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. Make separate sketches showing the forces acting on.

(a) the uppermost box (b) the middle box

Show that P>2μ W, where μ is the coefficient of friction between any two boxes.

Show also that, if P > 4uW,sliding takes place between the upper and middle boxes,and that if P ≤ 4μW, sliding between these boxes does not take place.

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| |””””””””|

| |””””””””|  P

|””””””””|__________