# 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 $m_Bg$ (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 $m_Bg$ acts downward. Since there is no net acceleration in the vertical direction, we get:

$\! N_{AB} = m_Bg \qquad (1)$

## Case of force on lower block

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## Case of force on upper block

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