# Help me understand E=mc^2

1. Jan 21, 2007

### linux kid

I have read the wikipedia article on this but my mind just can't seem to comprehend the meaning of this equation. I maybe unconsciously thinking too hard...but I'm still junior...

Someone please explain the meaning to me in plain English. :)

PS: BTW, did this equation lead to the discovery of nuclear technology?

Last edited: Jan 21, 2007
2. Jan 21, 2007

### ranger

I'm not sure what wiki article you read, but here is an easily understood description:

E = mc^2 is an important and well-known equation, which states an equivalence between energy (E) and mass (m), in direct proportion to the square of the speed of light in a vacuum (c2).
http://en.wikipedia.org/wiki/E=mc²

Essentially, this means a small amount of mass, will give us enormous amounts of energy. For example the atomic bomb, which is e = mc^2 in action.

3. Jan 21, 2007

### linux kid

But "small" is a relative term. What about a 3lb mass?

PS: that is the one I read.

4. Jan 21, 2007

### ranger

You should have all mass in kg. Why dont you try converting 3lb to kg and plug it in the equations and see what numbers you get. To give you can idea of the scale you are dealing with, the atomic bombs dropped in Japan were 63 TJ (Hiroshima) and 84 TJ (Nagasaki), Encyclopedia Americana. And by todays standards, these are small.

Last edited: Jan 21, 2007
5. Jan 21, 2007

### linux kid

I know the equation. I just don't know why/how it works. Why the speed of light?

6. Jan 21, 2007

### ranger

7. Jan 21, 2007

### Pathway

Because that's how much energy you get out of each bit of mass. So if you convert 1 kg of mass (= 2.2 lbs) to energy... you'll get
1 kg * c^2 of energy.

That's 1 kg * (3.0*10^8 m/s)^2 = 9 * 10^16 J of energy, or 9000 TJ. Compare that with those bombs.

To put that into perspective: most humans weigh more than 50 kg.

What e=mc^2 means is that mass is a form of energy and energy is a form of mass. They're different forms of the same thing.

Are you looking for how that equation was obtained? If so, here's the one from the Wikipedia article. I think we did it a simpler way in class, but it's in my pencil-and-paper physics notes.

http://en.wikipedia.org/wiki/E=mc2#Derivation