If you drop two different sized pieces of paper from the same height, several factors come into play that determine their motion and behavior as they fall. Here are a few things that may happen:
Air Resistance: The larger piece of paper will experience more air resistance compared to the smaller piece due to its larger surface area. This increased air resistance can slow down the larger piece of paper and cause it to fall more slowly than the smaller piece.
Falling Speed: In the absence of air resistance, both pieces of paper would fall at the same rate regardless of their size or mass. This principle is known as the equivalence principle or the principle of Galileo's free fall. However, due to air resistance, the larger piece of paper will generally fall more slowly than the smaller piece.
Terminal Velocity: As the falling speed increases, the air resistance also increases. Eventually, a point is reached where the air resistance matches the force of gravity acting on the falling object. At this point, the object stops accelerating and reaches a maximum speed called the terminal velocity. The larger piece of paper, with its greater surface area, will reach its terminal velocity at a lower speed compared to the smaller piece.
Falling Behavior: The larger piece of paper may exhibit more fluttering or oscillatory motion during its descent due to its greater susceptibility to air currents and turbulence. The smaller piece of paper, being more compact, may fall in a relatively straighter path.
It's important to note that the exact behavior can vary depending on the specific shape, weight distribution, and other factors of the paper pieces. Additionally, factors such as air density and humidity can also influence their motion.