that extra speed went to.

Since time slowed down, Light has more time to catch up to Flash.

That makes sense doesn’t it? Though we cannot imagine the perspective of light (due to the math which I will eventually get around to explaining)

So actually light moves at the same speed but time slows down to accommodate for people who decide to move.

But time slowing down isn’t enough. If you calculate the time change using the light clock experiment, it isn’t enough to account for the moving observer, so space also has to change, length has to shorten for light to move at the same speed.

Essentially light is like a super unreasonable boss. You have to conform to him, even if it means that you have to bend and change.

This is only half (actually 1/3) of the story. So far we have gone through Relativity of Space. There are two more parts of relativity which are sure to melt your mind (like it did to my mind when i tried to comprehend it). These are known as the Relativity of Time and the Relativity of Simulteinity. Look out for that in later posts.

And that is Special Relativity, a story about an unreasonable and selfish boss changing the fabric of our universe to make him the fastest thing in the universe.

I will be going through the calculations at a later date after i have completed the posts on the Relativity of Time and the Relativity of Simulteinity. In the meantime, if you have any other questions, go ahead and post them in the comments or send me a message via the contact page. If you find any part of this page to contain faulty logic/ wrong info, please post a comment or send me a message, you would be doing a service to everyone who reads this post after you.

Thank you for reading this and have fun changing space and time!

Clyde Lhui ūüôā

P.s: My favourite Superhero is Spiderman. LOL

P.s: Tell me if you’d like to see more illustrations in the future.

P.s: Watched and loved Age of Ultron

Photo References:

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Nuclear Fusion- Does Our Future Depend On It?

Hi Guys,

I’m sorry for the long pauses in between posts, I’m busy with my third year in secondary school and I simply do not have as much time to write these posts anymore. This year i will be participating in a lot more activities (Science Mentorship Programme, completing my novel etc.). Blogging has been really fun and i really wish that i can make time to do more of these blogs. However, it’s really tough to pull myself to blog after a long day at school. Furthermore i try to make my posts as good as possible and this makes blogging take even more time. In fact i have been working on this very post since mid-December. I will definitely continue to post more, but the frequency of posts will have to be reduced. I simply can’t bring myself to post something that I myself feel is of low quality.

Okay, enough talk, lets get back to the main topic of this post.

I have been thinking about fusion lately after watching a TED video regarding the issue. Fusion has always been something extremely fascinating to me ever since I learnt about it. (and yes, I am going to keep referring to nuclear fusion as fusion.)

When we, as a human race, try to solve engineering problems, we usually turn to nature to give us inspiration. From the minesweeper inspiring tumbleweed to lotus leaves that have inspired us to create hydrophobic surfaces, nature has helped us solve our issues again and again. Fusion is one of those instances where we have taken inspiration from nature, but this time instead of seeking that inspiration from living beings on earth, we have taken that inspiration from the skies.

When we gaze into the sky at night we see stars, hundreds, thousands, even millions of them. When we look into the sky in the day, we see the sun. All these majestic things that fill the sky are all powered by nuclear fusion, the very thing we seek to be able to utilise some day. The intense light and heat coming from the sun and the stars are all produced by tiny nuclei colliding into each other; resulting in part of their mass being converted into energy.

The amount of energy produced is insanely huge. How huge? To answer this question we must look at one of the most famous equations in human history. E=mc^2. E equals m c squared. The energy-mass equivalence formula. Whatever you call it. Developed by the famous Albert Einstein, this short equation reveals the power of nuclear power. Here are the definitions of the terms in the formula:

E- Energy

m- Mass

c- the speed of light

Well if you consider the fact that the speed of light is 300,000,000 m/s (or 300 million m/s) )and after squaring¬†the value¬†you get 90,000,000,000,000,000 (or 90 trillion), you can¬†convert 1 kilogram of mass into enough energy to keep the entire world¬†running for 6 seconds. Well, that ain’t bad considering¬†we burn 9,825,414,830 liters of oil in a day. That’s over 9 billion liters of oil and oil only.

