Car with a helium balloon on a string that is tied to the floor

03 February, 2014 - 2 min read

You’re in a car with a helium balloon on a string that is tied to the floor. The windows are closed. When you step on the gas pedal, what happens to the balloon—does it move forward, move backward, or stay put?
A. The near-universal intuition is that the balloon leans backward as you accelerate. Well, the intuition is wrong. Your job is to deduce how the balloon does move and to explain it to the interviewer.

One good response is to draw an analogy to a spirit level. For the not so handy, a spirit level is the little gizmo carpenters use to make sure a surface is horizontal. It contains a narrow glass tube of colored liquid with a bubble in it. Whenever the spirit level rests on a perfectly horizontal surface, the bubble hovers in the middle of the tube. When the surface isn’t so level, the bubble migrates to the higher end of the tube. The takeaway here is that the bubble is simply a "hole" in the liquid. When the surface isn’t level, gravity pulls the liquid toward the lower end. This pushes the bubble wherever the liquid isn’t— toward the opposite end.
Untie the helium balloon and let it hit the moonroof. It becomes a spirit level. The balloon is a "bubble" of lower-density helium in higher-density air, all sealed in a container (the car).
Gravity pulls the heavy air downward, forcing the light balloon against the moonroof.
When the car accelerates, the air is pushed backward, just as your body is. This sends a lighter-than-air balloon forward. When the car brakes suddenly, the air piles up in front of the windshield. This sends the balloon backward. Centrifugal force pushes the air away from the turn and sends the balloon toward the center of the turn. Of course, the same applies when the balloon is tied to something; it’s just less free to move. The short answer to this question is that the balloon nods in the direction of any acceleration.