A light pulley is suspended by an elastic wire of length 2 m, cross-sectional area 0.8 mm² and Young's modulus 2 × 10¹¹ Pa. A light string over the pulley carries masses 3 kg and 6 kg. Take g = 10 m/s². If the extension of the supporting elastic wire during the motion is N mm, find N.
Physics · Properties of solid and fluid · properties of solid stress ,strain and modulus of elasticity
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Question

A light pulley is suspended by an elastic wire of length 2 m, cross-sectional area 0.8 mm² and Young's modulus 2 × 10¹¹ Pa. A light string over the pulley carries masses 3 kg and 6 kg. Take g = 10 m/s². If the extension of the supporting elastic wire during the motion is N mm, find N.

Physics · Properties of solid and fluid · properties of solid stress ,strain and modulus of elasticity

G1 Physics · Accepted Answer

For the Atwood machine, T = [2m₁m₂g] / [m₁+m₂]. Therefore, T = [2×3×6×10] / 9 = 40 N. The supporting wire carries the downward pull of two string tensions: F = 2T = 80 N. Now, L = 2 m, A = 0.8 mm² = 0.8×10⁻⁶ m², Y = 2×10¹¹ Pa. Extension: ΔL = [FL] / [AY] = [80×2] / [(0.8×10⁻⁶)(2×10¹¹)]. Thus, ΔL = 1×10⁻³ m = 1 mm. Hence, N = 1.