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.