Sliding motion for adjacent blocks along an inclined plane

This article discusses a scenario/arrangement whose statics/dynamics/kinematics can be understood using the ideas of classical mechanics.
View other mechanics scenarios

The two blocks are adjacent to each other on the incline.

The scenario here is of two adjacent dry cuboidal blocks as shown in the figure, on an incline of a fixed inclined plane making an angle $\theta$ with the horizontal.

The upper mass is denoted as $m_{1}$, and the coefficients of static and kinetic friction between that mass and the incline are denoted $\mu _{s1}$ and $\mu _{k1}$. The lower mass is denoted as $m_{2}$, and the coefficients of static and kinetic friction between that mass and the incline are denoted $\mu _{s2}$ and $\mu _{k2}$.

The extremes are $\theta =0$ (whence, the plane is horizontal) and $\theta =\pi /2$ (whence, the plane is vertical).

We assume that the block undergoes no rotational motion, i.e., it does not roll or topple. Although the diagram here shows a block with square cross section, this shape assumption is not necessary as long as we assume that the block undergoes no rotational motion.

Behavior assuming system initially at rest

Note that the answer in the third column must be yes if the first two columns are yes and no if the first two columns are no.

Is $\tan \theta <\mu _{s1}$?	Is $\tan \theta <\mu _{s2}$?	Is $\tan \theta <(\mu _{s1}m_{1}+\mu _{s2}m_{2})/(m_{1}+m_{2})$?	Is $\mu _{k2}<\mu _{k1}$?	Behavior
Doesn't matter	Doesn't matter	Yes	Doesn't matter	Both blocks remain stationary.
Yes	No	Doesn't matter	Doesn't matter	$m_{2}$ slides down, $m_{1}$ stays stationary.