Q: A block P of mass m is placed on a horizontal frictionless plane. A second block of same mass m is placed on it and is connected to a spring of spring constant k, the two blocks are pulled by a distance A. Block Q oscillates without slipping. What is the maximum value of frictional force between the two blocks ?
(a) kA/2
(b) kA
(c) μs m g
(d) Zero
Ans: (a)
Sol: Angular frequency of the system $\large \omega = \sqrt{\frac{k}{m+m}}$
$\large \omega = \sqrt{\frac{k}{2 m}}$
Maximum acceleration of the system is
$\large a_{max}= \omega^2 A = \frac{k A}{2 m}$
This acceleration to the lower block is provided by friction
$\large f_{max} = m a_{max}$
$\large f_{max} = m (\frac{k A}{2 m}) = \frac{k A}{2}$