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A 1.0 x 10-3-kg house spider is hanging vertically by a thread that has a Young's modulus of 4.2 x 109 N/m2 and a radius of 18 x 10-6 m. Suppose that a 61-kg person is hanging vertically on an aluminum (Young's modulus 6.9 x 1010 N/m2) wire. What is the radius of the wire that would exhibit the same strain as the spider's thread, when the thread is stressed by the full weight of the spider?

  • physics -

    σ =Eε
    σ=Weight/A
    σ₁ =mg/πr²= E₁ε
    σ₂=Mg/πR² =E₂ε
    (mg/πr²):(Mg/πR²) = (E₁ε):( E₂ε)
    R =sqrt[ r²•M•E₁/m•E₂]=….

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