F1 car weight

[Marco]

I'm sure I read somewhere recently that someone far cleverer than me had proven that the weight of a battery changed with charge level. Can't find the article to back up my memory!
With that in mind does the weight of an F1 car alter following the harvest phase on a lap? I realise it's probably miniscule if at all but was a lengthy discussion during the GP on Sunday in our house.

[Lycoming]

I would like to see this article before I say anything more than the following, but my understanding of the fundamental working principles of batteries indicate that there should be no weight change with charge level.

[tim|away]

Yes it does, but the difference in mass is so small that you would have a hard time even measuring it.

Think of E=mc^2. Energy is equivalent to mass and the speed of light squared. So let's run some numbers for the 4MJ energy storage:

4m J / c^2 = 4.45 × 10^-11 kg = 44.5 nanograms.

Having said that, these are highly theoretical calculations that you'd have a hard time even proving in a lab, let alone on a track. Even the smallest dust contamination would have a significantly bigger impact on the mass of the battery than its own charging state.

[Trocola]

Yes it does, but the difference in mass is so small that you would have a hard time even measuring it.

Think of E=mc^2. Energy is equivalent to mass and the speed of light squared. So let's run some numbers for the 4MJ energy storage:

4m J / c^2 = 4.45 × 10^-11 kg = 44.5 nanograms.

That do not apply to batteries.

[Miguel]

Yes it does, but the difference in mass is so small that you would have a hard time even measuring it.

Think of E=mc^2. Energy is equivalent to mass and the speed of light squared. So let's run some numbers for the 4MJ energy storage:

4m J / c^2 = 4.45 × 10^-11 kg = 44.5 nanograms.

That do not apply to batteries.

What???? WHAT!??! It bloody well does. Special relativity is based on two principles: all inertial frameworks are equivalent, and the speed of light is constant and the same in all of them. This is true in batteries, and thus E=mc^2 does apply. If you think this only applies to kinetics, or dynamics, then think again. Electromagnetic energy as stored in batteries is just like any other kind of energy, and will distort spacetime.

Electromagnetism is *the* theory that pushed relativity out. As far as I know (condensed matter guy) electric charge, together with mass and angular momentum, are the only quantities of a black hole that matter.

[Lycoming]

It applies, but it's not really relevant. Sometimes people say that F1 teams are concerned with shaving nanograms of weight off their cars. When people say this, they never mean it in a literal sense.

[Trocola]

What???? WHAT!??! It bloody well does. Special relativity is based on two principles: all inertial frameworks are equivalent, and the speed of light is constant and the same in all of them. This is true in batteries, and thus E=mc^2 does apply. If you think this only applies to kinetics, or dynamics, then think again. Electromagnetic energy as stored in batteries is just like any other kind of energy, and will distort spacetime.

Electromagnetism is *the* theory that pushed relativity out. As far as I know (condensed matter guy) electric charge, together with mass and angular momentum, are the only quantities of a black hole that matter.

Are you serious? So, in an F1 there is a anti-mater reactor and they convert mass into energy. That must weight a lot and it would be very useful to todays energy problems around the world

On a battery you do not convert energy into mass. You store electrons, and they weight (not very much indeed) and that is all. E=mc2 do not apply to stored energy. it applies to nuclear fission

[elliott2705]

I realise we are getting quite off topic here but in the interest of closing it out for you Triocola i will reply.

To put it pure and simply energy IS mass. Mass IS energy. Thats what E=mc^2 is all about. It applies everywhere in the universe. No what this means in this context is that if an object gains energy it gains a proportionate mass (unlikely that you could measure it but that's not the point here). This one of the most fundamental principles to special relativity.

There is no anti-matter reactor in a car. There is however a device that converts mass to energy, its called an internal combustion engine. The energy lost to heat and work when the fuel is burned will correspond to the reduction in mass of the exhaust gases.


