Physics Puzzle: Helium Balloon in Car
May 13th, 2009
| Categories: Mechanics, Physics Puzzles
Level of difficulty: highschool
Here’s a classic. You’re sitting in a stationary car. There’s a helium balloon tied to its floor, floating in the air (Fig 1).
You next press down on the gas and accelerate forward. We all know that when you accelerate, you feel a force pushing you backwards. But what will happen to the Helium balloon? Will it also be pushed back, as shown in figure 2? Why? For the sake of this question, neglect air drag and resistance and any friction effects.
EDIT, 14/May/2009: A solution has been posted here.
I’ve seen this one before. The common mistake is to make the casual assumption (which is almost always correct) that the air is the least dense material involved in the problem.
So, having not assumed air is the least dense material, what would your solution be?
my guess is:
When the van accelerates, the air inside the van actually become more dense at the back of the van and less dense in front.
And helium being less dense than air will be pushed forward in the van instead of backwards.
It is a classical problem that can be solved by using the Equivalence Principle of General Relativity. The EP states that a non-inertial (i.e. accelerated or decelerated) motion is perfectly equivalent to a local gravitational field.
This means that when the van decelerates, everything inside will feel a constant gravitational field directed towards the front of the van. That is why we feel a force towards the front of the van. But the helium balloon weights less than the air it may contain. So it goes the opposite direction, because in normal gravity, people feel a force towards the center of the Earth, while helium baloons goes upwards. It is important to recognize that the shift of air inside the balloon or inside the van does not play any role.
Yep, that’s spot on. It’s precisely the solution I was going to publish - elegant, and it avoids all of the “air goes to the back, pushes Helium forward” sort of true yet flaky explanations often given.
I really like this problem. The most interessting problems are those that make you see something you’ve taken for granted from a different angle.
It certainly is the happiest thought of my day!
Fabio is nuts. Relativity has nothing to do with the phenomenon. It is a pure example of Newton’s First Law. When the car accelerates, the air inside the car obeys the first law — it tries to stay where it is until something external forces it to accelerate. The external force comes from the back of the car accelerating forward, and pressing against the air there. This creates a pressure gradient inside the car — higher pressure in the back, lower in the front. Pressure gradients are what cause balloons to float in the first place. The pressure on one side is greater than the pressure on the other, leading to a net force in the direction of lower pressure. In this case, the direction of lower pressure is toward the front of the car so the balloon floats in that direction. When at rest, the direction of lower pressure is straight up (since gravity also creates a pressure gradient in the air with higher pressure closer to the ground). In that case, the balloon floats straight up.
Fabio’s argument falls apart on three counts. First, it doesn’t account for balloons floating in a non moving car. Do they feel an upward gravitational force? Second, you are also inside the car. Do you feel a gravitational force toward the front? Any force you feel is the normal force of the car seat on your back, which is not gravitational and in any case feel like a force in the opposite direction. Third, it is a gross misunderstanding of the equivalence principle. The equivalence principle implies that there is no local way to measure a gravitational field. It can only be measured by comparison to a distant observer. But inside the car is local. Anything you observe there cannot possibly be a gravitational effect.
Trust me on this. My Ph. D. is in physics and my subspeciality is general relativity. I know what I’m talking about.