Question

A brass wire 1.8 m long at 27 °C is held taut with little tension between two rigid supports. If the wire is cooled to a temperature of –39 °C, what is the tension developed in the wire, if its diameter is 2.0 mm? Co-efficient of linear expansion of brass = 2.0 × 10–5 K–1 Young’* modulus of brass = 0.91 × 1011 Pa.

Answer 1

Initial temperature, T1 = 27°C

Length of the brass wire at T1, l = 1.8 m

Final temperature, T2 = –39°C

Diameter of the wire, d = 2.0 mm = 2 × 10–3 m

Tension developed in the wire = F

Coefficient of linear expansion of brass, α= 2.0 × 10–5 K–1

Young’* modulus of brass, Y = 0.91 × 1011 Pa

Young’* modulus is given by the relation:

(The negative sign indicates that the tension is directed inward.)

Hence, the tension developed in the wire is 3.8 ×102 N.