In answer to the original post: The is no noticeable increase in the mass of a battery between its charge or uncharged state. The only difference is a very very small E=mc^2 one as explained. Energy is stored in batteries as chemical potential energy, i.e when reactants change into different products electrical potential energy is released. The mass of the atoms in the reacting ions and the product ions is the same, hence no change in mass.

[beelsebob]

Urgh. No. You lot apparently know just enough to be dangerous.

The fact that there is an equation, does not mean it always applies. What E=mc^2 says is that you can gain a certain amount of energy by destroying a certain amount of mass. It does not say that there is no way to release stored energy that does not involve this equation. As an example. A rock falling down a hill gains kinetic energy while not changing mass whatsoever. The way it does that is by losing its gravitational potential energy as it falls. In an F1 car, the way we produce kinetic energy is by releasing chemical potential energy. not by converting mass into energy, as you might in a nuclear explosion, or a matter/antimatter explosion.

E=mc^2 is simply the wrong formula to apply.

[Marco]

As a mechanical engineer I'll leave now.....

[Miguel]

Urgh. No. You lot apparently know just enough to be dangerous.

The fact that there is an equation, does not mean it always applies. What E=mc^2 says is that you can gain a certain amount of energy by destroying a certain amount of mass. It does not say that there is no way to release stored energy that does not involve this equation. As an example. A rock falling down a hill gains kinetic energy while not changing mass whatsoever. The way it does that is by losing its gravitational potential energy as it falls. In an F1 car, the way we produce kinetic energy is by releasing chemical potential energy. not by converting mass into energy, as you might in a nuclear explosion, or a matter/antimatter explosion.

E=mc^2 is simply the wrong formula to apply.

I see another dangerous man...

As a matter of fact, you are right. Some equations don't always apply. That's particularly true with classical mechanics, and the E=T+V equation you've just used. Don't get me wrong, energy is always conserved in a theory where [H,t]=0 (these are commuters in quantum mechanics or poisson brackets in classical field theory). But mass is *not* constant. Fact. Proven to an amazing degree of accuracy.

In special relativity, wich supercedes Newtonian mechanics and extends classical electrodynamics, there are some conserved quantities, called Lorentz invariants, that have the same value no matter what inertial reference framework you are using. One of these is P_i * P^i (Minkowsky product), which is where E=mc^2 is derived from. And yes, this does mean that the falling rock will become heavier and heavier.

Think about it. If the rock didn't become heavier and heavier, there would be a height where you could throw a rock where it could exceed the speed of light. Which is not possible. Eventually, adding even a tiny bit more speed to get closer to c costs essentially an infinite amount of energy, and the speed of light remains safe.

Additionally, relativistic effects are enough to cause measurable changes in the energy spectrum of an isolated hydrogen atom.

But I wouldn't waste my time with special relativity for mostly anything F1 related.

[roller]

I am not a scientific thery expert, however, as far as I know....

Think of E=mc^2. Energy is equivalent to mass and the speed of light squared. So let's run some numbers for the 4MJ energy storage:

4m J / c^2 = 4.45 × 10^-11 kg = 44.5 nanograms.

That formula applies when you convert mass into energy (or viceversa). That means, those 44.5 nanograms, are what you'd have if you convert all this energy into mass (so you will loose the energy). But this is not the case, you are not converting energy into mass, you are only storing int.

As far as i know, in a F1 battery, you are converting kinetic energy in electric energy, nothing more.

There is no anti-matter reactor in a car. There is however a device that converts mass to energy, its called an internal combustion engine. The energy lost to heat and work when the fuel is burned will correspond to the reduction in mass of the exhaust gases.

There is no reduction in mass of the exhaust gases. In a combustion engine, you are converting chemical energy into thermal energy.

In special relativity, wich supercedes Newtonian mechanics and extends classical electrodynamics, there are some conserved quantities, called Lorentz invariants, that have the same value no matter what inertial reference framework you are using. One of these is P_i * P^i (Minkowsky product), which is where E=mc^2 is derived from. And yes, this does mean that the falling rock will become heavier and heavier.