So yes, fusion is powerful. Very powerful. So how does it work? In the stars, intense heat and pressure (and sometimes with a bit of luck), fusion occurs. The heat causes the atoms in the stars to move extremely quickly, this causes the atoms to collide into each other very frequently and with extreme speed and force. The pressure forces them closer to each other, further increasing the frequency of the collisions. With these ingredients, together with some nuclear fuel, the beautiful process occurs, generating large amounts of heat (the energy that is released from the process). PhdComics has made a video explaining the process of fusion.

Fusion makes use of nuclear fuel with small nuclei such as hydrogen and helium. The process can only fuse atoms up to iron. Atoms larger than iron are too heavy to be fused any further. This is opposite of nuclear fission where nuclear fuel with large nuclei are used. After iron, to produce larger nuclei, a supernova has to occur for heavier elements to form.

I recently found this joke on the website SGAG. To those Singaporeans out there, you should probably understand this joke:

fusion joke

 

The above is in fact true! The reason why supernovas are able to allow larger atoms to form is due to the fact that the force of the explosion generated by the supernova is so great that the iron actually manages to fuse into larger nuclei. Through the explosions of millions or even billions of supernovas, the atoms essential for life were formed.

You could say that you were born from a dying star ūüôā

“The most astounding fact is the knowledge that the atoms that comprise life on Earth, the atoms that make up the human body, are traceable to the crucibles that cooked light elements into heavy elements in their core under extreme temperatures and pressures.

These stars, the high mass ones among them went unstable in their later years. They collapsed and then exploded, scattering their enriched guts across the galaxy. Guts made of Carbon, Nitrogen, Oxygen and all the fundamental ingredients of life itself. These ingredients become part of gas clouds that condense, collapse, form the next generation of solar systems, stars with orbiting planets, and those planets now have the ingredients for life itself.

So when I look up at the night sky and I know that yes we are a part of this universe, we are in this universe, but perhaps more important than both of those facts is that the universe is in us, when I reflect on that fact, I look up, many people feel small cause they‚Äôre small and the universe is big, but I feel big because my atoms came from those stars. There‚Äôs a level of connectivity.”

Neil deGrasse Tyson (in a TIME magazine interview)

Essentially, why I study physics.

 

Our current nuclear power plants utilise nuclear fission. The reason for this is due to the fact that fusion is extremely difficult to produce in comparison to fission. Nuclear fission occurs naturally. If you left a block of uranium somewhere, it would literally begin to decay and release energy as heat. However if you leave hydrogen gas alone, it would most definitely not fuse to produce helium.

Stars can make fusion happen relatively easily; they can use their gravitational force to create the high pressures and their already present heat as heat to sustain the fusion. However, the Earth is nowhere near as large or as heavy as a star. To make fusion happen, we utilize multiple methods.

I shall discuss these methods in a future post. I’m sorry i have to cut the post here but i have been delaying this post by a very long time. I hope to release part 2 soon XD.

Regards,

Clyde Lhui ūüôā

 

P.s I’m still working on a lot of other posts at the same time, these posts will probably take quite a while to complete. Do tell me if you have any suggestions for new blog posts.

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Black Holes- Part 1

Hi guys,

New guy here ūüėÄ . I’m Jackson and you would have known me by now after being mentioned in some of the previous posts. However, if you are new to this blog, I am Clyde’s classmate and often discusses Science topics with Clyde. And yes, I am also the new admin here. As I am new here, I will start with an easy topic that requires not much concept ¬† ¬† ¬† ¬† ¬†— just fun facts and no Math at all– unlike the mind-boggling Special Relativity that Clyde is doing. Without further ado, let’s jump into one of the most interesting topic, ‘Black Holes’.

Okay, so What is a Black Hole? 

