The friction force on a nanometer-sized tip sliding on a surface is related to the thermally activated hopping of the contact atoms on an effective atomic interaction potential. A general analytical expression relates the height of this potential and the hopping attempt frequency to measurements of the velocity dependence of the friction force performed with an atomic force microscope. While the height of the potential is roughly proportional to the normal load, the attempt frequency falls in the range of mechanical eigenfrequencies of the probing tip in contact with the surface.