A slab rests on a frictionless floor. A block rests on top of the slab. The coefficient of kinetic friction between the block and slab is . A horizontal force of applied on block . Find the resulting acceleration of the slab.
Step 1: Given Data
Mass of the slab
Mass of the block
The coefficient of kinetic friction between the block and slab
The horizontal force of on direction.
Step 2: Calculate the Common acceleration
The total mass of the system,
Since acceleration is action on direction, the pseudo force will be acting on direction with a force of .
Step 3: Check acceleration of slab and block
Let us consider both the blocks move with the same acceleration.
Pseudo force on the slab
Pseudo force on the block
Again, the normal force
Therefore, limiting force,
Since , this is not the case here.
Step 4: Calculate resultant acceleration of slab
Therefore, the block and the slab do not move with the same acceleration.
If is the acceleration of the slab, then
Hence, the resulting acceleration of the slab is .