Just from the name itself, most of you would have guessed a hole, a tear in a paper, a pit in the ground. In fact, it is a hole in space time itself, a hole where time slows down so much that you will eventually reach a point where it stops, a hole with an attraction so great that not even light, the fastest thing in the universe can escape. It is an area in the universe where if you drop into…… whoosh, you will disappear, cease to exist, voided from the rest of the world. Sounds dreadful eh? The idea of Black Holes started of as just an abstract concept that was not supported by any evidence and not many scientist believed it exist. Only in 1931, when an astronomer by the name of Chandrasekhar calculated and gave mathematical evidence of potential high mass stars that could form Black Holes, did scientist started paying attention to it.

Even until this day, no scientist has truely understood this mysterious entity, all the laws of physics break down at the singularity of a Black Hole and since no information can escape, there is no way to observe the events at the singularity.

Let’s look at the science of a Black Hole.

Formation of a Black Hole

Imagine an object that is constantly being compressed, its volume will decrease while its mass remains the same, this causes the object’s density to increase as, desity = mass/volume, the mass is a constant hence, a lower volume divided would cause a higher density. An increase in density would also cause the object’s surface gravity increase. As the object is compressed, the object will eventually reach a size where it would have a surface gravity so great that not even light can escape, this is known as the ¬†Schwarzschild Radius. At this point, the object would no longer be able to hold against its own gravity and would collapse infinitely into a point in spacetime known as the singularity, forming a black hole.

However, compressing an object into its Schwarzchild Radius and making a self sustaining Black Hole with brute force is unrealistic and is immensely difficult (so don’t even think about squeezing your golfball into a star hungry galatic black hole of mass destruction to take over the human race). In fact, you will need the power of the stars.

Stars are fueled by nuclear fusion. The proccess of nuclear fusion is basically the combination of two atomic nuclei, releasing the binding energy within the atom. In this proccess, the total mass of the two nucleus decrases, as they are being converted into energy, hence proving the mass energy equivalence. You can find out how much energy is released by finding the change in mass of the atoms and multiplying it with the speed of light squared (3√ó10^8^2). As the speed of light is HUGE, the energy released, which uses the square of the speed of light, would be unimaginable.
Let’s get back to point, the stars in the universe all start out with one element, Hydrogen. These Hydrogen atoms undergo nuclear fusion and fuses together to form Helium. Helium would then continue fusing to form Carbon, Oxygen and so on. As fusion occurs in a star, energy would be given out as radiation. The radiation would be causing the outward force that prevents the star from collapsing into itself. Usually, an averaged sized star would not have enough energy to continue nuclear fusion after all the carbon has fused to form oxygen, they would cool down into a white dwarf. However, a star that is much more massive would continue the fusion proccess all the way until iron atoms are formed. As iron atoms can no longer fuse, the proccess stops. By then, so much pressure would have built up from the outward force the star is exerting against its own gravity to balance out. Once the fusion proccess stops and the star no longer emits radiation, the gravitational force would suddenly overwhelm the star’s outward force, and in a short period of time, all the matter rushes inwards to the center of the star.

This would be followed by an explosion known as supernova or sometimes even more powerful explosions known as hypernova. After that, the collapse would either stop, forming a neutron star (the densest and smallest stars known to exist in the universe, it is so compressed that all the electron have the energy state to combine with protons to form neutrons, in a proccess known as inverse Beta Decay) or have high enough mass to continue collapsing into a singularity, creating a black hole.

There is another way in which Black Holes can form from the collision of two neutron stars but I will not go into detail on that.

Thanks,
Tiong Jackson :p

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Newton’s Three Laws of Motion (Part 2)

Hi guys,

This is the second part of my ‘Newton’s Three Laws of Motion’ Series. I will be writing about Newton’s Second Law of Motion. This post will be rather short due to the simplicity of Newton’s Second Law of Motion.

The acceleration of a body is directly proportional to, and in the same direction as, the net force acting on the body, and inversely proportional to its mass. Thus, F = ma, where F is the net force acting on the object, m is the mass of the object and a is the acceleration of the object.

