  The analogy of classical repulsive interactions emerging from the exchange of
mediating particles is revisited with a quantitative approach. Simulations are
presented for a particular toy model which are accessible to undergraduate
students at any level in the physics curriculum. Analytic treatment of the
various regimes shows rigorously how effective force laws can emerge from an
underlying microscopic model and should be accessible to advanced undergraduate
physics majors. The analysis presented uses the concept of emergence as
motivation for students to gain experience building and testing simplified
models for complex physical processes.
