Thread: eqautions !!! i know that is spelt wrong!!1

equations have bothered me so much since being at school. can someone in leymans terms and in less than five minits please teach me what they are about like a+b =x and so forth i never get what the letters stand for so when i see a equation on tv i can never get my head around it becuause i dont know what the letters stand for i know e=mc2 e stand for energy and m is mass i dont know what the c is and why it is squered but i it all falls to peices when i think of old school day equatons that said e x 6 = 7 sqaured so that e cant stand for enegery again? is it that you need to be told what the letters are first or are you sposed to work out what the letters mean yourself like a cryptogram!?
it would propell me to nasa equivalent science if i could work it out simply

Equations are just a shorthand way of writing down calculations.

So in your a + b = x example a, b and x are just names used to represent whatever-it-is the equation is describing.

So, for example, if Alice gives you 5 dollars and Bob gives you 7 dollars, then you have a total of 12 dollars. But imagine you want to make a more general statement, so if Alice gives you "a" (some number) and Bob gives you "b" (some other number) then this equation tells you how to work out how much money ("x") you have in total (add "a" and "b" together).

The nice thing about this shorthand is that it makes it easier to manipulate the equation to work out other things. So, rather than saying, in words, "If I have 12 dollars and Alice gave me 5 dollars then I can take the difference to find out how much Bob gave me" you can simply do some standard manipulation of the equation and come up with: b = x - a (which is much shorter and applies no matter what the amounts of money are).

As for e=mc², you are right: e is energy and m is mass; c² is just a number that converts between them (e.g. if you convert m kilograms of mass into energy you would get e joules of energy). The value of c is the speed of light (just because of the way our units of measurement are defined). As for how the equation is derived, it isn't too complicated (but might be slightly over your head right now).

It is important to note that the names of variables in equations are arbitrary, they are just chosen for convenience. So "e" is clearly short for energy, and "m" for mass. But there might be another equation where "e" is engine size and "m" is miles or something else.

So, yes, anyone writing an equation should start off stating what the variables are. But some are so common that people don't bother, assuming others will know what they mean.

For example, in my field, if someone wrote V=I x R everyone would know they meant voltage, current (why is I current? I have no idea!) and resistance.

We use letters in equations to represent numbers that are either unknown, or variable.

As for you question about E=mc² ...."c" is what we use to designate the speed of light. So if someone says "It's traveling at .9c, then the object is traveling at 90% of the speed of light. I'll let someone else explain why it's a square of c.

edit: (ninja'ed by Strange

And if you want more information, you might want to check out this playlist of the Khan Academy:
https://www.khanacademy.org/math/algebra

It's worth noting that there are maths equations, physics equations, and even chemical equations, as well as equations belonging to other fields of study. Maths equations deal with numbers as well as other purely mathematical notions, physics equations are relations between physical quantities, chemical equations describe chemical reactions, and other fields of study have equations pertaining to the particular field. What the various symbols mean and how they are dealt with will be specific to the type of equation, though commonly they will take on numeric values and dealt with mathematically. Generally speaking, if you are not familiar with a particular field of study, then the equations from that field will be meaningless to you, and this is to be expected.

Sometimes equations are used to express general truths that stand for lots of individual truths. For example we know that when we are adding whole numbers, order doesn't matter. So 2 + 3 and 3 + 2 give the same answer. So we have a rule:

(Rule 1): 2 + 3 = 3 + 2

We also know that 45 + 12 = 12 + 45. So we have another rule.

(Rule 2): 45 + 12 = 12 + 45

If we keep going like this, we'd never get to the end of all the individual rules we need to write down. So the clever trick here -- and in truth, this was a great historical advance in human thinking -- we use symbols to stand for ALL possible numbers. So we say:

(Commutative law of addition) For all whole numbers x and y, we have x + y = y + x.

And now we're done! We only needed one rule, that we can express on one line of text, to stand for each of individual rules for all the special cases.

That's the power of algebra. We introduce variables, denoted by letters, that stand for a lots and lots of specific cases.

Here's a non-mathematical example. You have a kid and you teach your kid: Look both ways before crossing First Street. Look both ways before crossing Second Street. Look both ways before crossing Third Street ...

You see that you will never get to the end of it, and your kid still might not know to look both ways before crossing Broadway. So instead you say: For all streets X, look both ways before crossing X. Now you've taught your kid a general truth about ALL possible streets, without having to mention every specific street in the world.

Hope this helped. And for what it's worth, humans didn't always know how to use algebra. It was a great advance in human thinking. Someone had to figure it out and teach it to everyone else.

