The scan-velocity dependence of friction force microscopy (FFM) is characterized on gelatin films and related to the rate dependence of molecular relaxations. For selected scanning-parameter values the velocity dependence of frictional force is affected by the measurement process, because of energy imparted to the tip-sample contact region : a peak in the friction-velocity relationship, attributed to the glass-to-rubber transition, shifts to higher velocity for increasingly-perturbative scanning. Subsequent imaging at less perturbative scanning conditions reveals residual elevated frictional forces, but no corresponding morphological changes, in the perturbed regions. This is attributed to greater relaxational dissipation of energy from higher-energy molecular conformations attained in the rubbery state. Relaxation to lower-energy conformations in turn leaves the scanned region exhibiting lower frictional forces, i.e., in a less dissipative state characteristic of the scanning conditions during repeated imaging. The ability to image variations in frictional dissipation tens of nanometers in lateral size is demonstrated. These variations are sampled statistically over micrometer-scale regions to yield "friction spectroscopy" histograms, i.e., number of image pixels versus frictional force. Histogram breadth and symmetry apparently reflect the energy dispersion of relaxations characteristic of glassy or rubbery behavior. The fundamental understandings of FFM derived in this study are applied to assess crystallinity and aging in gelatin films.