  We present exact numerical results for the friction force and the contact
area for a viscoelastic solid (rubber) in sliding contact with hard, randomly
rough substrates. The rough surfaces are self-affine fractal with roughness
over several decades in length scales. We calculate the contribution to the
friction from the pulsating deformations induced by the substrate asperities.
We also calculate how the area of real contact, $A(v,p) $, depends on the
sliding speed $v$ and on the nominal contact pressure $p$, and we show how the
contact area for any sliding speed can be obtained from a universal master
curve $A(p)$. The numerical results are found to be in good agreement with the
predictions of an analytical contact mechanics theory.
