A physics question.

Orionaut

Orionaut

Orionaut

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Consider,

If you accelerate an object it has more KE, it also becomes ever so slightly more massive.

Is the increase in KE reflected in the increase in mass?

IE does <Delta>KE=<Delta>MC^2?

What made me think of this was a question regarding whether a battery gets heavier if you charge it?

The obvious answer is no. (A simplistic way of looking at it is that you don't put anything into a battery when you charge it. Simply move around stuff that the battery already contains) But is this correct.

Or is there a relativistic effect that actually results in an ever so slight mass difference between a flat or fully charged battery reflecting the greater energy contained within a fully charged one?
 
Relativistic effects are only relevant if the item is moving. And in the vast majority of cases (unless we're talking sub-atomic particles), relativistic mass increases are pretty much negligible. You have to be closing in on light speed for them to start having a profound effect.
 
fusion pretty much has it, in a battery you're effectively reversing a chemical reaction, and for most batteries the products are solely contained within the battery thus charging it has no effect on mass.

however some batteries (confined mainly to the research field atm) use air as part of the reaction, and these will get lighter/heavier as they charge/discharge as they output gas. of course the safety implications of lithium's fiery love affair with oxygen are the main reason these aren't mass market yet.

you could also consider fuel cells to some extent, although given they tend to be used in a way that has their reaction products simply exhausted from the system in the smaller scale they don't really count as "rechargable" in the normal sense, although if you included the larger loop of collecting the water outputs and re-splitting them into oxygen/hydrogen that would count.
 
Given E=mc^2
Then m=E/c^2
So, if E (kinetic energy) increases then m, the mass has to increase, since the speed of light, c must remain constant, otherwise it would violate Einstein's theory of Special Relativity.
Both mass and energy are interchangeable.
 
lunar said:
Given E=mc^2
Then m=E/c^2
So, if E (kinetic energy) increases then m, the mass has to increase, since the speed of light, c must remain constant, otherwise it would violate Einstein's theory of Special Relativity.
Both mass and energy are interchangeable.
Click to expand...

Kinetic energy doesn't equal mc^2. Kinetic energy equals 1/2mv^2. The increase in kinetic energy is down to the increased velocity, not the relativistic mass increase (as I said before, relativistic mass increase is negligible in most common mechanics-type problems).
 
I appreciate that, but even an object travelling 30mph will show a change in mass, though very small.
Another example, which similar is, if an object is raised and held static from the ground, it has gravitational potential energy (gpe). As a consequence the mass of the object would also increase, as it has stored energy.
Again, to determine the extra mass, we have
gpe=mgh (mass x mavity x height) and
E=mc^2
So taking E as gpe, the extra mass increase is given by gpe/c^2
 
No! There is NO increase in mass when an object has gravitational potential energy. Potential energy is just mg times delta h, where delta h is the change in height of the object from it’s original position. Dead easy. It’s got nothing to do with relativity, it’s just classical mechanics. You’ve even said yourself that the object is static in your scenario, where as relativistic mass increases only come when an object is moving.
 
Fusion said:
Kinetic energy doesn't equal mc^2. Kinetic energy equals 1/2mv^2. The increase in kinetic energy is down to the increased velocity, not the relativistic mass increase (as I said before, relativistic mass increase is negligible in most common mechanics-type problems).
Click to expand...
No.
0.5mv^2 is an approximation.
OP, you are correct. A charged battery has a tiny bit more mass.
 
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