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** **A thoughtful student makes the following observation. "If I try to
accelerate a small sphere through air, it will be resisted by the air.
If I drop an object, it will eventually reach a terminal velocity where
the air is resisting as much as gravity is trying to accelerate. The smaller
the ball the slower the terminal velocity. But you tell me the Maxwell
distribution says that the molecules of air move very rapidly. I estimate
that this is much faster than the molecule's terminal velocity, so it can't
move that fast. The Maxwell distribution must be wrong."

(a) The Newton drag law for a sphere moving through air is calculated
by a molecular model to be |*F*_{air} _{res}| = ρπ*R*^{2}*v*^{2}
where R is the radius of the sphere, ρ is the
density of the air, and *v* is the velocity of the object through the air.
Calculate the terminal velocity for a sphere the size and mass of an air
molecule falling through a fluid the density of air (ρ
= 1 kg/m^{3}).

(b) From your estimate in the previous problem, is this speed greater or less than the average speed the molecule should have given the M-B distribution? What is wrong with the student's argument?

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Page last modified November 28, 2004: M16