Please can someone explain the classic helium balloon in a car?

Of course you use effective mass.

In simplified cases that you may have studied in your introductory courses, mass and effective mass are the same thing. But in this case they are not, so you have to think a little bit more carefully than simply blindly lumping numbers into an equation.

The gravitational force is given by the 3-integral of the effective density distribution within the gravitational vector field. (You can use the 4-interval if you want to get into GM and tensor analysis but its not necessary). Your equation is simply a simplification of this.

Where in University/elsewhere did you learn this?
I can't find any reasonable definition of "effective mass" online, besides a few random articles about specific things - it doesn't seem like a general widely used physics term (?) I know what you mean by it, but the lack of evidence for it being a thing used for calculating gravitational force doesn't aid your assertion that "of course you use effective mass".

In my courses, we've used the actual mass - as it says in newton's equation. Which tells us that the force from mass 1 (the earth), onto mass 2 (the balloon) is equal to GMm/r^2. The force doesn't repel, it attracts mass 2 towards masss 1 (and vice versus)

I don't know how that's so difficult to understand It's basic/elementary physics that is taught from A-level onwards. And still applies today, when disregarding relativistic effects.

Its basic university physics. Unless you have a vacuum, then for one thing to move up, something else must move down. Gravity just rearranges things according to their mass, heavy things move down, light things move up. So there must be the same force pushing the light stuff up as there is pushing stuff down.

Perhaps you are reading the wrong books/ they are explaining it to you badly. I find a lot of physics is quite poorly explained, a lot of the undergrads I've taught in the past get confused over stuff I think should be incredibly obvious.

But don't worry: I'm explaining it to you now, so there is no reason to be confused.

What do you do? PhD/post grad physics?

I did, yes. Finished now, doing a second degree as a mature student.

Its basic university physics. Unless you have a vacuum, then for one thing to move up, something else must move down. Gravity just rearranges things according to their mass, heavy things move down, light things move up. So there must be the same force pushing the light stuff up as there is pushing stuff down.

Perhaps you are reading the wrong books/ they are explaining it to you badly. I find a lot of physics is quite poorly explained, a lot of the undergrads I've taught in the past get confused over stuff I think should be incredibly obvious.

But don't worry: I'm explaining it to you now, so there is no reason to be confused.

Cool. What degree are you doing now?

No-one's doubting that the balloon does move up - but to say that the gravitational attraction between the balloon and the earth repels the balloon away from the earth is straight up incorrect.

I'm applying elementary physics to a simple problem of how the force of gravity from the earth acts on a balloon of some mass (which is always positive) - whether it attracts or repels said balloon.
For some reason you seem to think that the force of gravity between 2 objects can repel.

What sorcery is this?!

Thank you!

You're assuming a vacuum when setting up the problem. That's fine for the type of interplanetary mechanics that Newton was thinking about, but its a wholely inappropriate oversimplification for the problem at hand.

A bubble with density 1 encased in a homogeneous fluid of density 2 rises under the force of gravity. Your equation says it would sink. That's 100% wrong. This means either your equation is wrong or you're applying it inappropriately.

In each instance, you would imagine the ballon if it were a normal object would stay motionless as the car moves. What we have to remember is that a helium balloon is lighter than air. In this case the air can be treated like an object moving to the back of the car for example when it speeds up. There is then an area of low pressure in front of the balloon, which the balloon will move towards.

In essence the air is behaving inertially and the helium ballon is just getting out of its way.

My equation doesn't say it will sink - it says that the force between the bubble of density 1 and the earth is attractive.

It doesn't tell you anything about the overall movement of the bubble at all because I haven't yet calculated the other forces acting on the bubble/the other forces in the situation (e.g. the gravitational attraction between the fluid and the earth)

I'm not trying to argue whether something will sink/won't sink in any given hypothetical situation - I'm saying that the gravitational force between 2 objects of positive mass will always be attractive.

Does that make more sense?

Alright, so do the rest of your calculation and get back to us.

I don't know how I would Well, or at least I'm just not going to Sorry. I'll have a think/possibly get some paper out.

I'd imagine that it would return the same result as whatever way you're doing it does, though I don't know that for sure.

I'm just confused why you think that the force between just the earth and just the bubble should change depending on the material surrounding the bubble.

Surely the fact that without stuff surrounding it it goes down, and with stuff it goes up, indicate that the stuff is doing something/acting in some way on the bubble?


Writing stuff down now/thinking of possible experiments of this - I guess something like oil in water rising to the top is simple enough.

Not negative mass, negative effective mass. We're not talking about dark matter, we're talking about helium balloons in air or air bubbles in water, both of which rise under gravity. Really everyday stuff.

Just like how we agreed that two like charges can attract, two masses can repel by the same logic, depending on their properties relevant to the medium.

Q) What is a repulsive force
A) Any force which induces objects to be pushed apart

Consider a system in equilibrium, a helium bubble encased in a homogeneous fluid. No gravitational force is felt, the system is completely in eqbm.

Now turn on gravity, what happens to the bubble? It moves AWAY from the source of the gravity. the movement can't have been caused by of any other force because the system was in equilibrium. So gravity has pushed the helium bubble away.

BY DEFINTION, the new force that has disturbed the equilibrium- gravity - must have exerted a repulsive force on the helium bubble.


Or to look at it another way, surely you concede that in the absence of a vacuum, all forces that act at a distance must be simultaneously repulsive and attractive?

You shouldn't be using negative effective mass in this case. If you want to look at how this problem works draw a diagram of the balloon, car and air in an inertial reference frame (the Earth frame). Have a look at what happens if you have an object that is more dense than air (eg a ball on the floor) and what happens to the rest of air in the car. Then look at what would happen if you switched it so you had the helium balloon instead.

You would find that the air, as it's more massive, has a greater inertia than the helium balloon. That basically means the air wants to stay where it is more than the helium ballon does. The air stays where it is, the car moves forwards (so now more air is towards the back of the car) and there's a small pressure gradient. It doesn't have to be much (we already know the balloon is light) because even a small force would cause a significant acceleration in something of that mass.

But that isn't the force of gravity on the bubble causing that, is it? It's the force of gravity exerted on the fluid which then does stuff to the bubble to make it go away from the source of gravity.

What's the difference? There is no difference. You're quibbling over semantics.

But we've already agreed that the gravity repels the bubble. Gravity is turned on, and the bubble is repelled. Gravity is the cause, repulsion of the bubble is the effect.

I really don't think I can state the facts any clearer than that. It is inconceivable that you cannot understand what I am saying.

You don't have to take a leap of faith, its just common sense. Just think about it for 30 seconds and you will agree with me.

That's quite possibly what I think we might be doing...

When I say the force of gravity from object 1 on an object 2, I mean the direct force arrow you'd draw between object 1 and 2. I think when you say the force of gravity you're meaning on the whole system, or something.

The force of gravity on the fluid around the bubble is the cause, not the force of gravity on the bubble. They're different forces. (or at least I'm 90% sure they are...)