We have studied the variation of frictional force with externally applied load for a Pt-coated atomic force microscope tip in contact with the surface of mica cleaved in ultrahigh vacuum. At low loads, the frictional force varies with load in almost exact proportion to the area of contact as predicted by the Johnson-Kendall-Roberts (JKR) theory [K. L. Johnson, K. Kendall, and A. D. Roberts, Proc. R. Sec. London Ser. A 324, 301 (1971)] of elastic adhesive contacts. The friction-load relation for a deliberately modified tip shape was proportional to an extended JKR model that predicts the area-load relation for nonparabolic tips, The tip shape was determined experimentally with a tip imaging technique and was consistent with the predicted friction behavior. This demonstrates that the frictional force is proportional to the area of contact between the tip and sample. Using the JKR/extended JKR model, interfacial surface energies and shear strengths can be estimated.