The Myth of the Feather Dropping First - Gravitational Equivalence and Air Resistance

When it comes to the classic physics question of whether a feather or a stone would hit the ground first after being thrown vertically upward, the concept of gravitational equivalence stands out. This principle, often demonstrated through thought experiments and real-world scenarios, reveals a fascinating insight into the nature of gravity and air resistance.

Gravitational Equivalence in a Vacuum

In theory, and in the absence of air resistance, objects of different masses fall at the same rate due to gravity. This phenomenon, known as gravitational equivalence, was famously demonstrated during the Apollo 15 mission on the moon.

On Earth, this equivalence is observed in a vacuum environment. In such an environment, both a stone and a feather would experience the same gravitational acceleration of approximately 9.81 m/s2. Consequently, they would reach the ground simultaneously from the same height and released at the same time.

Role of Air Resistance

However, in a non-vacuum environment, such as Earth's atmosphere, air resistance plays a significant role. This resistance, which depends on the surface area of the object, affects the fall of different objects differently.

Air Resistance and the Stone

The stone experiences less air resistance per gram of mass and therefore falls faster than a feather. This is primarily due to the size and shape of the stone, which offers less surface area exposed to the air compared to a feather. The stone is denser and has a more compact shape, resulting in lower overall air resistance and a faster descent.

Surface Area and Air Resistance

The feather, on the other hand, has a much larger surface area relative to its mass. Its thin, airy structure increases the surface area exposed to the air, thereby increasing the air resistance. This resistance significantly affects the feather's descent, making it fall much more slowly. For example, if gold were made into a very thin foil, it might fall even slower than a feather due to its large surface area and lower density.

Comparison of Objects with Same Mass and Surface Area

Even if two objects have the same mass but different surface areas, or the same surface area but different masses, the object with a larger mass (and hence greater density) will generally fall faster. As mentioned, if a stone and a feather have the same surface area but different masses, the stone's higher density will result in less air resistance per gram, causing it to fall at a greater velocity.

Throwing vs. Dropping

The question of which object reaches the ground first also depends on how the objects are launched. This introduces additional variables such as the initial upward velocity and the direction of the throw.

Thrown Sequentially

If the objects are thrown sequentially, the one thrown first will reach the ground first due to gravity always acting on the object regardless of when it was thrown.

Thrown Simultaneously in Opposite Directions

When two objects are thrown simultaneously in opposite directions (one upward and one downward), the one thrown downward will reach the ground first. This is because it is being pulled by gravity even while in motion, whereas the upward-thrown object is initially moving against gravity.

Thrown Concurrently with Different Starts

If two objects are thrown downward concurrently, but their throws’ windups start simultaneously, the feather will reach the release point earlier and thus be released with a higher velocity. Due to its increased surface area, the feather will experience more air resistance and decelerate more quickly, making the stone reach the ground first.

In conclusion, while the principle of gravitational equivalence ensures that all objects fall at the same rate in a vacuum, the reality of varying air resistance means that the stone will typically reach the ground first in a non-vacuum environment. The feather's light, airy structure makes it especially susceptible to air resistance, leading to a slower descent.

Keywords: gravitational equivalence, air resistance, feather drop myth, stone and feather drop