Question # A block ( P ) of mass ( m ) is placed on a horizontal frictionless plane. A second block of same mass ( mathrm{m} ) is placed on it and is connected to a spring of spring constant ( mathrm{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 block ( P ) of mass ( m ) is placed on a horizontal frictionless plane. A second block of same mass ( mathrm{m} ) is placed on it and is connected to a spring of spring constant ( mathrm{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) ( mathrm{kA} / 2 )

(b) kA

(c) ( mu_{mathrm{s}} mathrm{mg} )

(d) zero

Solution

Frictional force ( cdot F=m f(f rightarrow operatorname{ach} o f(operatorname{tg} S H M) )

( therefore quad F=m omega^{2} A )

( therefore omega=sqrt{frac{K}{m+m}}=sqrt{frac{K}{2 m}} )

[

F=m times frac{K}{2 m} times A=frac{1}{2} K A

]

Ans (a) frac{KA}{2}