A uniformly tapering conical wire is made from a material of Young's modulus Y and has a normal, unextended length L . The radii, at the upper and lower ends of this conical wire, have values R a

Question

A uniformly tapering conical wire is made from a material of Young's modulus Y and has a normal, unextended length L . The radii, at the upper and lower ends of this conical wire, have values R and 3 R , respectively. The upper end of the wire is fixed to a rigid support and a mass M is suspended from its lower end. The equilibrium extended length, of this wire, would equal:

TestHub · Accepted Answer

r = 2 R L x + R For a small section F A = Y d l d x ⟹ ∫ 0 L d L = ∫ 0 L M g d x π 2 R L x × R 2 Y ∆ L = M g π Y - 1 2 R x L + R 0 L × L 2 R = M g L 3 π R 2 Y L f = L + Δ L = L [ 1 + m g 3 π R 2 Y ]

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