# Homework Help: Equation for mass

1. Dec 4, 2005

### bkelly

what is the equation for mass when calculating its energy equivalent? For one gram of mass E = mc(squared) would be

E = m * ( 9*10 to the 16th meters per second squared)

what are the values I put in for m being 1 gram such that the end result will be energy. I have googled this but get all kinds of nonsense other that I want.

Thanks.

2. Dec 5, 2005

### mezarashi

In the equation:

$$E = mc^2$$

E is in Joules, m is in kilograms, and c is the speed of light in meters per second (~300,000,000 meters/sec).

3. Dec 5, 2005

### bkelly

I understand the mass is in kilograms (1000 grams) but what is the exact expression I put in to the equation to get this thing to work out to the right units for energy:

E = m * ( 9*10 to the 16th meters per second squared)

for 1 kilogram, what is the full text to be used for replacing m?

E = (1 kilogram) * ( 9*10 to the 16th meters per second squared)
I just don't get this to work out to the right units.

Thank you

4. Dec 5, 2005

### Fermat

If we check out the dimensions on the rhs of the eqn, mc², we get

[kg][m²/s²] = [kg.m/s²][m] = [N][m] = [J]

where we used units of kg for the mass and m/s for the speed.
We end up with the units/dimensions of mc² being equivalent to Joules, which is work done or energy.

So, if the mass that you are interestred in is, m = 1 kg, then the energy of this mass is,

E = mc²
E = 1[kg]*(3*10^8)²[m²/s²]
E = 9*10^16 [kg.m/s²][m]
E = 9*10^16 [J]
============

Hmm, just noticed. You have the speed squared as metres per second squared. That should have been metres squared per second squared.

5. Dec 5, 2005

### bkelly

I think I understand what you are saying. It seems I was putting too much into the definition of a (kilo)gram. So to put this in other words, if we could translate one kilogram of mass into its energy equivalent, we could get 9 * 10^16 watt seconds of electric power. Thats a lot of power.

Yes, I did forget that meters squared.