# 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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