Axels of the wheels are frictionless. Interface between the two blocks is rough

Question

Axels of the wheels are frictionless. Interface between the two blocks is rough with coefficients of static and kinetic friction mu-s and mu-k. Derive an exression for the minimum magnitude required for a horizontal force applied to M to prevent m from sliding down the front face of M.

Friction problem: derive an expression for the minimum applied force needed to keep m from sliding down. I know that the force of static friction is what will hold the block up, which comes from the F due to the resultant normal force but I dont know where to go from there....

Axels of the wheels are frictionless. Interface between two blocks is rough with coefficients of static and kinetic friction coefficients mus & muk, respectively. Derive an expression for the minimum magnitude required for a horizontal force applied to M to prevent m from sliding down the front face of M.

Explanation / Answer

downwards force on m = mg

upward friction force = mus*ma

a = F/(M+m)

so for balance, mg = mus*m(F/(m+M))

F = (m+M)g/mus

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