  A systematic study of the in-medium correction factor ($F$) on
nucleon-nucleon elastic cross section is performed within the
Ultra-relativistic Quantum Molecular Dynamics (UrQMD) model. The effects of the
beam energy dependence of $F$ on the directed, elliptic flow and nuclear
stopping in $^{197}$Au+$^{197}$Au collisions with energy ranging from $0.09$ to
$0.8A$ GeV are explored. It is found that the directed, elliptic flow and
nuclear stopping at relatively low energies are very sensitive to $F$, and the
sensitivity gradually weakens with increasing beam energy. The beam energy
dependent in-medium correction factor $F$ is deduced from the comparison of the
excitation functions of the directed, elliptic flow and nuclear stopping
between the calculated results and the FOPI experimental data.
