A brass rod is 185 cm long and 1.60 cm in diameter. What force must be applied to each end of the rod to prevent it from contract- ing when

Question

A brass rod is 185 cm long and 1.60 cm in diameter. What force must be applied to each end of the rod to prevent it from contract- ing when it is cooled from 120.0°C to 10.0°C?

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Sigridomena 4 years 2021-08-09T16:38:10+00:00 1 Answers 478 views 1

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    2021-08-09T16:39:59+00:00

    Answer:

    42000N

    Explanation:

    First you calculate how much it would contract, and secondly you then calculate the force to stretch it by that amount.

    1) linear thermal expansion coef brass 19e-6 /K

    ∆L = αL∆T = (19e-6)(1.85)(110) = 0.00387 meter or 3.87 mm

    Second part involves linear elasticity.

    for brass, young’s modulus is 15e6 psi or 100 GPa

    cross-sectional area of rod is π(0.008)² = 0.0002 m²

    F = EA∆L/L

    F = (100e9)(0.0002)(0.00387) / (1.85)

    F = 42000 or 42 kN

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