A systematic study of the dependence of fusion cross sections on the strength of the friction force has been performed by carrying out classical dynamical trajectory calculations for a number of heavy-ion target-projectile systems. On comparing the calculations with the available experimental data on fusion excitation functions for few typical light-heavy-ion systems, it was seen that in the high-energy region, where the fusion cross sections depend sensitively on the strength of the friction force, there appears to be a trend in the data, that is not easily explained by a simple linear velocity-dependent friction force. However, even in this region, the paucity of experimental data prevents one from drawing any definite conclusions.