CAIE M1 2012 November — Question 7

Exam BoardCAIE
ModuleM1 (Mechanics 1)
Year2012
SessionNovember
TopicPulley systems

7
\includegraphics[max width=\textwidth, alt={}, center]{631ddcd9-17c0-4a15-8671-40788c3a84d3-3_565_828_1402_660} Particles \(A\) and \(B\) have masses 0.32 kg and 0.48 kg respectively. The particles are attached to the ends of a light inextensible string which passes over a small smooth pulley fixed at the edge of a smooth horizontal table. Particle \(B\) is held at rest on the table at a distance of 1.4 m from the pulley. \(A\) hangs vertically below the pulley at a height of 0.98 m above the floor (see diagram). \(A , B\), the string and the pulley are all in the same vertical plane. \(B\) is released and \(A\) moves downwards.
  1. Find the acceleration of \(A\) and the tension in the string.
    \(A\) hits the floor and \(B\) continues to move towards the pulley. Find the time taken, from the instant that \(B\) is released, for
  2. \(A\) to reach the floor,
  3. \(B\) to reach the pulley.