The Equations Thread discussions

[hackenslash]

In this thread, we'll discuss the Equations thread, which can be found HERE. Use this thread to highlight any errors, ask questions, or discuss any equations that you would like to see unpacked. I am hoping that the physics and maths geeks will help me out by contributing.

[THWOTH]

Great idea for a thread.

[THWOTH]

Bookmarking.

[campermon]

Good idea!

I'll be back after a think or two!

[Pulsar]

I was about to start a Latex tutorial, however I encountered several problems with Mathjax:

• As noted before, you need \displaystyle{} to get large symbols like /int
• The comment symbol % doesn't work.
• \\ and \\[] for line breaks don't work; the former does work in the \begin{align}\end{align} environment, but the latter never does.
• Latex commands are not allowed inside the \text{} command.

And overall, the more Latex, the heavier the post is to load. Perhaps LIFE should experiment a bit more and improve the Mathjax settings, or look for alternatives.

[surreptitious57]

Energy is classed as liberated mass and
mass is classed as anticipated energy so to
reference the bag of sugar one could state that
it is in a zero state of energy as it is static : better
analogy would be a ball : when it is at rest it has zero
energy but when it is moving it has positive energy : even
more understandable analogy would be a car that is static even
though it has petrol : once it moves the petrol burns and shall expire
but if car remains motion less then no petrol will be burnt at all how ever

[hackenslash]

Energy is classed as liberated mass and mass is classed as anticipated energy so to reference the bag of sugar one could state that it is in a zero state of energy as it is static

That's not correct. Mass isn't 'anticipated' energy, it's more like 'bound' energy. What the equation tells us is the amount of energy contained within said mass. I chose a bag of sugar because (in the UK at least) sugar comes in bags of 1 Kg.

: better analogy would be a ball : when it is at rest it has zero energy

No, because that isn't correct. Whether the ball is at rest or in motion it contains energy. It contains more energy while in motion, but it is incorrect to say that it has zero energy at rest, because it is energy. What relativity is talking about is purely the energy contained within a given amount of mass.

but when it is moving it has positive energy : even more understandable analogy would be a car that is static even though it has petrol : once it moves the petrol burns and shall expire but if car remains motion less then no petrol will be burnt at all how ever

This misses the point, which is that the car is energy. The mass/energy relationship elucidated by relativity is robust. It could be said that matter and mass are not the same thing, but that's because, in matter, there is more energy, as there is a contribution to energy (and therefore mass) by the strong and weak forces and the electromagnetic force. Movement is a red herring in this regard (for this specific example, namely the equation under discussion) because the equation deals with the relationship between energy and mass. A body in motion embodies more energy, but take the motion away and there is still energy inherent in the mass of the body.

[hackenslash]

Excellent work, Darkchilde. I wonder if it could do with an explanation of the constants b and ω and their values for clarity. Oh, and maybe some discussion of the distinction between a vector and a scalar, which you touched upon with a word of caution.

[Darkchilde]

Excellent work, Darkchilde. I wonder if it could do with an explanation of the constants b and ω and their values for clarity. Oh, and maybe some discussion of the distinction between a vector and a scalar, which you touched upon with a word of caution.

To do so, would also require graphs, and more, as we are entering a bit of a more specialized world there. Maybe I will find some graphs etc. later on and go more detailed on pendulums and oscillatory motion.

[hackenslash]

That would be excellent.

My concern is to keep the thread as accessible as possible, as it's really for the benefit of those like myself whose mathematical understanding is less than stellar, and I know that, for many, the arcane symbols can be daunting. Maybe I should give some thought to some kind of glossary of terms, although maybe just a link to the Wiki on physical constants will suffice for the moment.

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

Not to detract from your excellent post, though.

[Darkchilde]

Oh, that one is an excellent resource Hack. It has a lot of useful constants and frankly, even physicists don't remember each and every constant by heart. Mostly physicists will remember the ones they use the most in their specialized field, and will have a table with the others. For example, an astrophysicist needs to remember the speed of light or the gravitational constant, but not Avogadro's number.

How about doing some differentiation? Differentiation is very easy, it has definite rules, and can be done by anyone with simple equations. I love differentiation... I am not talking differential equations here, which are worth more than one course, just simple differentiation.

[hackenslash]

Great idea!

[Darkchilde]

Okay, then, I will start tomorrow with Differentiation tutorials, maybe these will be better suited in maths, and link to and from the Equations thread?

[THWOTH]

I'm surprised that I very nearly understood most of your explanation there Darkchilde.

[Darkchilde]

I'm surprised that I very nearly understood most of your explanation there Darkchilde.

If you have any questions or something is not clear enough, then please ask away, and you shall receive an answer.

[THWOTH]

I shall think about it and try and pin it down.

[Darkchilde]

:D I shall think about it and try and pin it down.

Also read the post by campermon, it ties perfectly with mine.

[campermon]

I was thinking of solving the problem again, but this time using the equivalence of gravitational and kinetic energy.

[katja z]

Excellent idea

So I have worked through the first post and even though the equation described is a relatively familiar one, I think going over it again more slowly has been helpful. *glances uneasily at the bar of chocolate beside the computer, in case the sugar contained in it decided to explode*

I do have one question.

So, let's plug in some numbers (actually, just 1 number, namely the mass). Let's take our mass to be 1 Kg for simplicity. First, though, we need to square the speed of light in a vacuum. So, we get [math](3\times10^8)\times(3\times10^8) which gives us [math]9\times10^{16}, which we multiply again by 1 Kg, which gives us [math]9\times10^{16} Kg /m^2s^{-2}. This last result can be converted directly to joules, as the units are given in metres per second. From this, we obtain the result that the energy contained in a mass of 1 Kg, is equal to [math]9\times10^{16} joules, or 90,000,000,000,000,000 joules.

Shouldn't the bit in this passage that goes "9x1016kg/m2s-2" actually read 9x1016kg m2s-2?

(Apologies for not using latex, but I wanted to post this question today, not some time next year )

[campermon]

Shouldn't the bit in this passage that goes "9x1016kg/m2s-2" actually read 9x1016kg m2s-2?

You're quite right!