  Let $F(M,k)$ be the configuration space of ordered $k-$tuples of distinct
points in the manifold $M$. Using the Fadell-Neuwirth fibration, we prove that
the configuration spaces $F(M,k)$ are never contractible, for $k\geq 2$. As
applications of our results, we will calculate the LS category and topological
complexity for its loop space and suspension.
