Exam-Style Problem

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June 2014 p43 q7
3919

A smooth inclined plane of length 160 cm is fixed with one end at a height of 40 cm above the other end, which is on horizontal ground. Particles P and Q, of masses 0.76 kg and 0.49 kg respectively, are attached to the ends of a light inextensible string which passes over a small smooth pulley fixed at the top of the plane. Particle P is held at rest on the same line of greatest slope as the pulley and Q hangs vertically below the pulley at a height of 30 cm above the ground (see diagram). P is released from rest. It starts to move up the plane and does not reach the pulley. Find

  1. the acceleration of the particles and the tension in the string before Q reaches the ground,
  2. the speed with which Q reaches the ground,
  3. the total distance travelled by P before it comes to instantaneous rest.
problem image 3919
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