Originally Posted by Strange

For example, in my field, if someone wrote V=I x R everyone would know they meant voltage, current (why is I current? I have no idea!) and resistance.

Wow, I've been using this for decades and never once thought about why current is I. It turns out that it was started by Mr. Ampere himself.

The conventional symbol for current is , which originates from the French phrase intensité de courant, or in English current intensity.

Electric current - Wikipedia, the free encyclopedia

Essentially a duplicate of Harold's post.

I thought the reason they used "I" was because if enough current runs through you, you yell "I ya Yah!!!"

Originally Posted by Harold14370

Wow, I've been using this for decades and never once thought about why current is I.

Same here. Thanks for looking it up for me!

I wondered it too...I thought it was because "C" was already taken for capacitance.

Originally Posted by Dywyddyr

Essentially a duplicate of Harold's post.

I'll use that the next time Markus posts an explanation in the physics or maths section.

Since we are asking about E=mc²Does this formula have any relation to the formula for kinetic energy : E=1/2m V² ?

Originally Posted by MacGyver1968

Since we are asking about E=mc²Does this formula have any relation to the formula for kinetic energy : E=1/2m V² ?

Yes.

I have a truly marvellous proof of this, which this margin is too small to contain (P. de Fermat)

So why is the 1/2 dropped?

Originally Posted by PhDemon

The two aren't related.

E=mc² is derived here using a conservation of momentum argument.

...

Putting this into the equation of motion where vf and vi are intial and final velocities and s is distance travelled

...



This is why kinetic energy is

ETA: This is the cue for a real physicist to kick the shit out of this and say it ain't that simple

It ain't that simple. The mass in E = m c² is not the mass used in deriving , and E = m c² is the full energy of the particle, not the kinetic energy.

[sardonic grin]

Rock on...thanks for the explanation Phd.

Originally Posted by PhDemon

Originally Posted by mvb

Originally Posted by PhDemon

The two aren't related.

E=mc² is derived here using a conservation of momentum argument.

...

Putting this into the equation of motion where vf and vi are intial and final velocities and s is distance travelled

...



This is why kinetic energy is

ETA: This is the cue for a real physicist to kick the shit out of this and say it ain't that simple

It ain't that simple. The mass in E = m c² is not the mass used in deriving , and E = m c² is the full energy of the particle, not the kinetic energy.

[sardonic grin]

I know that , sorry I thought I'd made it clear by the separate derivations that they weren't related, I guess I didn't put what was in my head down on the page effectively, my bad... I was more thinking that my reasoning for where the 1/2 came from in the kinetic energy formula was too simplistic. I've edited the above post to emphasise they are separate.

OK, I think I had better take my grin off and show why I thought you were relating the two equations. If we keep track of the masses, by writing the relativistic mass as m and the rest mass as m₀ , we can start with

E=mc²

and define the kinetic energy as K = mc² - m₀c² , since m₀c² is the full energy in the absence of potentials and in a frame where the particle is not moving. With the well-known relation

m = m₀ c²
= (1- v²/c²)^1/2 m₀ c²

Since this is the math subforum, I'll assume that everyone knows that for v<<c,

(1- v²/c²)^1/2 = 1 - (1/2)(v/c)²

so that for v<<c

E = m₀c² - (1/2)m₀v²

Now we can use the formula for K to get K= (1/2) m₀v² directly, in the limit v<<c .

If we need better a better approximation, we keep more terms. If we want to put potential energies into the picture, we have some work to do.

Originally Posted by MacGyver1968

Since we are asking about E=mc²Does this formula have any relation to the formula for kinetic energy : E=1/2m V² ?

Yes, at least according to Einstein. Here is his argument (I paraphrase)

Consider a material body with energy content . Let emit a "plane wave of light" for some fixed period of time . One easily sees that the energy content of is reduced by , which depends only on .

Let i.e.the light energy "withdrawn" from .

Now, says Einstein, consider the situation from the perspective some body moving uniformly at velocity with respect to [tex]B[tex]. Then, evidently, by Lorentz time dilation, the light energy withdrawn depends only on , which is .

The difference between and is simply . By expanding as a Taylor series, and dropping terms of order higher than 2 in (since he is assuming ), he finds that

.

With a flourishing hand-wave Einstein now says something like this: the above is an equation for the differential energy of bodies in relative motion; but so is , the equation for kinetic energy - these can only differ by an irrelevant additive constant, so set

and so .

But, says he, is simply a "quantity" of energy, light in this case, that now depends only on and so......


.