Why will a sheet of paper fall slower than one that is crumpled into a ball?

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A sheet of paper falls slower than one that is crumpled into a ball due to air resistance and surface area effects.

When a sheet of paper is spread out, it has a large surface area in comparison to its mass. As it falls through the air, this large surface area interacts with a lot of air molecules. This interaction with the air creates a form of friction known as air resistance or drag. The large surface area of the flat sheet presents more resistance to the air through which it is falling, causing it to fall more slowly.

On the other hand, when the paper is crumpled into a ball, the surface area is greatly reduced. This smaller surface area means that there is less air resistance acting against the motion of the falling ball of paper. With less air resistance, the crumpled ball of paper falls faster than the uncrumpled sheet.

Additionally, the flat sheet of paper tends to flutter and may even catch air currents that keep it aloft longer, while the ball shape is more aerodynamic and will generally not experience such effects.

In the absence of air (in a vacuum), both the flat sheet and the crumpled ball of paper would fall at the same rate due to gravity. However, in Earth's atmosphere, air resistance affects the rate at which objects with different shapes and surface areas fall.

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