Q.
A block $P$ of mass $m$ is placed on a 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) Angular frequency of the system,
$\omega = \sqrt{\frac{k}{m + m}} = \sqrt{\frac{k}{2m}}$
Maximum acceleration of the system will be, $\ \omega^{2}A\ or\ \frac{kA}{2m}$ . This acceleration to the lower block is provided by friction.
Hence, $f_{\max} = {ma}_{\max}$
$= m\omega^{2}\ A = m\left( \frac{k\ A}{2m} \right) = \frac{k\ A}{2}$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.