  In this paper we consider different classical effects in a model for a scalar
field incorporating Lorentz symmetry breaking due to the presence of a single
background vector v^{\mu} coupled to its derivative. We perform an
investigation of the interaction energy between stationary steady sources
concentrated along parallel branes with an arbitrary number of dimensions, and
derive from this study some physical consequences. For the case of the scalar
dipole we show the emergence of a nontrivial torque, which is distinctive sign
of the Lorentz violation. We also investigate a similar model in the presence
of a semi-transparent mirror. For a general relative orientation between the
mirror and the v^{\mu}, we are able to perform calculations perturbatively in
v^{\mu} up to second order. We also find results without recourse to
approximations for two special cases, that of the mirror and v^{\mu} being
parallel or perpendicular to each other. For all these configurations, the
propagator for the scalar field and the interaction force between the mirror
and a point-like field source are computed. It is shown that the image method
is valid in our model for the Dirichlet's boundary condition, and we argue that
this is a non-trivial result. We also show the emergence of a torque on the
mirror depending on its orientation with respect to the Lorentz violating
background. This is a new effect with no counterpart in theories with Lorentz
symmetry in the presence of mirrors.
