# Helium balloon problem?

## Main Question or Discussion Point

Not sure if I understand why the helium-filled balloon hovering in a closed train car, upon acceleration of the train, "will fly forward inside the train car till it hits the front, it wont touch the back of it at all." - quoted from klockan3

I believe the problem ignores wind effects.

I would've thought the back of the train would meet the balloon?

To see why, imagine instead, if the balloon were outside the train instead, different Z* coordinates but the same X,Y. Now if the train accelerated, the balloon would stay where it is (hovering above the ground instead of the train floor) and the back of the train would approach the balloon but not touch it (since both have different Z coordinates).

What is so special about the balloon being INSIDE the train that yields a different outcome as opposed to being OUTSIDE?

* Z-axis being the one created when an imaginary line perpendicularly strikes the plane of a train window on each side

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rcgldr
Homework Helper
Not sure if I understand why the helium-filled balloon hovering in a closed train car, upon acceleration of the train.
If it's hovering, then the average density of the balloon and whatever the balloon is supporting is the same as the surrounding air at that height in the train car. It could end up accelerating at the same speed as the train.

If the balloon had less density than the air, it would be "resting" on the ceiling of the train car, and in that case, acceleration of the train would cause the higher density air to accelerate backwards, creating a pressure gradient that increases with distance from the front of the train car, resulting in a forwards force on the balloon and accelerating it forwards, until it reached some relatively low terminal velocity speed due to drag. Eventually the balloon would endup "resting" at the front and ceiling of the train car.

ZapperZ
Staff Emeritus
Not sure if I understand why the helium-filled balloon hovering in a closed train car, upon acceleration of the train, "will fly forward inside the train car till it hits the front, it wont touch the back of it at all." - quoted from klockan3

I believe the problem ignores wind effects.

I would've thought the back of the train would meet the balloon?

To see why, imagine instead, if the balloon were outside the train instead, different Z* coordinates but the same X,Y. Now if the train accelerated, the balloon would stay where it is (hovering above the ground instead of the train floor) and the back of the train would approach the balloon but not touch it (since both have different Z coordinates).

What is so special about the balloon being INSIDE the train that yields a different outcome as opposed to being OUTSIDE?

* Z-axis being the one created when an imaginary line perpendicularly strikes the plane of a train window on each side
The helium balloon is less dense than the surrounding air. That's why it floats in the first place.

When the train accelerates, the surrounding air gets pushed back towards the back of the vehicle more than the balloon, due to the heavier density. Thus, the air displaces the balloon and the balloon will tend to float forward. If it is floating while attached to a string, it will tilt the string forward. I've seen this many times while riding the train, and no one else seemed to notice this counter-intuitive observation.

BTW, you may not realize that you already know this, and that this is a common occurrence. Since gravity is equivalent to an acceleration, what is going on on earth is can be thought of as us accelerating "upwards". So things tend to want to be pushed downwards (just like the back of the accelerating train). Yet, a helium balloon, when you let go of it, floats upwards (in the direction of the front of the train). Same principle. The more dense air would tend to be pushed more downwards, and thus, displacing the balloon upwards.

In physics, there are many seemingly different phenomena that we discover and understand to be of the same origin.

Zz.

sophiecentaur
Gold Member
Of course the problem "ignores wind effects". It's a totally closed train!! The experiment would, naturally, be affected by open windows or an open top.

Borek
Mentor

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rcgldr
Homework Helper
If you look at the video posted by Borek the balloon is not hovering, but "resting" against the celing of the car. If the balloon was actually hovering, it probably wouldn't move much.

ZapperZ
Staff Emeritus
If you look at the video posted by Borek the balloon is not hovering, but "resting" against the celing of the car. If the balloon was actually hovering, it probably wouldn't move much.
Actually, the reverse is true.

If it is resting against the ceiling, then the friction between it and the ceiling may hinder its "free motion". The fact that the balloon still moves forward probably means that the acceleration was large enough that the air is pushing quite a bit onto the balloon. So it would have moved even MORE had it been hovering.

Again, this is something that is easily tested, so I recommend people to do it for themselves.

