A lift of mass 1600 kg is supported by a thick iron wire of radius 4 mm. The maximum tensile stress that the wire can withstand is 4×10⁸ N·m⁻². Taking g = 10 m·s⁻² and π = 3.14, what is the maximum upward acceleration that the lift can have without exceeding the stress limit?
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Question

A lift of mass 1600 kg is supported by a thick iron wire of radius 4 mm. The maximum tensile stress that the wire can withstand is 4×10⁸ N·m⁻². Taking g = 10 m·s⁻² and π = 3.14, what is the maximum upward acceleration that the lift can have without exceeding the stress limit?

Options

G1 Physics · Accepted Answer

Maximum allowed tension in the wire is T(max) = stress × cross-sectional area = σπr². Here, σ = 4×10⁸ N·m⁻², r = 4 mm = 4×10⁻³ m. Thus, T(max) = 4×10⁸ × 3.14 × (4×10⁻³)² = 20096 N. For maximum upward acceleration a, T(max) - mg = ma. Therefore, 20096 - 1600×10 = 1600a. So, 4096 = 1600a, a = 2.56 m·s⁻². Correct option: A.