A $$40$$ kg slab rests on a frictionless floor as shown in the figure. A $$10$$ kg block rests on the top of the slab. The static coefficient of friction between the block and slab is $$0.60$$ while the kinetic coefficient of friction is $$0.40$$. The $$10$$ kg block is acted upon by a horizontal force $$100$$ N. If g $$=$$ $$10$$ $$m/s2$$, the resulting acceleration of the slab will be

Question

A $$40$$ kg slab rests on a frictionless floor as shown in  the figure. A $$10$$ kg block rests on the top of the slab. The static coefficient of friction between the block and slab is $$0.60$$ while the kinetic coefficient of friction is $$0.40$$. The $$10$$ kg block is acted upon by a horizontal force $$100$$ N. If g $$=$$ $$10$$ $$m/s2$$, the resulting acceleration of the slab will be

Infinity Learn · Accepted Answer

Limiting friction between block and $$slab=$$μ$$smAg=0.6$$×$$10$$×$$10=60NBut$$ applied force on block A is $$100N$$. So, the block will slipover a slab.Now kinetic friction works between block and $$slabFk=$$μ$$kmAg=0.4$$×$$10$$×$$10=40NThis$$ kinetic friction helps to move the slab∴  Acceleration of slab $$=40mB=4040=1m/s2$$

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