$A$ block $P$ of mass m is placed on a frictionless horizontal surface. Another block Q of same mass is kept on $P$ and connected to the wall with the help of a spring of spring constant k as shown in the figure. ${\mu _s}$ is the coefficient of friction between$ P$ and $ Q$. The blocks move together performing SHM of amplitude $A$. The maximum value of the friction force between $P$ and $Q$ is
IIT 2004, Difficult
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(b) When two blocks performs simple harmonic motion together then at the extreme position ( at amplitude $=A$)
Restoring force $F = KA = 2ma$ $⇒$ $a = \frac{{KA}}{{2m}}$
There will be no relative motion between $P$ and $Q$ if pseudo force on block $P$ is less than or just equal to limiting friction between $P$ and $Q$.
i.e. $m\;\left( {\frac{{KA}}{{2m}}} \right) = $ Limiting friction
$\therefore $ Maximum friction $ = \frac{{KA}}{2}$
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