Randall D. Knight — Dynamics I: Motion Along a Line: Problem 54

A large box of mass $M$ is pulled across a horizontal, frictionless surface by a horizontal rope with tension $T$. A small box of mass $m$ sits on top of the large box. The coefficients of static and kinetic friction between the two boxes are $\mu_s$ and $\mu_k$, respectively. Find an expression for the maximum tension $T_{max}$ for which the small box rides on top of the large box without slipping.