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, 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 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, 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

Infinity Learn · Accepted Answer

Let Q is displaced through a small distance x. Now force exerted by spring on Q is k x If the initial acceleration of the system be A, then $$kx$$−$$f=mA$$      ... (1)  for the upper blockfurther   $$f=mA$$      ... (2)  for the lower block∴$$kx$$−$$mA=mA$$ or $$kx$$$$=2mAorA=($$$$kx$$$$/2m)From$$ eq. (2), f $$=(m$$ k x $$/2$$ $$m)$$ $$=$$ (k$$ x $$/2).

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