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\includegraphics[max width=\textwidth, alt={}, center]{db77a63a-6ff8-4fe5-bdd0-15afb7eb4866-4_419_419_274_735} Particles \(A\) and \(B\) are attached to the ends of a light inextensible string. The string passes over a smooth fixed pulley. The particles are released from rest, with the string taut, and \(A\) and \(B\) at the same height above a horizontal floor (see diagram). In the subsequent motion, \(A\) descends with acceleration \(1.4 \mathrm {~m} \mathrm {~s} ^ { - 2 }\) and strikes the floor 0.8 s after being released. It is given that \(B\) never reaches the pulley.

1. Calculate the distance \(A\) moves before it reaches the floor and the speed of \(A\) immediately before it strikes the floor.
2. Show that \(B\) rises a further 0.064 m after \(A\) strikes the floor, and calculate the total length of time during which \(B\) is rising.
3. Sketch the ( \(t , v\) ) graph for the motion of \(B\) from the instant it is released from rest until it reaches a position of instantaneous rest.
4. Before \(A\) strikes the floor the tension in the string is 5.88 N . Calculate the mass of \(A\) and the mass of \(B\).
5. The pulley has mass 0.5 kg , and is held in a fixed position by a light vertical chain. Calculate the tension in the chain
   (a) immediately before \(A\) strikes the floor,
   (b) immediately after \(A\) strikes the floor. \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 (OCR) 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. OCR 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. }