Background Essay: Buoyancy Brainteasers: Balloon-in-Car Puzzler

The Greek mathematician Archimedes first noted that any object immersed or partly immersed in a fluid (i.e., a liquid or a gas) is buoyed upward by a force equal to the weight of the fluid displaced by the object. The crucial factor in determining an object's buoyancy is its density, the relationship between its weight, which is pulling it down, and its volume. If an object placed in water weighs more than an equal volume of water -- in other words, if the density of the object is greater than the density of water -- then the downward force of gravity will be greater than the upward buoyant force, and the object will sink. On the other hand, if the object weighs less than the fluid it would displace if submerged, it will sink only to the point where it displaces the amount of fluid equal to its weight. At that point, the upward force of the fluid equals the downward force of gravity, and the object floats.

The helium-filled balloon featured in this brainteaser is less dense than the air it displaces. The air around the balloon pushes up on it with a force greater than that of gravity pulling it down, and it floats in air, just as a piece of wood floats in water. As a result, it rises to the top of the car. When the driver of the car hits the accelerator and the car jerks forward, everything in the car gets pushed forward and accelerates along with the car. The driver is pushed forward by the force of the seat moving forward, and the air in the car is pushed forward by the force of the air just behind it moving forward. The helium balloon is also pushed forward by the force from the surrounding air. However, because the helium balloon has less mass than the air it displaces, which is also pushed forward, the balloon accelerates even more than the car, the person, and the air, and as a result, it moves to the front.