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A block A of mass m is placed on a frict...

A block A of mass m is placed on a frictionless horizontal surface. Another block B of the same mass is kept on A and connected to the wall with the helpf of a spring of force constant K as shown in the figure. The coefficient of friction between the blocks A and B is `mu`. The blocks move together execting simple harmonic motion of amplitude 'a'. What is the maximum value of the fricitional force between A and B ?

A

kA

B

`(kA)/(2)`

C

Zero

D

`mu_(s)mg`

Text Solution

Verified by Experts

The correct Answer is:
B
When two blocks performs simple harmonic motion together then at the extreme position (at amplitude =A)
Restoring force F=KA=2ma
`impliesa=(KA)/(2m)`
There will be no relative motion between P and Q if pseudo force on block P is less than or just equal to limiting friction between P and Q.
i.e. `m((KA)/(2m))=` Limiting friction
`:.` Maximum friction `=(KA)/(2)`
Aliter : Let `omega` bet the angular frequency of the system
The maximum acceleration of the system
`a=omega^(2)A=((k)/(2m))A` [as `omega=sqrt((k)/(m+m))=sqrt((k)/(2m))`]
The force of friction
`f=ma=m((kA)/(2m))=(kA)/(2)`
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