In the arrangement depicted in the figure, let m₁ = 1 kg , m₂ = 2 kg and m₃ = 3 kg . Determine the accelerations of the masses m₁ , m₂ , and m₃ . When the system is released from rest, the string segment from the upper pulley to m₁ measures 20 cm . How much time will elapse before m₁ strikes the upper pulley?

Step-by-step solution

Let T₁ be the tension in the string connected to m₁ and T₂ be the tension in the string connecting m₂ and m₃ . Since the lower pulley is massless, T₁ = 2T₂ . Let a₁ be the upward acceleration of m₁ . The lower pulley will have a downward acceleration of a₁ . Let a' be the downward acceleration of m₃ relative to the lower pulley. Then m₂ has an upward acceleration a' relative to the lower pulley. The absolute downward accelerations of m₂ and m₃ are a₂ = a₁ - a' and a₃ = a₁ + a' . Writing the equations of motion for