Friction On Stacked Block

A slab (dark brown) of mass $m_1 = \SI{40}{\kilo\gram}$ rests on a frictionless floor (orange), and a block (light brown) of mass $m_2 = \SI{10}{\kilo\gram}$ rests on top of the slab. The block $m_2$ is pulled by a horizontal force $F$.

What is the greatest force, $F_\textrm{max}$ (in $\si{\newton}$), such that $m_1$ and $m_2$ will move together?

Assumptions and Details

• Use $g = \SI[per-mode=symbol]{9.8}{\meter\per\second\squared}$
• The coefficients of static friction and kinetic friction between the block and the slab are $\mu_s = 0.6$ and $\mu _k = 0.4$, respectively.