  This paper deals with an application of the notion of barrier in mixed
constrained nonlinear systems to an example of a pendulum mounted on a cart
with non-rigid cable, whose dynamics may switch to free-fall when the tension
of the cable vanishes. We present a direct construction of the boundary of the
potentially safe set in which there always exists a control such that the cable
never goes slack. A discussion on the dependence of this set with respect to
the pendulum and cart masses is then sketched.
