When observing objects fall, it is common to notice that a feather drifts gently to the ground while a rock plummets quickly. This everyday experience might lead one to believe that heavier objects inherently fall faster. However, the explanation for this difference is more nuanced, involving an interplay of forces beyond just an object’s weight.
Gravity’s Universal Acceleration
In a vacuum, gravity acts upon all objects consistently, causing them to accelerate equally. This was famously demonstrated by astronaut David R. Scott on the Moon, where he dropped a hammer and a feather simultaneously, and both struck the lunar surface at the same instant. On Earth, the acceleration due to gravity (‘g’) is approximately 9.8 meters per second squared (m/s²) or 32 feet per second squared (ft/s²). This constant value means that, without air, an object’s speed increases by 9.8 meters per second every second it falls, regardless of its mass.
The Role of Air Resistance
The Earth’s atmosphere is not a vacuum; it is a fluid of air molecules. As an object moves through this fluid, it encounters air resistance, also called drag. This force opposes the object’s motion, slowing it down. Air resistance arises from collisions between the object’s surface and the air molecules it displaces.
Its magnitude increases as the object’s speed rises. As a falling object accelerates due to gravity, the opposing drag force also grows. This counteracting force is the primary reason why objects fall at different speeds in the real world, unlike in a vacuum.
Understanding Terminal Velocity
As an object falls, its speed increases, and air resistance also increases. Eventually, the upward force of air resistance equals the downward force of gravity (the object’s weight). At this point, the net force on the object becomes zero, and it stops accelerating. This constant speed, where air resistance perfectly balances gravity, is called its terminal velocity. A skydiver, for example, reaches a terminal velocity around 150 miles per hour (240 kilometers per hour) in a spread-eagle position, while a raindrop falls at about 9 m/s (20 MPH).
Factors Influencing Falling Speed
Several characteristics determine an object’s air resistance and, consequently, its falling speed and terminal velocity.
Shape
The shape of an object significantly impacts drag. A streamlined shape allows air to flow around it more easily, reducing air resistance, while a blunt shape increases it. This is why a bullet falls faster than a crumpled piece of paper of similar mass.
Cross-sectional Area
The cross-sectional area, facing the direction of motion, also plays a substantial role. A larger cross-sectional area results in greater air resistance. For instance, a flat sheet of paper falls slower than the same paper crumpled into a ball because the flat sheet presents a larger surface area to the air.
Mass and Density
While gravity accelerates all mass equally, actual falling speed in air is heavily influenced by an object’s mass and density in relation to its air resistance. A more massive object, for a given size and shape, has a greater gravitational force pulling it down. This means it requires a higher speed to generate enough air resistance to reach terminal velocity, allowing it to accelerate longer or achieve a greater maximum speed. Denser objects, which pack more mass into a smaller volume, experience less air resistance relative to their weight, enabling them to fall faster than less dense objects of the same mass.