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A 90 cm length of steel wire with a diameter of 0.5 mm is stretched between the inside walls of an oven the wire is just taut with no tension when the temperature in the oven is 250 °C. What is the the tension force in the wire when the oven cools to a temperature of 150 °C? The distance between the oven walls does not change as the oven cools.

  • physics -

    The length of the wire IF UNSTRETCHED decreases by an amount
    delta L = 90 cm*alpha*100C,
    where alpha is the coefficient of thermal expansion of steel. Look that up.

    But since the wire does not stretch, it is under tension T that can be calculated using Young's modulus of steel, E. Look that one up, too.

    Stress = strain * E
    = (deltaL/L) *E
    = E*alpha*deltaT

    (L cancels out)

    The tension force is the stress times the wire cross-sectional area.

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