  We investigate the effects of atomic collisions as well as optomechanical
mirror-field coupling on the optical bistability in a hybrid system consisting
of a Bose-Einstein condensate inside a driven optical cavity with a moving end
mirror. It is shown that the bistability of the system can be controlled by the
s-wave scattering frequency which can provide the possibility of realizing a
controllable optical switch. On the other hand, by studying the effect of the
Bogoliubov mode, as a secondary mechanical mode relative to the mirror
vibrations, on the cooling process as well as the bipartite mirror-field and
atom-field entanglements we find an interpretation for the cooling of the
Bogoliubov mode. The advantage of this hybrid system in comparison to the bare
optomecanical cavity with a two-mode moving mirror is the controllability of
the frequency of the secondary mode through the s-wave scattering interaction.
