Question

Three blocks $A,B$ and $C$ of equal mass $m$ are placed one over the other on a frictionless surface (table) as shown in the figure. Co-efficient of friction between any two blocks $A,B$ and $C$ is $\mu$. The maximum value of force $F$ so that the block $A,B$ and $C$ move without slipping over each other it (pulleys and strings are light).

Answer 1

When a force is applied to block A, then A will move with an acceleration.

For the motion of B and C, we need to take A as the reference frame.

A is a non-inertial frame and hence friction forces will act on B and C, in the backward direction.

The magnitude of this force is $mass\times acceleration.$

The force of friction acting on C is equal to the reaction force to gravity applied by B on C multiplied by $\mu$ $Friction=\mu mg$ here g is the acceleration due to gravity.

The maximum driving force should be $\le$ frictional force

If we do not want C to slip then the maximum force should be $\mu mg$

If we are okay with C to slip, but don't want B to slip then the maximum force should be $2\mu mg$ because of the mass kept above B.