Dragging motion for pile of blocks

This article discusses a scenario/arrangement whose statics/dynamics/kinematics can be understood using the ideas of classical mechanics.
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The two blocks scenario

Consider one block placed on top of another. The blocks are cuboidal with a horizontal surface of contact. Suppose the lower block is $A$ and the upper block is $B$, and the lower block is resting on a fixed floor. Suppose the coefficients of friction are:

• ${\mu }_{s1}$ is the limiting coefficient of static friction between $A$ and the floor.
• ${\mu }_{k1}$ is the coefficient of kinetic friction between $A$ and the floor.
• ${\mu }_{s2}$ is the limiting coefficient of static friction between $A$ and $B$.
• ${\mu }_{k2}$ is the coefficient of kinetic friction between $A$ and $B$.

We assume that there are no external forces in the vertical direction, other than the gravitational and normal force.

Normal force and gravitational force

On the upper block

KEY FORCE CONCEPT (ACTION-REACTION): Just because two forces are equal in magnitude and opposite in direction does not imply that they form an action-reaction pair in the sense of Newton's third law of motion. An action-reaction pair is a pair occurs between two bodies that exert forces on each other, not for a pair of forces both acting on the same body. The normal force on the upper block and

$m_{B}g$

(the gravitational force) are equal and opposite but do not form an action reaction pair.

If we denote by $N_{AB}$ the normal force between the blocks, then $N_{AB}$ acts upward on the upper block. The gravitational force $m_{B}g$ acts downward. Since there is no net acceleration in the vertical direction, we get:

$N_{AB}=m_{B}g(1)$

Case of force on lower block

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Case of force on upper block

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