FYKOS Year 26 Series 6 Problem 2 — stupid wire · FYKOS 26 #26.6.2

Physics · mechanics · electromagnetism

Problem

What is the minimal length of a wire so that if you hang it from a ceiling, it will break due to its own mass? The wire's density is ρ=7900  kg⋅m−3ρ=7900\;\mathrm{kg}\cdot \mathrm{m}^{−3}, it has a diameter D=1  mmD=1\;\mathrm{mm}, and it breaks at σmax=400MPaσ_{max}=400MPa. Assume that everything takes place in a homogeneous gravitational field g=9.81  m⋅s−2g=9.81\;\mathrm{m}\cdot \mathrm{s}^{−2}. Bonus: If the wire's length is maximal possible so that it does not break, how much will it stretch (in percents)? Young's modulus of the wire's material is E=200GPaE=200GPa.

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