# Homework Help: Mass difference between charged and uncharged battery - Special Relativity

1. Feb 26, 2010

### EnSlavingBlair

1. The problem statement, all variables and given/known data

A rechargeable AA battery with a mass of 25.0g can supply a power of 1.20W for 50.0mins.
What is the difference in mass between a charged and an uncharged battery?

2. Relevant equations

W = Pt
W = K = gmc^2 - mc^2
where g = 1/(1-(v/c)^2)^(-1/2)
E (total) = gmc^2 = K + E (rest) = K + mc^2

3. The attempt at a solution

W = 1.20 * 3.00x10^3 = 3600J = K

I am unsure of where to go from there, or even if this is the right way to start. The question does not make it clear (for me) if the 25.0g of the battery relates to the rest energy or the charged energy. Assuming it was clear which the mass relates to, I do not know what to use for the velocity in g.

There is also the possibility (in my mind, at least) that in part this is a trick question. That there is no mass difference, as while the battery is not in use the electrons are not moving. But I'm sure that's not what the question means, as it goes on to ask what fraction of the total mass the mass difference is.

Thank you

2. Feb 26, 2010

### EnSlavingBlair

I think I may have just solved it.

2. Relevant equations

E = W = Pt

Dm = DE/c^2 (where D is delta)

3. The attempt at a solution

I read this in a text book

"Wherever additional energy DE in any form is stored in an object, the rest mass of the object is increased by DE/c^2"
-Paul A. Tiper 1978, Modern Physics, Worth Publishers, Inc. New York

Which I take to mean (in relation to my question)

DE = K = W = Pt = 1.2*5400 = 6480J

As the kinetic energy is the change in energy in the system, allowing DE = W

Dm = DE/c^2 = 6480/(3*10^8)^2 = 7.2*10^-14 kg

I'm fairly sure this is correct, but a second opinion never goes astray :)