A light pulley is suspended from a ceiling by a vertical elastic wire of length L, cross-sectional area A and Young's modulus Y. A light inextensible string passes over the pulley and carries masses m and 2m at its two ends. The system is released and moves freely. Neglect the mass of the pulley. What is the extension of the supporting elastic wire during the motion?
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Question

A light pulley is suspended from a ceiling by a vertical elastic wire of length L, cross-sectional area A and Young's modulus Y. A light inextensible string passes over the pulley and carries masses m and 2m at its two ends. The system is released and moves freely. Neglect the mass of the pulley. What is the extension of the supporting elastic wire during the motion?

Options

G1 Physics · Accepted Answer

For the Atwood machine, m₁ = m, m₂ = 2m. The string tension is T = [2m₁m₂g] / [m₁+m₂]. Therefore, T = [2(m)(2m)g] / [3m] = 4mg/3. The pulley is pulled downward by two string tensions. Hence the force stretching the supporting elastic wire is F = 2T = 8mg/3. Extension of the elastic wire is ΔL = [FL] / [AY]. Therefore, ΔL = [(8mg/3)L] / [AY] = [8mgL] / [3AY]. Correct option: C.