An Atwood machine has two blocks of masses 2.0 kg and 3.0 kg . Determine the work done by gravity during the fourth second after releasing the system from rest.

Step-by-step solution

The acceleration of the blocks in the Atwood machine is given by: a = m₂ - m₁ m₁ + m₂ g Substituting the given masses m₁ = 2.0 kg and m₂ = 3.0 kg : a = 3.0 - 2.0 3.0 + 2.0 g = g 5 The displacement of the blocks during the 4^ th second is: s₄ = u + a 2 (2n - 1) s₄ = 0 + g/5 2 (2(4) - 1) = 7g 10 The net work done by gravity on the system is the sum of the work done on each block. Since the heavier block moves downwards and the lighter block moves upwards: W = m₂ g s₄ - m₁ g s₄ = (m₂ - m₁) g s₄ W = (3.0 - 2.0) g ( 7g