A stell wire of cross-sectional area `0.5mm^2` is held between teo fixed supports. If the wire is just taut at `20^C`, determine the tension when the temperature falls to `0^C`. Coefficient of linear expansion of steel is `1.2 xx 10^(-5) 0^C(-1)` and its Young's modulus is `2.0 xx 10^11 N m^(-2).

Explanation

Given ` A= 0.5mm^2 = (0.5 xx (10^-6) (m^2))`
` T_1= 20^@C, T_2= 0^@C `
` alpha_s= (1.2 xx 10^-5/(^@C))`
` gamma= 2 xx (10^11)N/m^2`
Decrease in length due to compression
`=(L alpha Delta theta) …….(1)`
` gamma = stress/strain = F/A xx (L/(Delta L))`
` rArr (Delta L )=(FL/AY)`
Tension is developed due to (1) and (2).
Equation (1) and (2)
` (L alpha Delta theta) = (FL/AY)`
` rArr F= (alpha Delta) (theta AY)`
`= (1.2 xx (10^-5) xx (20-0)`
` xx 0.5 xx (10^-6) xx 2 xx (10^11) )`
` =1.2 xx 20 = 24N`