# Conveting Mass Into Energy Problem

1. Jan 28, 2007

### Delzac

1. The problem statement, all variables and given/known data
The annual energy requirement of the USA is of the order $$10^20$$ J. If we could find a 100% efficient process that could change matter into energy, how many kilograms of material would be needed to meet this requirement?

2. Relevant equations
$$E = mc^2$$

3. The attempt at a solution

Well, i simply sub $$10^2^0$$ in to $$E = mc^2$$
And i obtain, $$\frac{10^2^0}{(3.0*10^8)^2}$$
then $$m=11,111.1111$$

Is this correct? It looks to me like too simple a question, since this is the last question of my tutorial.

Last edited: Jan 28, 2007
2. Jan 28, 2007

### koofle

It might have just been a question put in to make you think about the possible consequences. But theres a slight miscalculation - you're off by one decimal place: ~1,111 Kg. Whats so special about this? Dividing by 365 to get the daily rate, you arrive at the conclusion that to support the energy needs of the USA on a daily basis would require 3 Kg of matter to be completely transformed into energy. Maybe you could compare it to the magnitude of fuel used nowadays? Just food for thought.

3. Jan 28, 2007

### Delzac

K, thanks for the help.