Its pretty self-explanatory, the net/resultant force applied to an object is the product of its mass and its acceleration. This formula is the cornerstone to Classical Physics as it can be differentiated or integrated into many of the other formulas in Classical Physics.

What is ‘net force’? Net force is the force that is applied to an object after all other forces have been taken into consideration. Do remember that the SI Units for Force, Mass and Acceleration are the Newton, N, the Kilogram, kg and Metres per second per second or metres per second squared , m/s^2.

So how do you use this formula?

Lets imagine that a 5kg metal cube is being pushed with 10N of net force. What is the acceleration of the object?

F=ma

10N=5kg(a)

a=10N/5kg

a=2m/s^2

Therefore we can deduce that the object is accelerating at 2m/s^2.

 

And that’s the end of Part 2 of Newton’s Three Laws of Motion.

It was pretty short but it shows us how simple yet powerful Newton’s Second Law is. It supports the whole of Classical Physics yet it can be simplified to just 4 characters: F=ma.

 

Thank you for reading this post. Once again, please post any errors or additional points in the comments to benefit the other readers and feel free to comment or send me a message via the contact form page.

See you soon!

Clyde Lhui ūüôā

References:

http://en.wikipedia.org/wiki/Newton%27s_laws_of_motion

 

Home, Science, Science Concepts

Reference Frames

Hi guys,

In my previous post about Newton’s First Law of motion:

When viewed in an inertial reference frame, an object either is at rest or moves at a constant velocity, unless acted upon by an external force.

I did not explain reference frames which may have confused some of you. So i shall be explaining reference frames in this post.

Essentially, reference frames are frames which can be used to describe a location of an event(something that occurs at a very specific point and does not include things that occurs in an area).

To further explain what is an event, imagine you are in a science fair (preferably one with lots of amazing science experiments being carried out (but it doesn’t really matter)) to you the science fair may seem like an event, however in terms of reference frames, the science fair is not¬† an event (because it occurs over an area).

So you may be thinking right now: What in the world is an event since practically everything has a volume and takes up space? Well classically nothing can physically be an event, reference frames are just used to describe things based upon (non-existent) events or “events” (objects which still take up space) in classical physics.

However in quantum physics, events do physically exist in the form of elementary particles in the standard model of particle physics. Examples of such particles include: Electrons, quarks, muons and all three types of neutrinos (electron neutrino, muon neutrino and tau neutrino). These particles supposedly do not take up any space/volume however they do have mass. (This is where classical physics and quantum physics clashes. Since these particles posses a certain amount of mass but no volume, they posses an infinite density and in classical physics they would be black holes/singularities) i may do an in depth post about the standard model of particle physics in the future.

So how do these reference frames look like? They have a x, y and z axis which each represent a dimensions in our 3 dimensional world. However in the context of physics, there is a fourth dimension of time which is represented as t not within the reference frame.

Reference frames

Fig 1.1: two reference frames with the origins being O and O’

Notice that any point in space can be described using coordinates taken with reference to the origin of the reference frames hence the name “Reference frames”

NOTE: Coordinates can also hold a negative value so events behind the origin can still be described by using a reference frame.

In the above example, observer O is ‘stationary’ and observer O’ is ‘moving’. You may wonder why i use inverted commas to describe their motion. That is due to the fact that there is no such thing as an object that is absolutely moving or absolutely stationary (although there was once an ‘ether’ which was an absolute reference frame, however it was later dismissed through a ‘ether wind’ experiment)

Now I shall move on to Galilean and Lorentz Transformations.

So what are these? Galilean and Lorentz transformations are a set of formulas which can be used to calculate the velocity, location and time that is relative to one observer by using values obtained from the other observer and the first observer him/herself.

What is the difference between Galilean and Lorentz Transformations? Galilean Transformations reflect Galilean Relativity which is based upon common sense. While Lorentz Transformations reflect Einstein’s Theory of Special Relativity which is based upon the idea that the speed of light is constant in any reference frame.

