Mass Versus Weight - Buoyancy and Weight

Buoyancy and Weight

Usually, the relationship between mass and weight on Earth is highly proportional; objects that are a hundred times more massive than a one-liter bottle of soda almost always weigh a hundred times more—approximately 1,000 newtons, which is the weight one would expect on Earth from an object with a mass slightly greater than 100 kilograms. Yet, this is not always the case and there are familiar objects that violate this mass / weight proportionality.

A common helium-filled toy balloon is something familiar to many children. When such a balloon is fully filled with helium, it has buoyancy—a force that opposes gravity. When a toy balloon becomes partially deflated, it will often become neutrally buoyant and can float about the house a meter or two off the floor. In such a state, there are moments when the balloon is neither rising nor falling and—in the sense that a scale placed under it will have no force applied to it—is, in a sense perfectly weightless (actually as noted below, weight has merely been redistributed along the Earth's surface so it cannot be measured). Though the rubber comprising the balloon has a mass of only a few grams, which might be almost unnoticeable, the rubber still retains all its mass when inflated.

Again, unlike the effect that low-gravity environments have on weight, buoyancy does not make a portion of an object’s weight vanish; the missing weight is instead being borne by the ground, which leaves less force (weight) being applied to any scale theoretically placed underneath the object in question (though one may perhaps have some trouble with the practical aspects of accurately weighing something individually in that condition). If one were however to weigh a small wading pool that someone then entered and began floating in, they would find that the full weight of the person was being borne by the pool and, ultimately, the scale underneath the pool. Whereas a buoyant object (on a properly working scale for weighing buoyant objects) would weigh less, the object/fluid system becomes heavier by the value of object's full mass once the object is added. Since air is a fluid, this principle applies to object/air systems as well; large volumes of air—and ultimately the ground—supports the weight a body loses through mid-air buoyancy.

The effects of buoyancy don’t just affect balloons; both liquids and gases are fluids in the physical sciences, and when all macro‑size objects larger than dust particles are immersed in fluids on Earth, they have some degree of buoyancy. In the case of either a swimmer floating in a pool or a balloon floating in air, buoyancy can fully counter the gravitational weight of the of the object being weighed, for a weighing device in the pool. However, as noted, an object supported by a fluid is fundamentally no different than an object supported by a sling or cable—the weight has merely been transferred to another location, not made to disappear.

The mass of "weightless" (neutrally buoyant) balloons can be better appreciated with much larger hot air balloons. Although no effort is required to counter their weight when they are hovering over the ground (when they can often be within one hundred newtons of zero weight), the inertia associated with their appreciable mass of several hundred kilograms or more can knock fully grown men off their feet when the balloon’s basket is moving horizontally over the ground.

Buoyancy and the resultant reduction in the downward force of objects being weighed underlies Archimedes' principle, which states that the buoyancy force is equal to the weight of the fluid that the object displaces. If this fluid is air, the force may be small.