Energy = Mass

[mark&2cats]

E= MC2

 

This might not be possible, but I was hoping that someone could explain to me what the speed of light has to do with the amount of energy contained within a given chunk of mass. Please bear in mind that I have no schooling (past high school), and must use all my fingers to count up to ten.

 

I may need a definition of mass; I tend to think of mass as weight. Is that wrong within the context of this equation?

 

If not, then say a clot of mass on earth weighs 3.2kg, then its energy = 3.2 times 300000 squared (90000000000) which comes to...

 

E=288000000000 (if I've figured that correctly - it takes a lot of finger counting)

 

Anyway, 288000000000 what? Horsepower?

 

And again, why is mass multiplied by light speed to get energy? And why square light speed? Nothing goes faster than light, eh - so why is it squared?

 

*sigh*

 

Wish I had been born smarter and had gone to school

[John Cuthber]

Well, the simple answer first

You can use any set of units and, with the right ones you would get an answer in horsepopwer.

The number you get from E=MC2 depends on the units you use.

If you use feet per second and (I think) a rather odd unit of mass called the slug then you get the answer in foot pounds per second.

A horsepower is 550 foot pounds per second, so you divide by 550 to get the answer in horsepower.

 

Normally we use the SI units in science.

We measure distance in metres, mass in kilograms and time in seconds.

The speed of light is about 300,000,000 metres per second and so the square of that is about 90,000,000,000,000,000 metres squared per second squared (a very odd unit, but never mind)

 

For your lump of stuff weighing 3.2 Kg the energy comes out at 288,000,000,000,000,000 kilogram metres squared per second.

The nice thing about the SI set of units is that they are "consistent".

That means that the answer automatically comes out in the right units. (without having to use weird units like the slug and then dividing by 550)

The SI unit of energy is the Joule so the energy is 288,000,000,000,000,000 Joules.

A joule of energy is roughly equal to the energy released by dropping a baseball of a table.

 

The answer to the question why do we square the speed of light is a bit trickier.

The simple answer is that it takes more energy to get a car from 10 MPH to 20 than it does to get it from 0 to 10 even though the change in speed is the same.

So energy is not simply proportional to the speed, it increases faster than the speed. It turns out that the energy increases as the square of the speed.

This might help explain it.

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

 

Anyway, it turns out that energy is related to the square of the speed and the same happens with E=MC2

 

You might want to get hold of a copy of the book called "Why does E=MC2?"

[lemur]

The answer to the question why do we square the speed of light is a bit trickier.

The simple answer is that it takes more energy to get a car from 10 MPH to 20 than it does to get it from 0 to 10 even though the change in speed is the same.

So energy is not simply proportional to the speed, it increases faster than the speed. It turns out that the energy increases as the square of the speed.

This might help explain it.

http://en.wikipedia..../Kinetic_energy

Intuitively, the car example made sense to me but then I wondered if this isn't because of wind and tire resistance increasing at higher speeds. Then I thought about the equation F=MA and it shouldn't matter whether the acceleration is from 0-10 or 10-20, if it's the same amount of mass, the same force is required, but I know that force isn't the same thing as work, power, or energy so now I'm confused about why energy increases proportional to speed - unless you are talking about relativity equations where energy (and mass?) increase with speed increases close to the speed of light, in which case nevermind because I was thinking you meant that this same logic applied to a significant degree at speeds @10mph.

[swansont]

Intuitively, the car example made sense to me but then I wondered if this isn't because of wind and tire resistance increasing at higher speeds.

 

No, it has absolutely nothing to do with wind and tire resistance.

[IM Egdall]

OK, I'll take a wack at this commonly asked question - why speed of light squared in E = mc^^2? (Without doing the usual mathematical derivation ala Einstein):

 

An object's energy of motion (kinetic energy) is equal to its mass times its velocity squared. This is the Newton physics formula, which works really well for speeds which are small compared to the speed of light. We can see this in a number of physical examples.

 

Einstein discovered that a mass at rest has intrinsic energy- in fact it has the maximum energy it can have. Now tThe speed of light is the maximum speed -- nothing can go faster than the speed of light per Einstein. So the rest energy of an object is its mass times the maximum allowed velocity squared, which is mass the speed of light squared.

 

I think this makes sense. Does it help?