Do remember the following points:

  1. x=Length
  2. y=Height
  3. z=Breadth
  4. t=Time
  5. c=Speed of Light (3.0 x 10^8)

Points 1-4 are the four dimensions of reference frames that you should take note of. Do note that there is also a velocity transformation which has the values u and v which are the velocities of the two observers.

Allow me to reuse Figure 1.1 as an example to describe the Galilean Transformations.

Reference frames

In Figure 1.1, there are 2 observers: Observer O and Observer O’

Observer O’ is moving forward at a velocity of v relative to Observer O who is moving at a velocity of u.

Galilean Transformations are as follows:

x’=x-vt

y’=y

z’=z

t’=t

u’=u-v

After transforming the values, you will get a different value, which is what observer O observes. An example will be if observer O was moving at a speed of 3m/s and observer O’ was moving at 5m/s, observer O will see observer O’ moving forward at a velocity of 2m/s relative to him. In this case what is the true velocity of observer O’? It is both 5m/s and 2m/s, this is due to the fact that these 2 velocities are observed in different reference frames, and are thus both correct.

Lorentz transformations are different from Galilean transformations as they take into account the change in time and space due to the velocity of the observers (aka Special Relativity). I/Jackson will explain this phenomenon in a later post.

The Lorentz Transformations are as follow:

x’=((x-vt))/‚ąö(1-v^2/c^2 )

y’=y

z’=z

t’=(t-(vx/c^2))/‚ąö(1-v^2/c^2)

The Lorentz Velocity Transformations are a little difficult to understand due to the definitions of u, v and u’ and will be explained in the Special relativity post.

As previously mentioned in the post, an ‘Ether’ Reference Frame was proposed.

This was to resolve the conflict between the Galilean Relativity and Maxwell’s Theory. Maxwell’s Theory is essentially the idea of which Special Relativity was based upon. They are based on 4 equations (The 4 Maxwell’s Equations) which are named after James Clerk Maxwell, the publisher of the early form of the equations which are the foundation of classical electrodynamics. Maxwell’s equations prove that the Speed of Light-c is a constant. and this is in direct conflict of Galilean Relativity which show that if you move a t a sufficiently high velocity, you will be able to see light moving.

Therefore to solve this conflict, the ‘Ether’ Reference Frame was proposed. This reference frame is an absolute reference frame, meaning objects which are stationary relative to this reference frame are truly at rest and objects which are in motion relative to this reference frame are truly in motion.

However this was dismissed due to the Michelson-Morley Experiment which tested for ‚ÄėEther Wind‚Äô.

Capture

Fig 1.2: The Michelson-Morley experiment. On the left is a directed light source. The beam of light is directed at a beam splitter which splits the beam of light and directs them in 2 directions toward 2 mirrors of equal distance. The mirrors bounce the light back which then is sent to a light detector.

How does this experiment prove the ‘Ether’ Reference Frame wrong? This experiment was conducted on Planet Earth of course. During that period, it was already known that Earth rotates around an axis. thus the setup of the experiment would be rotating together with the Earth. This would mean that should the ‘Ether’ Reference Frame be present and correct, the light going toward the mirror on the right would take shorter/longer (depending on whether the experiment was set-up facing the east or the west) as compared to the light hitting the top mirror. However the detector detected that the light was hitting together at the same time, thus dismissing the idea of the ‘Ether’ Reference Frame. This also prompted the development of Einstein’s Theory of Special Relativity.

Reference Frames are key in the understanding of both Classical and Quantum Physics as they are useful in the understanding of many experiments and theories.

And with that i end this post on Reference Frames.

Should you spot any mistakes or have any questions, please leave a comment to benefit the other readers and of course myself! We will be posting the second part to Newton’s Laws of Motion and another post on Black Holes by my new co-writer Jackson! Lastly, we will be blogging about new upcoming projects in the series ‘The Power Surge’ (For reals this time). If you have any ideas for more projects, please feel free to comment/contact me in the contact form.

