# Problem on friction

## Homework Statement

##A## and ##B## are two objects with mass ##m_1## and ##m_2## respectively. The floor is frictionless. The kinetic friction coefficient between ##A## and ##B## is ##\mu## ; A constant force ##F## is applied on ##A##. Assume, ##F## is greater than the limiting static frictional force. So, ##B## will apply a frictional force, ##f = \mu m_2 g## on ##A##. According to Newton's third law, ##A## will also apply the same force ##f## on ##B## in the opposite direction. So, ##A## and ##B## both will be accelarated (Suppose, ##f < F##). Let, the accelaration of ##A## and ##B## be ##a_1## and ##a_2## respectively.
If, ##a_1 > a_2##, at some moment the situation will be like this:

And, if ##a_2 > a_1## , it will be like this:

What will happen afterwards?

## Homework Equations

##\mu = \frac {f}{R} ##

## The Attempt at a Solution

In the first case, ##B## will rotate and fall down. But what will be the axis of rotation and angular velocity?
In the second case, after a moment, the center of gravity of ##B## will be ahead of the edge of ##A##. So, the normal reaction is ##0## on the surface between ##A## and ##B##, so the frictional force is also ##0##. Hence, B will not be accelerated forward anymore, but ##A## will. And so, ##A## will catch the center of gravity of ##B## again in a moment. So, I think ##B## will not fall in this situation and will remain as it is in the third picture.

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