Question

A force of 75 N is applied to two boxes stacked on top of each other. The coefficient of kinetic friction between the bottom box and the floor is 0.3. If the box on top is to accelerate at the same rate as the box on the bottom, what must the minimum coefficient of static friction between the two boxes be?

Answer 1

I guess you push the bottom one? mb is bottom mass, mt the top
75 - .3 (mb+mt) g = (mb + mt)a
a = [75 -.3(mb+mt)g]/(mb+mt)
max friction force on mt = mu mt g = mt a
mu g = a
so
mu = [ 75/g -.3(mb+mt)] /(mb+mt)