Which would fall to the ground faster...
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Which would fall to the ground faster...

[From: ] [author: ] [Date: 12-02-03] [Hit: ]
why would that be?thanks!-The larger drop falls faster.If there would be no friction (air drag), then they would fall at the same speed.The friction is proportional to the speed of the drop and to the cross sectional area of the drop.......
... a smaller raindrop, or a larger one? Also, why would that be?

thanks!

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The larger drop falls faster.
If there would be no friction (air drag), then they would fall at the same speed.
The friction is proportional to the speed of the drop and to the cross sectional area of the drop. The cross sectional area is proportional to the square of the linear dimensions. Newton's second law thus gives for a drop of mass m and radius r

m a = m g - c r^2 v

with c a constant.
After a few meters the gravity and friction will balance and the drop will fall at an ultimate speed (the terminal velocity V) :

m g = c r^2 V
V = m g / ( c r^2)

Here's the point: the mass of a drop is proportional to its volume, hence proportional to r^3 .

All in all you see that the terminal velocity will be proportional to r^3/r^2 = r .

So a larger drop will have a larger terminal velocity.

Note that very tiny drops fall so slowly that you hardly notice it. That's called fog...

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Neither. Their weight doesn't affect their speed at which they fall, gravity acts upon them equally, as gravity on earth is a Constant. (varying slightly at different altitudes) but not important. the big thing here is that Gravity is a constant, so the raindrops will fall at an equal rate.

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well the larger rain drop will eventually slit into other smaller rain drops from the friction in the air as it falls so there is no definite answer. So im guessing at the same time
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