A block of mass m is placed on another blocks of mass M which itself is lying on a horizontal surface. The coefficient of friction between the two blocks is
µ₁ and that between the block of mass M and horizontal surface is pr. What maximum horizontal force can be applied to the lower block so that the two blocks move without separation ?

Question

A block of mass m is placed on another blocks of mass M which itself is lying on a horizontal surface. The coefficient of friction between the two blocks is

µ₁ and that between the block of mass M and horizontal surface is pr. What maximum horizontal force can be applied to the lower block so that the two blocks move without separation ?

Infinity Learn · Accepted Answer

Here the force applied should be such that the force on block of mass m should not exceed from the force of friction $$($$µ$$1$$ m $$g)$$. Let the system move with accelerationa. ThenF−μ$$2(M+m)g=(M+m)a$$   …(1)For$$ block of mass m,$$F1=ma=$$μ$$1mg$$  or  $$a=$$μ$$1g$$   …$$(2)From$$ eqs. $$(1) and (2), we $$getF=$$μ$$2(M+m)g+(M+m)$$μ$$1g$$ $$=(M+m)g($$μ$$1+$$μ$$2)$$

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