A wood block of mass m rests on a larger wood block of mass M that rests on a wo

Question

A wood block of mass m rests on a larger wood block of mass M that rests on a wooden table. The coefficients of static and kinetic friction between all surfaces are µs and µk , respectively.
What is the minimum horizontal force, F , applied to the lower block that will cause it to slide out from under the upper block?
Express your answer in terms of some or all of the variables m, M, µs, µk, and appropriate constants

I got (m+M)gµs but it said the final answer has to be in terms of µk so im confused.

Explanation / Answer

fbd give FOR WHOLE BODY

F-f=(M+m)a

f= FRICTIONAL FORCE DUE TO GROUND

f=K N

f=K (M+m)g SO

a=F-K (M+m)g/(M+m)

AND fbd FOR SMALL ONE GIVES

f1=ma

S N= ma N=mg

SUB a

WE GET

S g=F-K (M+m)g/(M+m)

SO F=(S+k)g(M+m)

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