Q. 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
A) $kA$
B) $\frac{kA}{2}$
C) Zero
D) $\mu_{s}mg$
Explanation
(b) When two blocks performs simple harmonic motion together then at the extreme position (at amplitude $= A$)
Restoring force $F = KA + 2ma$
$\Rightarrow a = \frac{KA}{2m}$
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 $= \frac{KA}{2}$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.