Why Does a Force Greater Than 4µW Cause Sliding Between Stacked Boxes?

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furor celtica
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Homework Statement



three identical boxes, each of weight W, are to be stacked one on top of another against a vertical wall. The lowermost box is in contact with the wall, and the other two boxes are positioned as shown in the diagram. The middle box is pushed into position by the application of a horizontal force of magnitude P.
Show that if P>4µW (where µ is coefficient of friction between any two boxes), sliding takes place between the upper and middle boxes (i.e. friction is not strong enough for the upper box to follow the middle box in its movement).

Homework Equations





The Attempt at a Solution



I don't understand why it is 4µW, shouldn't it be 3µW or 2µW? I'm not sure.
Firstly the middle box must be able to move, i.e. P>(friction from lowermost box), P>(normal reaction) x µ, P> 2µW. However, the frictional force between the upper and middle boxes is only Wµ, os shouldn't the 2µW force be enough? Or 3µW if both frictional forces are added, I'm not even sure, but any way i can't get to 4µW.
 

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The question is if the middle or upper boxes move together or not if a force P>4µW is applied. Just draw the free body diagram and solve for the accelerations of both blocks. Take care to the normal forces acting on the middle box.

ehild