Atwood machine, vertical strings

A question is this type if and only if it involves two particles connected by a string over a smooth pulley with both particles hanging vertically, requiring finding acceleration and tension in the string.

2 questions · Moderate -0.2

3.02d Constant acceleration: SUVAT formulae3.03k Connected particles: pulleys and equilibrium
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CAIE M1 2007 June Q4
7 marks Moderate -0.8
4 \includegraphics[max width=\textwidth, alt={}, center]{f7a22c07-44e3-4891-be60-cbab772f45df-3_702_709_269_719} Particles \(P\) and \(Q\), of masses 0.6 kg and 0.2 kg respectively, are attached to the ends of a light inextensible string which passes over a smooth fixed peg. The particles are held at rest with the string taut. Both particles are at a height of 0.9 m above the ground (see diagram). The system is released and each of the particles moves vertically. Find
  1. the acceleration of \(P\) and the tension in the string before \(P\) reaches the ground,
  2. the time taken for \(P\) to reach the ground.
Edexcel M1 Q5
12 marks Standard +0.3
Two metal weights \(A\) and \(B\), of masses 2.4 kg and 1.8 kg respectively, are attached to the ends of a light inextensible string which passes over a smooth fixed pulley so that the string hangs vertically on each side. The system is released from rest with the string taut.
  1. Calculate the acceleration of each weight and the tension in the string. [6 marks]
\(A\) is now replaced by a different weight of mass \(m\) kg, where \(m < 1.8\), and the system is again released from rest. The magnitude of the acceleration has half of its previous value.
  1. Calculate the value of \(m\). [6 marks]