Why Falling Feels Weightless. The Hammer and Feather

We all know the feeling of losing weight when we fall, as if we've been freed from our bodies. But if we really lose weight, why does it come back with a vengeance the moment we land? Is weight some mysterious presence that appears and disappears on a whim? The reality is that we never actually feel our weight, as weight is a force we apply to other objects, not to ourselves. What we wrongly perceive as our weight is the reaction force that the ground or another supporting structure applies to us.

Fig. 1. Artist’s illustration of the strange sensation of weightlessness during free fall.

What is weight?

In free fall, there is no support and therefore no reaction. As we associate our weight with the reaction force, in its absence, we perceive ourselves as weightless. But what actually happens to our weight when support is gone? Is it still somewhere there, or do we lose it entirely? To answer this, we need to turn to formulas based on objective facts rather than subjective feelings. This is crucial because weight is one of the most confusing concepts in physics, as is also free fall.

Weight is determined by the formula W = mg, where m is mass and g is acceleration due to gravity. Your mass remains the same, whether you are in free fall or standing on the ground. The acceleration g depends solely on Earth's mass and the distance from its center. All essential components are in place; the only element missing is the supporting structure beneath us. And we can't exert force on nothing.

Action and reaction

In Fig. 2, a woman lies on the bed with a cat resting on top of her. She feels the cat's weight, mg, while the cat feels a reaction from the woman's body, known as a normal force (N), equal to the cat's weight. Together, they press down on the bed with a combined weight W(total) = Mg + mg. The bed reacts with the upward force N = W(total), which the woman interprets as her weight.

Fig. 2. A woman supports a cat while the bed supports their combined weight, illustrating how weight is transmitted through contact forces.

Interestingly, we recognize that we support a pet, yet we overlook the bed's support. This makes us miss a crucial point. If we feel the cat's weight, the bed should feel our weight, not us. All scales operate based on this principle. They don't actually measure our weight but rather the reaction from the scale. Take a bathroom scale. When you stand on the platform, it reacts by pushing up to balance your weight. On a flat surface, this upward force matches your weight, resulting in an accurate reading.

In water and in the air

When we are in water, we feel lighter because this upward force, called buoyancy in liquids, is weaker. It can no longer counterbalance our weight, which explains why we can't walk on water as we do on solid ground. In the air, the sensation of losing weight intensifies because the support from air, known as air drag, decreases further to a level where even swimming becomes impossible.

The thinner the medium becomes, the less support it provides for our bodies. However, whether we are on the ground, in water, or in the air, our weight remains consistent. It is not our weight that changes; it is the medium. We believe that we get lighter merely because we mistake the upward reaction of the medium for an indication of our true weight.

Hammer and feather in a vacuum and in the air

In a vacuum, a hammer and a feather accelerate at the same rate of g, as there is no matter to resist their movement and slow them down. Weight is a contact force that cannot manifest without matter. Gravity acts through a field, pulling all objects with equal strength, g, which depends only on Earth's rather than the objects' mass. Therefore, two objects with different masses, such as a hammer and a feather, accelerate concurrently and hit the ground simultaneously when dropped from the same height.

Fif. 3. A hammer plunges while a feather drifts, revealing how air resistance affects falling objects differently.

The air brings matter back into the equation and makes the weight of objects, mg, relevant again. The atmosphere provides support and a resistive force called air drag, which slows down the fall. Similar to the buoyant force in a liquid, air drag is dependent on a body's volume rather than its mass. Thus, we have a following situation. The heavier object pushes stronger on the air than the lighter object, yet the air resists them both roughly equally. As a result, the heavier object plunges through the air faster.