Teaching Physics with the Physics Suite

Edward F. Redish

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Is the M-B distribution wrong?

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 |Fair res| = ρπR2v2 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/m3).

(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