Aristotle is sometimes quoted as claiming that a body falls at a speed proportio

Question

Aristotle is sometimes quoted as claiming that a body falls at a speed proportional to its mass. Galileo refuted this, both by logical argument and by dropping different masses from the Leaning Tower of Pisa (if, indeed, he actually performed the experiment). Suppose, however, that Aristotle's assertion was based on his experience with objects falling in air, with Stokes'-Law drag, essentially at their terminal speeds. If Aristotle considered spherical objects, say, all of the same size but of different materials (wood, stone, brass for example) what would the actual relation between terminal fall speed and mass be? That is, if the terminal speed is written vT = K f(m), where f(m) is a function only of mass and K contains all the factors independent of mass, find the function f(m). Remember, you must show work justifying your result.

Explanation / Answer

Pulling out all of the terms which are not related to mass, we find vt = k *(m)^(1/2), so the terminal velocity would increase with the square root of the mass of the object, i.e. f(m) = (m)^(1/2)

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