In a tapping-mode atomic force microscope, a power is dissipated in the sample during the imaging process. While the vibrating tip taps on the sample surface, some part of its energy is coupled to the sample. Too much dissipated power may mean the damage of the sample or the tip. The amount of power dissipation is related to the mechanical properties of a sample such as viscosity and elasticity. In this paper, we first formulate the steady-state tip-sample interaction force by a simple analytical expression, and then we derive the expressions for average and maximum power dissipated in the sample by means of sample parameters. Furthermore, for a given sample elastic properties we can determine approximately the sample damping constant by measuring the average power dissipation. Simulation results are in close agreement with our analytical approach.