HSC Physics Atwood's Machine

Atwood’s machine, the name given to two blocks connected by a light inelastic string passing over a smooth pulley, is used in many mechanics experiments.

1. A single Atwood's machine is suspended from the roof of an elevator. Masses of of m₁ and m₂ are connected by a light inelastic string that passes over the smooth pulley. Find the acceleration of the elevator if m₁ and m₂ are at rest relative to the elevator.
2. A double Atwood’s machine consists of a fixed pulley with a string connected to a mass m₁ passing over it, with another Atwood’s machine connected to the other end of the string passing over the first pulley. On the second Atwood’s machine there are masses of m₂ and m₃ connected by a light inelastic string. We neglect the mass of each pulley.Show that the acceleration of the second pulley is given by a = g(4 m₂ m₃ - m₁(m₂+ m₃))/(4 m₂ m₃ + m₁(m₂ + m₃))