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\includegraphics[max width=\textwidth, alt={}, center]{dafc271d-a77b-4401-9170-e13e484d6e5f-4_246_665_253_739} Two rectangular boxes \(A\) and \(B\) are of identical size. The boxes are at rest on a rough horizontal floor with \(A\) on top of \(B\). Box \(A\) has mass 200 kg and box \(B\) has mass 250 kg . A horizontal force of magnitude \(P\) N is applied to \(B\) (see diagram). The boxes remain at rest if \(P \leqslant 3150\) and start to move if \(P > 3150\).

1. Find the coefficient of friction between \(B\) and the floor. The coefficient of friction between the two boxes is 0.2 . Given that \(P > 3150\) and that no sliding takes place between the boxes,
2. show that the acceleration of the boxes is not greater than \(2 \mathrm {~m} \mathrm {~s} ^ { - 2 }\),
3. find the maximum possible value of \(P\). \footnotetext{Permission to reproduce items where third-party owned material protected by copyright is included has been sought and cleared where possible. Every reasonable effort has been made by the publisher (UCLES) to trace copyright holders, but if any items requiring clearance have unwittingly been included, the publisher will be pleased to make amends at the earliest possible opportunity. University of Cambridge International Examinations is part of the Cambridge Assessment Group. Cambridge Assessment is the brand name of University of Cambridge Local Examinations Syndicate (UCLES), which is itself a department of the University of Cambridge. }