Thank you For Reading and I hope to see you soon!

Clyde Lhui ūüôā

 

P.s: An Inertial Reference Frame is a reference frame that either is stationary or moving at a constant speed.

References:

Special Thanks to Mr Damian Boh for his explanation of the topic to me which greatly aided me in the writing of the content of this blog post.

Home, Science, Science Concepts

Newton’s Three laws of motion (Part 1)

Hi guys,

I’m terribly sorry for being inactive for such a long time. I have been extremely busy lately therefore not having time to update the blog. So to make up for it i’m going to explain Newton’s three laws of motion. I will be posting these in 3 separate posts, explaining 1 law per post and this is part 1. I feel that this fundamental concept is extremely important in understanding other concepts as it is extremely simple, easy to understand and at the same time very significant.

Okay so on to the three laws of motion.

So what are the three laws of motion? They are Laws of physics which can predict the motion of an object pretty accurately (Although not as accurately as Quantum Physics which was developed by Einstein around 300 years after Newton formulated these laws.)

The three laws of motion are as follows:

  1. When viewed in an inertial reference frame, an object either is at rest or moves at a constant velocity, unless acted upon by an external force.
  2. The acceleration of a body is directly proportional to, and in the same direction as, the net force acting on the body, and inversely proportional to its mass. Thus, F = ma, where F is the net force acting on the object, m is the mass of the object and a is the acceleration of the object.
  3. When one body exerts a force on a second body, the second body simultaneously exerts a force equal in magnitude and opposite in direction to that of the first body.

Okay that might have been a little too complicated. but on to the explanations.

——————————————————————————————–

Let’s analyze Newton’s first Law of Motion

“When viewed in an inertial reference frame, an object either is at rest or moves at a constant velocity, unless acted upon by an external force.”

So what does this mean?

Newton’s first law of motion is also known as the law of inertia and inertia is the tendency of an object to remain in its state of motion be it not moving at all or moving at 10000000 km/h. Heavier bodies possess more inertia while lighter objects possess less inertia so heavier objects are more difficult (requires more force) to speed up but more difficult to stop and lighter objects though easier to speed up, are easier to stop.

Imagine a bus and a feather in front of you. Which is easier to move? The feather. Imagine the bus is now moving at 40 km/h and the feather is also moving at 40 km/h. Which one is easier to stop now? The feather.

So what does any of that have to do with anything?

Well simply put Newton’s first law of motion states that an object will stay stationary or continue moving in a constant velocity in a straight line if no forces (resultant) are acting upon it. This idea is expressed in terms of mass with inertia.

So why do things eventually stop?

Well that is because there are other forces acting upon the object.

Friction, Gravity, Normal Forces and practically any type of force can oppose other forces, cancelling them out and thus causing the object to stop.

Try pushing both you hands against each other and use as much force as possible to push your hands against each other. Despite applying so much force, your hand remains fairly stable and in roughly the same place. Why does this happen? The forces cancel each other out, therefore your hand remains stationary.

As you may have noticed, I have been using the word “resultant” very often. Why is this so?

Resultant force is the final value of the force acting upon an object after taking into account all other forces. Lets say we have a book that is falling. In this case there are 2 forces acting on the object: Gravity and Air resistance. Assuming the gravity acting upon this book is 10N and the air resistance acting on the book is 5N the resultant force will be 5N downward with gravity.

This resultant force value can be calculated with a simple formula which I will explain in my second post.

And with that I end this post. Thanks for your continuous support of my blog and I wish you a good day!

 

Best Wishes,

Clyde Lhui ūüôā

 

P.s: Once again im very sorry for being so inactive. I had to spend quite some time catching up with school work but I promise that I will work on this whenever I can!

Home, Science, Science Concepts

Terminal Velocity

Hi guys,

As I mentioned certain scientific terms in my previous post, i would like to go in depth on those concepts,beginning with terminal velocity, it being the most fundamental concept in my post.

