Friction forces between a sharp silicon nitride tip (radius of curvature, 10 nm) and mica were measured using a friction force microscope. Under low load conditions (<60 nN) the friction force is nearly proportional to the 2/3-power of the load. This shows that friction forces between a single spherical asperity and a flat surface have been measured. These measurements are the first experimental results indicating that the continuum Hertz contact theory possibly also holds for atomic scale contacts. A composite-tip model, in which the tip is composed of the actual silicon nitride tip and contaminant molecules present in cavities between the tip (with nanometer-size roughness) and the mica, is proposed to explain the observed behavior. This model was tested by changing the environmental conditions during friction measurements. Under ambient conditions, resulting in a high level of contamination, single-asperity friction was observed. For the same tip under Ar-gas conditions, resulting in a low level of contamination, multi-asperity friction was observed. This difference indicates that the level of contamination has a profound effect on the nature of the friction observed.