Think about it. If the rock didn't become heavier and heavier, there would be a height where you could throw a rock where it could exceed the speed of light. Which is not possible. Eventually, adding even a tiny bit more speed to get closer to c costs essentially an infinite amount of energy, and the speed of light remains safe.

The increase of mass is proportional to the speed, not the energy. In fact, if that rocks accelerates only because of the effects of the gravity, the energy was actually there since the begining, and its total value has not changed (it has only been converted from potential energy to kinetic energy).

But I wouldn't waste my time with special relativity for mostly anything F1 related.

I totally agree with you


cheers!

[Miguel]

I should have stayed silent... Anyway:

1. Storing energy is converting it in a way you can easily make use of later.
2. Electromagnetic energy is just another kind of energy. It has its associated equivalent mass, but it is ridiculosuly small most of the time. Wikipedia has a couple of interesting links. The concept of self-energy is very complex, but very useful in modern theoretical physics.
3. The same applies to every other kind of energy. Example: one proton is a conglomerate of two up quarks and one down quark. The mass of a proton is very different from the sum of the masses. It is, however, possible to compute the mass of a proton by solving the energetics of the three quark system. The answer is pretty much what you expect [1].
4. In my earth example, of course the potential energy was there. It's the mass of the earth. And the kinetic energy of the stone, as seen from somewhere far far away that was initially statick with respect to the stone, will have to include a mass varying term (see next point). Technically, this is a scalar relativistic approximation, and not a proper treatment.
5. The observed mass is not proportional to the speed. The exact formula, for a given rest mass, is
   

Look, I know it's very nice to think that this relativity stuff or that quantum stuff don't really apply in the "real" world, and that the formulas in the classic textbooks are right. Well, they are, but only in the slow limit approximation, when things aren't too small or too big. There are times when one must use full quantum or relativistic theories to obtain reasonable answers. Time in satellites is one of these cases. Semiconductor behaviour is yet another.

You may also feel tempted to say these things are rubbish, and they may well be, but they both lead to tested extremely accurate predictions, with more tested significant figures than I could possibly imagine. Their replacement will have to be a damn good theory, making even more amazing testable predictions.

[1] http://arxiv.org/abs/0906.3599

[Trocola]

There is no anti-matter reactor in a car. There is however a device that converts mass to energy, its called an internal combustion engine. The energy lost to heat and work when the fuel is burned will correspond to the reduction in mass of the exhaust gases.

The energy you get from the ICE comes from a chemical reaction. The Carbon and the Hydrogen on the gasoline combines with the Oxygen of the air and it oxidates the gasoline, creating water an carbon dioxide (and a bit of carbon monoxide and nitrous oxydes, but they are minimal). The energy you obtain comes from the changes in energy states the atoms suffer when they are combining. Thats 8th grade chemistry

the ecuation E=mc2 tells us that energy can be "stored" as mass, not that all energy is mass

Urgh. No. You lot apparently know just enough to be dangerous.

The fact that there is an equation, does not mean it always applies. What E=mc^2 says is that you can gain a certain amount of energy by destroying a certain amount of mass. It does not say that there is no way to release stored energy that does not involve this equation. As an example. A rock falling down a hill gains kinetic energy while not changing mass whatsoever. The way it does that is by losing its gravitational potential energy as it falls. In an F1 car, the way we produce kinetic energy is by releasing chemical potential energy. not by converting mass into energy, as you might in a nuclear explosion, or a matter/antimatter explosion.

E=mc^2 is simply the wrong formula to apply.

That's what I was trying to explain. My english is not very good and it takes me a lot to explain myself

[Miguel]

the ecuation E=mc2 tells us that energy can be "stored" as mass, not that all energy is mass

No. That equation tells you that *all* mass is just another form of energy. If you go past special relativity to general relativity, it will also tell you that all energy deforms spacetime the same way an equivalent mass would.