You work for a balloon delivery service and you are delivering a single, helium-filled balloon in your car. To prevent the balloon from bouncing around on the ceiling while you are driving you have tied a string with a weight on it to the balloon. The weight is resting on the floor and the balloon is floating just below the ceiling.

When you accelerate, does the balloon stay where it is, move backward, or move forward? What does it do when you make a turn?

Assume all the windows are closed and the vents are turned off so there is no air flow inside the car to affect the balloon.

Although the fact that air is denser than helium is the standard way to think about this problem, there's another interesting way to solve it.

Acceleration causes you to experience a force "pulling" you backwards. Likewise, gravity is a force that is pulling you downwards. In fact, gravity *is* acceleration, and, were you were in a closed box, you would have absolutely NO way of knowing whether the force you were experiences was caused by acceleration or by gravity (this is an important part of the theory of relativity).

So, taking as our premise that you aren't allowed to have any means of knowing whether you are accelerating forwards, or merely standing still but with the car standing upwards on its back end, the balloon in both cases must act in the exact same manner. If your car were standing on its back end, the balloon would float upwards towards the front of the car. Likewise, if the car is accelerating forwards it would also have to float towards the front.

If it moved towards the back, you'd suddenly know that you were accelerating, not being pulled by gravity. You can't ever know this, though, so the balloon must go forwards.

...And the same reasoning can be applied to a car turning left or right.

Edited on December 16, 2004, 3:55 pm

Posted by Sam on 2004-12-16 15:52:59