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A steel wire, 2mm in diameter, is just s...

A steel wire, 2mm in diameter, is just stretched between two fixed points at a temperature of `30^(0)C`. Determine its tension when the temperature falls to `20^(0)C`. (Coefficient of linear expansion of steel `=0.000011//""^(0)C`, Young.s modulus for steel `=2.0xx10^(11)Nm^(-2)`)

Text Solution

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Theremal stress `=(F)/(A) =Y alpha Delta t`
Tension in the wire `=Y alpha A(t_(2)-t_(1))`.
Here, `Y=2.0xx10^(11)Nm^(-2) , alpha =11xx10^(-6) //""^(0)C`,
`t_(2) =30^(0)C, t_(1) =20^(0)C, `radius = 1mm `=1xx10^(-3)m`,
`A=pi r^(2)=pi(1xx10^(-3))^(2) = pi xx 10^(-6) m^(2) `
The tension in the wire
`=2.0xx10^(11) xx11 xx 10^(-6) xx pi xx 10^(-6) xx (30-20)=69.14 N`
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