So what is terminal velocity?

Terminal velocity is the velocity of an object when the drag force (dependent on the fluid the object is travelling through) acting upon it is equal to the downward force of gravity acting upon it. Simply put, when the air resistance of a falling object cancels out the gravitational force which is pulling it downwards and accelerating it.

So how do these forces affect the motion of the object? The forces cancelling each other out make the object remain at a constant rate of motion.

You may ask why does the object still move when the forces cancel each other out. This is due to the fact that in the beginning the force of gravity still manages to overcome the drag force, allowing the object to gain speed (accelerate) initially. But as the object increases in velocity, the drag force increases, this effect can also be seen in the case of friction (Drag and friction are pretty much the same thing). Lets assume that a boy is dragging a heavy box, full of files, across a distance of 100 meters, now we will imagine this scenario in two different ways, firstly in the case whereby the boy is walking slowly and in the second whereby the boy is running. So in the first case the boy walks, when he reaches the end, he feels the bottom of the box, where the box and the floor meet, it still feels the same as before, now in the second case, he runs, he once again feels the bottom of the box, this time it feels warmer than before. So what can we infer from this scenario? Before I reveal the answer, i would like to state a few properties of friction:

  1. Friction opposes motion
  2. Friction causes wear and tear
  3. Friction produces heat when kinetic energy is converted into thermal energy

So what can we infer? In the second scenario, there was more heat, therefore we can assume that there was more frictional force produced in the second case.

Now lets go back to what i mentioned previously, air resistance increases (Drag Force) as the object’s velocity increases. As seen in the example above, we can tell that this statement is true.

That’s essentially the definition of terminal velocity. Before we move on, lets do a recap:

  1. Terminal velocity is the velocity an object is at when the gravitational force acting upon it is equal to the drag force acting upon it in the opposite direction therefore cancelling out all forces therefore having a resultant force of 0
  2. The drag force acting upon the object increases as the object accelerates due to the downward force of gravity.

Ok so lets move on to the math behind terminal velocity and some examples of it.

The formula for terminal velocity is as follows: V_t= \sqrt{\frac{2mg}{\rho A C_d }}

Vt=Terminal Velocity

m=Mass of falling object

g= Acceleration of the object due to gravity

ŌĀ=¬†Density of fluid which the object is travelling through

A= Projected area of the object

Cd= Drag Coefficient

I went through everything in my previous post but lets do a recap on these terms:

mass= Amount of matter in an object (SI Unit : kg)

Acceleration = Rate of increase of speed (SI Unit: m/s^2)

Gravitational force= how much gravitational force does an object exert on another object (SI Unit: N/kg)

Density= Mass per unit volume of matter (SI Unit: kg/m^3)

Projected Area= Area of a falling object which is in contact of the air flowing through it. (SI Unit: m^2)- Same as Area

Drag coefficient= A value which depends on the shape of an object and can only be calculated by using the drag force of the object and other factors or by doing actual testing. This value has no units.

That’s all the terms. So now I shall be doing some examples.

So assuming I drop a metal cube which has a mass of 3 kg and has a projected area of 1 m^2 on Earth 90 degrees downward, through air at a temperature of 25 degrees Celsius, what would the Terminal velocity of the cube be?

All we have to do is input all the values into the formula. The acceleration due to gravity on earth is 9.81 m/s^2. The density of air at 25 degrees Celsius is 1.1839 kg/m^3 and the drag coefficient of a cube is 1.05 facing downward. The result is : 6.881101581m/s.

So there’s Terminal Velocity for you!

I would like to thank Mr Tan Ping Hock and Mr Yao Zhi Wei Adrian, My current and previous physics teachers respectively for clearing my doubts about certain concepts within this topic of terminal velocity!

Thanks for reading!

Clyde Lhui

References:

http://en.wikipedia.org/wiki/Drag_coefficient

http://en.wikipedia.org/wiki/Density_of_air

http://en.wikipedia.org/wiki/Terminal_velocity