A $$40$$ kg slab rests on a frictionless floor. A $$10$$ kg block rests on the top of the slab as shown in figure.The static coefficient of friction between the block and the slab is $$0.60$$ while the kinetic coefficient $$is0.40$$. The $$10$$ kg block is acted upon by a horizontal force of $$100$$ N. If g $$=$$ $$9.8$$ $$ms-2$$, the resultingacceleration of the slab will be

Question

A $$40$$ kg slab rests on a frictionless floor. A $$10$$ kg block rests on the top of the slab as shown in figure.The static coefficient of friction between the block and the slab is $$0.60$$ while the kinetic coefficient $$is0.40$$. The $$10$$ kg block is acted upon by a horizontal force of $$100$$ N. If g $$=$$ $$9.8$$ $$ms-2$$, the resultingacceleration of the slab will be

Infinity Learn · Accepted Answer

Force of limiting friction for block $$=$$μ$$smg=0.60$$×$$10$$×$$9.8=58.8$$ NIf the applied force is greater than $$58.8$$ N, then the block will move over the slab.Kinetic friction acting on the block towards $$right=$$μ$$kmg=0.40$$×$$10$$×$$9.8=39.2$$ NThis is also equal to the force of friction acting on slab towards left. This is the only force acting on slab.So, acceleration of the sIab,  $$a=Fm=39.240=0.98$$ $$ms-2$$

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