In a rolling workshop, an aluminum sheet with an initial thickness of $10$ mm and a width of $120$ mm is rolled through $4$ consecutive passes and is converted into a strip with a thickness of $3$ mm$.$ The deformation applied in all four passes is identical and applied to the maximum possible extent. The tensile strength of the metal is $350$ MPa, and the roller diameter is $400$ mm$.$ Calculate the coefficient of friction between the sheet$-$roller contact surfaces.