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In an Atwood-type system with ideal massless strings, four blocks A, B, C, D are connected such that m_A > m_B > m_C > m_D. The system is initially in static equilibrium. Thread DE is suddenly cut. If the magnitudes of accelerations of blocks A, B, C, D just after cutting thread DE are a_A, a_B, a_C, a_D respectively, which of the following is correct?
- a_A > a_B > a_C > a_D
- a_A = a_B < a_C = a_D
- a_A < a_B < a_C < a_D
- a_A = a_D < a_C = a_B
Correct answer: a_A = a_B < a_C = a_D
Solution
In a standard nested Atwood machine arrangement: A and B are connected over one pulley, C and D are connected over another sub-pulley which is hung by thread DE. When DE is cut, the sub-pulley (with C and D) experiences free fall or the net force due to removed support. A and B remain connected over their pulley and will have equal and opposite accelerations (or the system reconfigures). The net effect is a_A = a_B (constrained by string over their pulley) and a_C = a_D (constrained by string over their pulley), and since the imbalance for C, D is greater relative to their smaller masses, a_C = a_D > a_A = a_B. Hence a_A = a_B < a_C = a_D.
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