Two particles over single pulley

A question is this type if and only if it involves two particles connected by a light inextensible string passing over a single smooth pulley, where both particles hang vertically or one is on a horizontal surface, requiring you to find acceleration, tension, or subsequent motion using Newton's second law for each particle.

2 questions · Moderate -0.8

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CAIE M1 2009 June Q1
3 marks Easy -1.2
\includegraphics{figure_1} A block \(B\) of mass 5 kg is attached to one end of a light inextensible string. A particle \(P\) of mass 4 kg is attached to other end of the string. The string passes over a smooth pulley. The system is in equilibrium with the string taut and its straight parts vertical. \(B\) is at rest on the ground (see diagram). State the tension in the string and find the force exerted on \(B\) by the ground. [3]
OCR M1 2007 January Q3
8 marks Moderate -0.3
\includegraphics{figure_3} A block \(B\) of mass 0.4 kg and a particle \(P\) of mass 0.3 kg are connected by a light inextensible string. The string passes over a smooth pulley at the edge of a rough horizontal table. \(B\) is in contact with the table and the part of the string between \(B\) and the pulley is horizontal. \(P\) hangs freely below the pulley (see diagram).
  1. The system is in limiting equilibrium with the string taut and \(P\) on the point of moving downwards. Find the coefficient of friction between \(B\) and the table. [5]
  2. A horizontal force of magnitude \(X\) N, acting directly away from the pulley, is now applied to \(B\). The system is again in limiting equilibrium with the string taut, and with \(P\) now on the point of moving upwards. Find the value of \(X\). [3]