We study the collision of two spin polarized Fermi clouds in a harmonic trap using a simulation of the Boltzmann equation. As observed in recent experiments we find three distinct regimes of behavior. For weak interactions the clouds pass through each other. If interactions are increased they approach each other exponentially and for strong interactions they bounce off each other several times. We thereby demonstrate that all these phenomena can be reproduced using a semiclassical collisional approach and that these changes in behavior are associated with an increasing collision rate. We then show that the oscillation of the clouds in the bounce regime is an example of an unusual case in quantum gases: a nonlinear coupling between collective modes, namely the spin dipole mode and the axial breathing mode which is enforced by collisions. We also determine the frequency of the bounce as a function of the final temperature of the equilibrated system.