Condition of Sliding of a Block over another Block

The concept of friction is very important in variety of of problems involving  Newton’s Laws of Motion. Whenever a block is placed over the rough surface of another block then it is also important to analyze the condition on external effects under which the upper block starts sliding. Several problems are framed on such condition.

When a body is subjected to external forces
and if it is at rest relative to the surface on which it is placed then the
friction acting at the contact would be static friction. If external force is
increased the magnitude of static friction between bodies will increase and as
it approaches limiting value, bodies will start sliding. This concept can be
easily applied when the lower block is at rest but when both blocks are in
motion, we need to be very careful while solving the equations of Laws of
Motion as the analysis is now done relative to lower block. See the below video
on how to apply the concept in finding the condition of sliding when a block is
moving over another block –

To apply the logic in various situations,
see the examples explained in below videos –

Misconception: While solving problem of
finding condition of sliding of a block over another the most common mistake
students do by simply calculating static friction and equate it with limiting
friction in the reference frame of lower block and ignore the motion of lower
block. Due to acceleration of lower block the static friction on upper block
changes. If you analyze the problem in the reference frame of lower block which
is accelerating always consider the Pseudo Force on the upper block relative to
lower block.

There can be variety of problems which can
be framed on this concept of sliding of a body over another body. See the below
advance illustrations to develop a thorough understanding on application of
this concept.

Ashish Arora is the Head of Academics at the Allen Career Institute, Jaipur, Rajasthan. He is also the Founder and Chief Mentor at the His passion for physics has inspired many IIT aspirants.