Balloon Bafflement (October 2023 Challenge Question)

Déjà vu.

This is the first comment to offer an good analogy. Another good one is a bubble level.

I have been in a car when the climate control (A/C) had only cooled a portion of the interior air, then turned it off. When I turned to the right and had been sitting in the cooler area of the car's interior air, I found myself suddenly in warmer air.

The balloon will start to move in a direction opposite to the change in direction taken by the car. Turn right--moves left, turn left--moves right, accelerate--moves rear, brake--moves front. The air mass in the car is going to respond to changes in direction the same as a person sitting in the car.

--JMM

Good answer. It's maybe a bit easier to visualize if you think of the air as tending to remain at the same velocity it had prior to the vehicle acceleration. This causes a pressure increase away from the direction of acceleration. In other words, air has inertia, and because it is more dense than the helium balloon, the pressure differential pushes the balloon toward the direction of acceleration.

I predict the opposite result with an air-filled balloon - it will act more like the plumb bob.

Another good one. First comment to address the density of the gases in the car.

The Statement said the Balloon comes with a long string attached so as the Balloon is filed with Helium it will rise to the roof of the vehicle. Due to Static generated between the Balloon and the Headliner of the vehicle the balloon will attach itself to the headliner like a magnet and will not move no matter which direction you move in.

Bottom line: The air in the car is heavier than the balloon. The direction that the inertial forces move the heavier air, the lighter balloon will move in the opposite direction.

Last time we had this discussion, someone introduced a slightly more difficult question.

Suppose the balloon is neutrally buoyant with no string and floating in free space towards the rear of the cabin when the car starts to accelerate. Which way does it go?

Suppose the balloon is neutrally buoyant with no string and floating in free space towards the rear of the cabin when the car starts to accelerate. Which way does it go?

Here's what I'm thinking...

When the car is standing stationary or moving uniformly in a straight line, the air in the car is very slightly denser at the floor than at the roof. There is a horizontal plane between the floor and the roof where the air is of average density, and somewhere on this plane the balloon would settle.

If the car accelerates, decelerates, or turns, this horizontal plane of average density gets tilted, rotating about the center of gravity point of the air, and the balloon will then move toward the closest point on the new tilted plane.

I don't think you need to worry about the density gradient from bottom to top.

When the car accelerates the density and pressure of the air towards the back will increase: because the balloon is towards the back it will shrink; the ratio of rubber to helium will increase making the balloon denser at a slightly higher rate than the surrounding air. The balloon will therefore start to fall and move towards the back.

Suppose you have a perfectly weighted balloon in a stationary car. The helium gas inside has a higher pressure than the air outside because of the curvature of the balloon surface and the elasticity of the rubber. The balloon size adjusts until the pressure difference equals the forces exerted by the rubber.

If the car suddenly accelerates, there is a very slight* air pressure gradient, just as there is up/down due to gravity. Say, for example, the balloon now finds itself in a higher pressure. It shrinks, but also the air around it becomes more dense. If the balloon shrinks more than the air around it, it will move to an even higher pressure area. If it shrinks less, it will move back to a lower pressure point until it reaches an equilibium point. Likewise, if the balloon is in a lower pressue area and expands less than the air, it will return to an equilibrium point, but if not, it will continue to diverge. It all depends how the balloon reacts under pressure.

If you inflate a balloon, first it requires a high pressure to get it started (when the surface curvature is high), then less pressure as it expands (less curvature) and finally more again when the rubber reaches its elastic limit.

A little calculation shows that the neutral buoyant balloon isn't going to do much in any case. A cubic inch of air weighs 0.000046709 pounds. So for 1G acceleration (gravity, or aggressive acceleration, braking, or turning) the pressure gradient would be 0.000046709 psi per inch.

If you want to experiment with neutrally buoyant balloons, James Orgill has some tips:

Great post.

In my mind experiment I felt certain that the pressure gradient from the front to back of the car when accelerating would be significant whereas the gradient from top to bottom would be negligible. Of course: even if the car has the huge acceleration of g the two gradients would be the same.