A block P of mass m is placed on a frictionless other 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. μ 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:

Question

A block P of mass m is placed on a frictionless other 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. μ 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) k A (B) (k A/2) (C) zero (D) μs m g

Tardigrade Admin · Accepted Answer

f max =m ω2 A With ω2=(k/m+m)=(k/2 m) Hence, f max =m((k/2 m)) A=(k A/2)

k A

$\frac{k A}{2}$

zero

$μ_{s} m g$

$f_{m a x} = m ω^{2} A$
With $ω^{2} = \frac{k}{m + m} = \frac{k}{2 m}$
Hence, $f_{m a x} = m (\frac{k}{2 m}) A = \frac{k A}{2}$

k A

2kA​

zero

μs​mg

fmax​=mω2A With ω2=m+mk​=2mk​ Hence, fmax​=m(2mk​)A=2kA​

$\frac{k A}{2}$

$μ_{s} m g$

$f_{m a x} = m ω^{2} A$
With $ω^{2} = \frac{k}{m + m} = \frac{k}{2 m}$
Hence, $f_{m a x} = m (\frac{k}{2 m}) A = \frac{k A}{2}$