Zz.

sophiecentaur
Gold Member
Just imagine the train was half full of water. Which direction would all the air go when the train accelerates and which direction would the more dense water go?

rcgldr
Homework Helper
If the balloon was actually hovering, it probably wouldn't move much.
Actually, the reverse is true.
If the balloon was hovering (not tethered, but actually hovering), then it's density would be the same as the surrounding air at that "altitude", so it wouldn't move much, depending on it's initial location (front to back).

Again, this is something that is easily tested, so I recommend people to do it for themselves.
You'd need a very tall train car to end up with sufficient pressure differential versus alititude to get a balloon to truly hover at some fixed altitude within the train car.

Assuming that the balloon had just enough density to hover 50% of the way off the floor, than under acceleration, the balloon would tend to hover about midway between front and back of the train car.

It would probably easier to do this in a large tank filled with water and a "hovering" submarine, since the pressure gradient (pressure change versus alititude) would be much greater than air.

ZapperZ
Staff Emeritus
If the balloon was hovering (not tethered, but actually hovering), then it's density would be the same as the surrounding air at that "altitude", so it wouldn't move much, depending on it's initial location (front to back).

You'd need a very tall train car to end up with sufficient pressure differential versus alititude to get a balloon to truly hover at some fixed altitude within the train car.
Well now we're changing what is commonly seen here. When I used the term "hovering", I assume that it simply doesn't touch anything else, so it definitely means that it is tethered to something, such a string and a fixed object/weight, which is what is commonly done. If it isn't then it hits the roof of whatever vehicle it is in. Very seldom (in fact, I don't recall ever seeing it) do you see a balloon just hovering in a vehicle without being attached to something. Such a situation is uncommon, and it would have been a terrible difficult situation to demonstrate. This isn't the situation being described here.

Zz.

rcgldr
Homework Helper
it is tethered to something
It wasn't clear to me if the original post was considering the theorectical (abstract thought problem) case of a balloon actually hovering in a train car, versus the more real world case of floating balloon tethered in the train car, or the balloon "resting" on the ceiling of the train car. I should have covered the tethered case in my previous posts.

sophiecentaur
Gold Member
I think this thread has gravitated to nit-picking. The OP clearly quotes a scenario of a tethered balloon and all the conventional arguments surely apply. If we are really considering a 'hovering' balloon then we could replace it with a region of air, contained within an envelope of the same density as air. That wouldn't move forwards or backwards. But a "helium balloon" was in the situation described so I think we can interpret the word "hovering" in a generous way.

As for the inside and outside contrasting scenarios - when the train is moving, the air inside it (and the balloon) is travelling at the same speed as the train. When outside,neither air nor balloon is travelling. Two very different things. Which would we like to discuss some more in agonising detail but would we achieve much?

In future should we all employ lawyers to make sure the wording of all questions is totally precise, lest we be jumped on by over-enthusiastic pedants?

rcgldr
Homework Helper
The OP clearly quotes a scenario of a tethered balloon and all the conventional arguments surely apply.
It wasn't clear to me since the OP also states that the balloon travels all the way to the front of the train car under acceleration, which wouldn't be possible if the balloon was tethered (since a train car is longer than it is tall), so I assumed he meant that the balloon was "hovering" on the ceiling of the train car, which I mentioned in my first post of this thread. I mentioned the truly "hovering" situation in case that was being considered in the OP. Not having read what ever it was that "klockan3" had written, I wasn't sure, so I covered both situations.

It wasn't clear to me if the original post was considering the theorectical (abstract thought problem) case of a balloon actually hovering in a train car, versus the more real world case of floating balloon tethered in the train car, or the balloon "resting" on the ceiling of the train car. I should have covered the tethered case in my previous posts.
Yeah, it was the former way. I tend to think very abstractly and so when I was given the problem by ZapperZ and told him that the back of the train would meet the train, I was shocked to hear by him that this was wrong.

I guess the way I translate things in my head and think very abstractly, ignoring detail, really does solidify the argument that I should major in philosophy instead of physics.