ln the arrangement shown in figure, mA $$=$$ mB $$=$$ $$2$$ kg. String is massless and pulley is frictionless. Block B is resting on a smooth horizontal surface, while friction coefficient between blocks A and B is μ $$=$$ $$0.5$$ The maximum horizontal force F that can be applied so that block.A does not slip over the block B is

Question

ln the arrangement shown in figure, mA $$=$$ mB $$=$$ $$2$$ kg. String is massless and pulley is frictionless. Block B is resting on a smooth horizontal surface, while friction coefficient between blocks A and B is μ $$=$$ $$0.5$$ The maximum horizontal force F that can be applied so that block.A does not slip over the block B is

Infinity Learn · Accepted Answer

Maximum value of friction on A, fmax $$=$$ μmg $$=$$ $$0.5$$ × $$2$$ × $$10$$ $$=$$ $$10$$ NHence, the block B is subjected to this frictional force in the forward direction. Since the block A does not slip on B, both of them move with a common acceleration. The acceleration of B is the same as the acceleration of A. To determine acceleration of 'a', we find that mBamax $$=$$ fmaxamax $$=$$ $$102$$ $$=$$ $$5$$ $$m/s2Fmax$$ $$=$$ $$(mA+mB)amax$$ $$=$$ $$4$$ ×$$5$$ $$=$$ $$20$$ N

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