The onset or demise of Kondo effect in a magnetic impurity on a metal surface can be triggered, as often observed, by the simple mechanical nudging of a tip. This mechanically-driven quantum phase transition must reflect in a corresponding mechanical dissipation peak; yet, this kind of effect has not been focused upon so far. Aiming at the simplest theoretical modeling, we initially treat the impurity as a non-interacting resonant level turned cyclically on and off, and obtain a dissipation per cycle which is proportional to the hybridization $Gamma$, with a characteristic temperature dependent resonant peak value. A better treatment is obtained next by solving an Anderson impurity model by numerical renormalization group. Here, many body effects yield a dissipation whose peak value is now proportional to $T_K |log T|$ so long as $Tsim T_K$, followed for $Tsim Gamma$ by a second high temperature regime where dissipation is proportional to $Gamma|log T|$. The detectability of Kondo mechanical dissipation in atomic force microscopy is discussed.
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