Experiments indicate that frictional resistance to sliding between macroscopic, clean, dry surfaces depends on the average rateV at which the surfaces are translated relative to each other. Using a new lattice automaton, we obtain results suggesting that rate-dependent macroscopic dynamics may arise from microscopic interactions between contact points which decay from a metastable state with a finite lifetimeΓ. Sliding is accommodated by clusters, or avalanches, of failed lattice contact points, and corresponds to successive quenches into the metastable state by an electromechanical loading system with a finite response timeΔ. Under the quasistatic assumptionΔ ≫Γ, rate dependence is a consequence of the increase in correlation length ξd of clusters of failed lattice points as quench rate increases. Special cases of the model are isomorphic to the selforganized criticality model for sandpiles, and to block-spring models of the type first studied by Burridge and Knopoff for earthquakes.