The observation that a rock plummets while a feather drifts suggests that heavier objects fall faster, but this contradicts the fundamental laws of physics. The difference in falling speed is not due to gravity itself, but rather the result of a continuous contest between two primary forces acting on any object moving through the atmosphere. The actual rate at which an object falls is determined by how effectively it resists the decelerating effects of the surrounding air while responding to the constant pull of gravity.
The Constant Acceleration of Gravity
In the absence of air, the force of gravity acts as a consistent accelerator for all objects. Experiments in a vacuum establish that mass does not affect the rate of fall. Although gravity pulls harder on a massive boulder than a small pebble, the boulder requires a proportionally greater force to accelerate it, meaning the net effect is identical.
On Earth’s surface, the constant acceleration due to gravity is approximately \(9.8\) meters per second squared (\(9.8 \text{ m/s}^2\)). This means that for every second an object falls, its downward speed increases by \(9.8\) meters per second. This rate remains unchanged regardless of the object’s composition or weight.
If a hammer and a feather were dropped simultaneously in a chamber void of air, they would strike the ground at the exact same moment. This demonstration illustrates the ideal scenario where gravity is the only force at play. The consistency of this acceleration is the baseline physical law dictating how all matter behaves when subject only to the Earth’s pull.
The Force That Opposes Gravity: Air Resistance
The ideal conditions of a vacuum do not exist in the real world; the atmosphere introduces a second, opposing force called air resistance, or drag. This force is a type of friction that arises when an object pushes through the surrounding air molecules. These molecules collide with the object’s surface, creating a force that always acts opposite to the object’s motion.
Air resistance directly interferes with the constant acceleration caused by gravity, slowing the object’s rate of descent. The magnitude of this force is not constant; it is highly dependent on the object’s speed. As a falling object moves faster, it encounters and pushes aside more air molecules per second, causing the drag force to increase proportionally.
Because air resistance grows stronger with speed, an object’s acceleration continuously decreases as it falls. Only at the moment of release is the object accelerating at the full \(9.8 \text{ m/s}^2\), since air resistance is zero at zero velocity. The presence of the atmosphere transforms the physics of falling into a dynamic balance between two ever-changing forces.
Object Characteristics That Determine Drag
The amount of air resistance an object experiences is determined by its physical characteristics, specifically its size and ability to move through the air cleanly. The overall drag force is a function of these characteristics. This explains why two objects with the same mass can fall at vastly different rates in the atmosphere.
Cross-Sectional Area
The exposed cross-sectional area is a major factor, as a larger area results in more air molecules being pushed out of the way. A flat sheet of paper falls slowly because its broad surface generates significant drag. If the paper is crumpled into a small ball, the reduced cross-sectional area decreases the drag, allowing it to fall much faster.
Shape and Drag Coefficient
The object’s shape, quantified by the drag coefficient, dictates how smoothly the air flows around it. Streamlined shapes, like a bullet’s nose, minimize turbulence and reduce drag, allowing higher speeds. Conversely, blunt, irregular shapes create turbulent wakes, which significantly increases the resistance force.
Mass-to-Surface-Area Ratio
The primary factor determining the final falling speed is the object’s mass-to-surface-area ratio. Gravity’s downward pull is proportional to mass, while drag depends on size and shape. Heavy, dense objects, such as a rock, have a high mass relative to their surface area, meaning gravitational force overwhelmingly exceeds air resistance. Lighter objects, like a feather, have a low mass-to-area ratio, so air resistance quickly becomes a large portion of the overall forces, causing them to fall much slower.
When Falling Stops Accelerating: Terminal Velocity
As an object continues to fall, its speed increases, causing the air resistance to increase. Eventually, the upward force of air resistance becomes exactly equal to the downward force of gravity. When these two opposing forces achieve a perfect balance, the net force acting on the object becomes zero.
At this point of force equilibrium, the object stops accelerating and continues its descent at a constant speed known as terminal velocity. This velocity represents the maximum speed the object can attain while falling through the atmosphere. The object maintains this steady rate until it hits the ground or the air density changes.
Terminal velocity depends entirely on the object’s size, shape, and mass. A skydiver in a spread-eagle position reaches a relatively low terminal velocity of around 120 miles per hour (55 meters per second). If the skydiver pulls into a streamlined tuck, the reduced drag allows them to reach a much higher terminal velocity. Denser objects, like a steel ball, have an extremely high terminal velocity, while lighter objects, like a snowflake, reach their low terminal velocity almost immediately.