Elastic string two-particle system

Two particles are connected by or attached to elastic strings (possibly through a hole or ring), requiring energy methods to find speeds, extensions, or distances when one or both particles move under gravity and possibly friction.

1 questions · Challenging +1.2

3.03k Connected particles: pulleys and equilibrium6.02i Conservation of energy: mechanical energy principle
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AQA M2 2013 June Q9
14 marks Challenging +1.2
9 Two particles, \(A\) and \(B\), are connected by a light elastic string that passes through a hole at a point \(O\) in a rough horizontal table. The edges of the hole are smooth. Particle \(A\) has a mass of 8 kg and particle \(B\) has a mass of 3 kg . The elastic string has natural length 3 metres and modulus of elasticity 60 newtons.
Initially, particle \(A\) is held 3.5 metres from the point \(O\) on the surface of the table and particle \(B\) is held at a point 2 metres vertically below \(O\). The coefficient of friction between the table and particle \(A\) is 0.4 .
The two particles are released from rest.
    1. Show that initially particle \(A\) moves towards the hole in the table.
    2. Show that initially particle \(B\) also moves towards the hole in the table.
  2. Calculate the initial elastic potential energy in the string.
  3. Particle \(A\) comes permanently to rest when it has moved 0.46 metres, at which time particle \(B\) is still moving upwards. Calculate the distance that particle \(B\) has moved when it is at rest for the first time.