conservation of energy… revisited e = mc 2 ?? a thinking duck ??

Conservation of Energy… Revisited

E = mc2 ??

E = mc2 ??

A thinking duck ??

A thinking duck ??

Conservation of Energy… Revisited

I’m a goose!I’m a

goose!

A thinking duck ??

A thinking duck ??

E = mc2

E = mc2

OK, egghead. So what’s this

all about then?

OK, egghead. So what’s this

all about then?

This equation simply shows how matter and energy

are related.

This equation simply shows how matter and energy

are related.

Let me put this in a way that a duck can understand…

Let me put this in a way that a duck can understand…

Goose!Goose!

Let’s say you have 100 Euros and you want to convert it to US Dollars…

What DO you do?

Friendly Neighborhood European Bank

Well, you could go to the bank.

Friendly Neighborhood European Bank

Well, you could go to the bank.

They will calculate, using the current EXCHANGE RATE,

how many American Dollars you can get for 100 Euros. (for our purposes, let us ignore the inevitable service charge)

100 EUROS ?? US DOLLARS=

According to the exchange rate for Euros into Dollars, you get 1.5 Dollars for every 1 Euro.So €100 gets you $150.

€ 100




€ 100 EXCHANGE RATE


$ 150


€ 100 EXCHANGE RATE


So, in the transformation of Euros into Dollars, the amount of dollars ($) is obtained by multiplying

the amount of Euros (€) by the exchange rate (x).

We can express this in a formula:

$ = € x

where x = 1.5 dollars per euro

Now, let’s say you have Matter

with a mass of 100 kilograms (kg)that you want to convert to

Energy, which we shall measure in joules (J)…

What DO you do?

Well, first we have to go to a different bank.

Universal Bank of the Universe (Local Group Affiliate)


Nature will calculate, using herEXCHANGE RATE,

how many joules of Energy (E) you can get for a mass (m) of 100 kg. (again, we shall assume that there is no service charge)



100 kilograms ?? joules=

mm E

According to the exchange rate for mass into energy, you get 90,000,000,000,000,000 J of energy (E) for every 1 kg of mass (m).

So 100 kg gets you 9,000,000,000,000,000,000 J !


mm E

mm

100 kg


So 100 kg gets you 9,000,000,000,000,000,000 J !


mm E

EXCHANGE RATE

mm

100 kg


So 100 kg gets you 9,000,000,000,000,000,000 J !

E

9,000,000,000,000,000,000 JEXCHANGE RATE

mm

100 kg


mm E


So 100 kg gets you 9,000,000,000,000,000,000 J !

So, in the transformation of mass into energy, the amount of energy (E) is obtained by multiplying

the amount of mass (m) by the exchange rate. But unlike the first bank, Nature’s exchange rate is fixed,

and it has a value of 90,000,000,000,000,000 joules per kilogram.

This is no arbitrary value. It is the square of the speed of light.





The speed of light is a universal constant and is given the symbol ‘c’.The value for c is 300,000,000 m/s ,

so c × c = c2 =90,000,000,000,000,000 m2/s2

(You should convince yourself that m2/s2 and J/kg are equivalent units. See “Units” in the Background Materials.)





The speed of light is a universal constant and is given the symbol ‘c’.The value for c is 300,000,000 m/s ,

so c × c = c2 =90,000,000,000,000,000 m2/s2

(You should convince yourself that m2/s2 and J/kg are equivalent units. See “Units” in the Background Materials.)

We can express all of this in a formula:

E = mc2

So you see, my feathered friend…

So you see, my feathered friend…

…at the bank I can transform

one CURRENCY into another.

…at the bank I can transform

one CURRENCY into another.

Both are money, but they are in

different forms.

Both are money, but they are in

different forms.

Matter and energy are also simply different

forms of the same thing…

Matter and energy are also simply different

forms of the same thing…

— I prefer to call it

MASS-ENERGY.

— I prefer to call it

MASS-ENERGY.

The one can be transformed

into the other.

The one can be transformed

into the other.

In the transformation of mass to energy…

In the transformation of mass to energy…

…the EXCHANGE RATE is the square of the

speed of light:c2


speed of light:c2


speed of light:c2


speed of light:c2

Does this guy ever shut up?


And since c has a VERY large value and we are squaring it…

And since c has a VERY large value and we are squaring it…



…we get an enormous amount of energy…




OK,thank you

OK,thank you

…for a tiny amount of matter.

…for a tiny amount of matter.

OK,thank you

OK,thank you

Now, the transformation

energy to mass,


energy to mass,


energy to mass,


energy to mass,

You know, I just remembered,

I have an appointment…



…you know, that can

happen, too!

…you know, that can

happen, too!





Energy can transform into mass!


sighsigh



Let’s say you now have 100 US Dollarsand you want to convert it into Euros…

100 DOLLARS ?? EUROS=

100 DOLLARS ?? EUROS=

Remembering that $ = €x, then rearranging gives

$x−€ =

Let’s say you now have 100 US Dollarsand you want to convert it into Euros…

You will get

100 ÷ 1.5 = € 66.67

You will get

100 ÷ 1.5 = € 66.67

$ 100

$ 100 € 66.67=

You will get

100 ÷ 1.5 = € 66.67

Likewise, to convert energy to mass we rearrange E = mc2 and use

Em c2−=

So, for example…


Em c2−=

100 J

E

So, for example…


Em c2−=

100 J =

E

So, for example…

0.0000000000000011 kg

And…?And…?

That’s it.That’s it.

Would you like to see

my monkey?

Would you like to see

my monkey?

HOW EINSTEIN ACTUALLY PHRASED IT…

"It followed from the special theory of relativity that mass and energy are both but different manifestations of the same thing – a somewhat unfamiliar conception for the

average mind. Furthermore, the equation E = mc2, in which energy is put equal to mass, multiplied by the square of the velocity of light, showed that very small amounts of mass may be converted into a very large amount of energy and vice versa. The mass and energy were in fact equivalent,

according to the formula mentioned above."

And finally, a word about those bank service charges:



If we want to take advantage of the very large amount of energy that can be obtained from a very small amount of mass, then we could get it from a nuclear reaction.

But there will be a service charge on that exchange — and it is huge: For example, only a tiny fraction of the mass of fissionable uranium is converted into

energy. The rest goes into making lighter elements. That is the fee.



If we want to take advantage of the very large amount of energy that can be obtained from a very small amount of mass, then we could get it from a nuclear reaction.

But there will be a service charge on that exchange — and it is huge: For example, only a tiny fraction of the mass of fissionable uranium is converted into

energy. The rest goes into making lighter elements. That is the fee.

However, when matter and antimatter annihilate, the conversion from mass to energy is absolute.

There is no service charge with this particular transformation of mass to energy.


conservation of energy… revisited e = mc 2 ?? a thinking duck ??

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