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Which raindrops fall faster, the small ones or the large ones?
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(Explain your answer using verifiable physical principles, if possible.)
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The larger raindrops fall faster.
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Large raindrops fall faster because a falling raindrop is subject to two opposing forces -- gravity and air resistance.
Air resistance is proportional to the drop's cross section, and it increases with velocity.
At first, the slowing effect of air resistance is very small, and the drop keeps falling faster because of the constant force of gravity.
As the speed increases, so does air resistance -- until the speed is so great that the force of air resistance equally opposes the force of gravity.
From that point the drop starts falling at a uniform speed, the so-called
terminal velocity.
By the time raindrops are observed falling on earth they have long ago already reached their
terminal velocity.
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Comparing different sizes of raindrops:
The force of gravity grows in proportion to the drop's volume, which is the cube of the radius.
On the other hand, air resistance builds up at the cross-section area of the drop, which is the square of the radius.
As the drops radius increases, the force of gravity increases faster than the opposing force of air resistance.
The larger drop can reach a greater
terminal velocity before the air resistance catches up with it.
Consequently, larger drops have a higher
terminal velocity, which means they fall faster.