  We consider an optical cavity enclosed by a freely moving mirror attached to
a spring and we study the quantum friction effect exerted by the dynamical
Casimir emission on the mechanical motion of the mirror. Observable signatures
of this simplest example of back-reaction effect are studied in both the
ring-down oscillations of the mirror motion and in its steady-state motion
under a monochromatic force. Analytical expressions are found in simple yet
relevant cases and compared to complete numerical solution of the master
equation. A circuit-QED device allowing for experimental observation of the
effect with state-of-the-art technology is proposed and theoretically
characterized.
