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Two identical boxes, each of mass 400 kg , are at rest, with one on top of the other, on horizontal ground. A horizontal force of magnitude \(P\) newtons is applied to the lower box (see diagram). The coefficient of friction between the lower box and the ground is 0.75 and the coefficient of friction between the two boxes is 0.4 .
- Show that the boxes will remain at rest if \(P \leqslant 6000\).
The boxes start to move with acceleration \(a \mathrm {~m} \mathrm {~s} ^ { - 2 }\).
- Given that no sliding takes place between the boxes, show that \(a \leqslant 4\) and deduce the maximum possible value of \(P\).