A nylon thread is subjected to a 8.5-N tension force. Knowing that E 5 3.3 GPa and that the length of the thread increases by 1.1%, determin

Question

A nylon thread is subjected to a 8.5-N tension force. Knowing that E 5 3.3 GPa and that the length of the thread increases by 1.1%, determine (a) the diameter of the thread, (b) the stress in the thread.

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Sigridomena 5 years 2021-08-24T09:59:46+00:00 1 Answers 934 views 1

Answers ( )

  1. Gerda
    1
    2021-08-24T10:00:53+00:00
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    Answer:

    a)diameter of the thread = 0.546mm

    b) stress in the thread = 36.3MPa

    Explanation:

    Hooke’s law

    E = \frac{Stress}{Strain} \\

    strain = 1.1% = 0.011

    Stress = strain* Young’s modulus

    = 3.3 × 10⁹ × 0.011

    = 36.3 × 10⁶Pa

    stress = 36.3MPa

    stress in the thread = 36.3MPa

    b) Now,

    stress = Force / area

    Force = 8.5N

    Stress = 36.3 × 10⁶

    Area = Force / stress

    =  8.5 /  36.3 × 10⁶

    = 0.234 × 10⁻⁶m²

    Area =

    \frac{\pi }{4} d^2\\Thus,\\d^2 =0.234 \times 10^-^6. \frac{4}{\pi } \\d = \sqrt{0.298 \times 10^-^6 } \\= 5.46 \times 10^-^4m\\=0.546mm

    diameter of the thread = 0.546mm

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