Body Motion in a Resistive Medium at Temperature T

TL;DR

This paper derives an exact expression for the force on a body moving in a resistive medium at temperature T, unifying Stoke's and Newton's laws across different speed regimes.

Contribution

It provides a novel exact formula for the effective force considering a family of collision inelasticities in a resistive medium.

Findings

Force reduces to Stoke's law at low speeds

Force reduces to Newton's law at high speeds

Derived an exact expression for the force as a function of speed and restitution coefficient

Abstract

We consider a macroscopic body propagating in a one-dimensional resistive medium, consisting of an ideal gas at temperature $T$. For a whole family of collisions with varying degree of inelasticity, we find an exact expression for the effective force on the moving body as a function of the body's speed and the value of the restitution coefficient. At low and high speeds it reduces to the well-known Stoke's and Newton's law, respectively.