Edited April 3, 2011 by I ME

[Janus]

Intuitively, the car example made sense to me but then I wondered if this isn't because of wind and tire resistance increasing at higher speeds. Then I thought about the equation F=MA and it shouldn't matter whether the acceleration is from 0-10 or 10-20, if it's the same amount of mass, the same force is required, but I know that force isn't the same thing as work, power, or energy so now I'm confused about why energy increases proportional to speed - unless you are talking about relativity equations where energy (and mass?) increase with speed increases close to the speed of light, in which case nevermind because I was thinking you meant that this same logic applied to a significant degree at speeds @10mph.

 

While F=ma, E=Fd, where d is the distance over which the force is applied. Taking your 0-10 and 10-20 example, A car accelerating from 0-10mph covers less distance during accleration than a car starting at 10 mph and accelerating to 20 mph. Since energy is equal to the force applied times the distance, it takes more energy to go from 10-20 mph than it does to go from 0-10 mph.

[TonyMcC]

Well, the simple answer first

You can use any set of units and, with the right ones you would get an answer in horsepopwer.

The number you get from E=MC2 depends on the units you use.

If you use feet per second and (I think) a rather odd unit of mass called the slug then you get the answer in foot pounds per second.

A horsepower is 550 foot pounds per second, so you divide by 550 to get the answer in horsepower.

 

"

 

Correct me if I am wrong, but I think you cannot get horse power from E=MC2.

Power being the rate of usage of energy. Its a bit like saying my car has 10 gallons of fuel so how powerful is it?

Edited April 3, 2011 by TonyMcC

[John Cuthber]

Correct me if I am wrong, but I think you cannot get horse power from E=MC2.

Power being the rate of usage of energy. Its a bit like saying my car has 10 gallons of fuel so how powerful is it?

Oops!

You are quite right. you would get an answer in horsepower seconds.

I get muddled when I use unfamiliar units.

[Xerxes]

Oops!

You are quite right. you would get an answer in horsepower seconds.

I get muddled when I use unfamiliar units.

[steevey]

I think its that for every amount of matter you have, there is a specific amount of energy required to allow you to have that amount of matter, and since light is pure electro-magnetic energy, it can be used as a constant to compare the outcome energy with.

[Xerxes]

Well, it has nothing to do with units, tyres, wind or anything else. I ME got close. Given the OPer's self-confessed lack of expertise in simple mathematics, I doubt that the following will quite hit the spot, though high-school graduation with a mathematical content should suffice. But, maybe, who knows, somebody somewhere may find it useful.....

 

So, here's Einstein in 1905 (hugely paraphrased):

 

Consider a material body B with energy content [math] E_{\text{initial}}[/math]. Let B emit a quantity of light for some fixed period of time [math] t[/math]. One easily sees that the energy content of B is reduced by [math]E_{\text{initial}} - E_{\text{final}}[/math], which depends only on [math]t[/math].

 

Let [math]E_{\text{initial}} - E_{\text{final}} = L[/math] i.e.the light energy "withdrawn" from B.

 

Now, says Einstein, consider the situation from the perspective some body moving uniformly at velocity [math]v [/math] with respect to B. Then, evidently, by Lorentz time dilation, the light energy withdrawn from [math]B[/math] is measured (from the perspective of the moving body) as [math]L'[/math] which likewise depends only on [math]t'[/math], which is [math] t(1 - \frac{v^2}{c^2})^{-\frac{1}{2}}[/math] (this is Lorentz time dilation)

 

The difference between [math]L[/math] and [math]L'[/math] is simply [math]L' - L = L[(1 - (\frac{v^2}{c^2})^{-\frac{1}{2}} - 1].[/math]. By expanding [math](1 - \frac{v^2}{c^2})^{-\frac{1}{2}}[/math] as a Taylor series, and dropping terms of order higher than 2 in [math]v/c[/math], he finds that

 

[math]L(1 + \frac{v^2}{2c^2} - 1) = L \frac{v^2}{2c^2} = \frac{1}{2}(\frac{L}{c^2})v^2[/math].

 

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 [math]E = \frac{1}{2}mv^2[/math], the equation for kinetic energy, and these can only differ by an irrelevant additive constant, so from the above set

 

[math]\frac{L}{c^2} = m[/math] and so [math]L= mc^2[/math].

 

But, says he, [math]L[/math] is simply a "quantity" of energy, light in this case, that now, from the above, depends only on [math]m[/math] and [math]c^2[/math] so......

 

[math]E = mc^2[/math].

 

It's fun, but slightly audacious of the old boy, wouldn't you say?

 

PS. He wrote this down when he was 28 or so, and is said to have written to a friend something along the lines that "this seems inescapable, but maybe the gods are laughing at me!"