We describe a simple mechanism of quantum friction for a particle moving parallel to a dielectric, based on a fully relativistic framework and the assumption of local equilibrium. The Cherenkov effect explains how the bare ground state becomes globally unstable and how fluctuations of the electromagnetic field and the particle's dipole are converted into pairs of excitations. Modelling the particle as a silver nano-sphere, we investigate the spectrum of the force and its velocity dependence. We find that the damping of the plasmon resonance in the silver particle has a relatively strong impact near the Cherenkov threshold velocity. We also present an expansion of the friction force near the threshold velocity for both damped and undamped particles.