Rain Drops falling down in a uniform cloud

AI Thread Summary
The discussion focuses on analyzing a rain drop falling through a uniform cloud of smaller drops, emphasizing the relationship between the drop's velocity and the densities of the drops and the cloud. It highlights the need to establish a differential equation to describe the motion of the larger drop, noting that the equation is non-linear. The absence of air resistance is mentioned, but the possibility of incorporating linear resistance from air is suggested as a potential approach to finding a solution. The participants are seeking logical assumptions to simplify the problem. Overall, the discussion revolves around the dynamics of falling rain drops in a cloud environment.
Erfan
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Homework Statement


Consider a uniforms cloud of density ρ1 which consists of many little drops that are approximately still.Consider a special rain drop that is a little more bigger than the others so that it starts to fall down.Water drops stays spherical all the way.But the radius gets higher as it falls down.Also water's density is ρ0.
(a) Find a relation between \dot{r}, velocity of the drop, and the two densities.
(b) Find rain drop's acceleration.

Homework Equations





The Attempt at a Solution


The differential equation is non-linear.
 
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Any thoughts on how to go about this? Any logical assumptions?
 
We have no air resistance force.But it might be possible to find a solution when the air exerts linear resistance force.
 
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