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

A steel wire, 2mm in diameter, is just stretched between two fixed poi

1.	A steel wire, 2mm in diameter, is just stretched between two fixed points at a temperature of 30^@C . Determine its tension when the temperature falls to 20^@C . (Coefficient of linear expansion of steel = 0.000011//""^@C, Young's modulus for steel = 2.0xx10^11Nm^(-2))
Answer» Solution :THERMAL stress `= F/A = Y alpha Delta t ` Tension in the WIRE ` = Y alpha A (t_2 - t_1)` Here `Y = 2.0 xx 10^11 NM^(-2), alpha = 11 xx 10^(-6) //""^@C, t_2 = 30^@C, t_1 = 20^@C, ` radius = 1mm ` = 1 xx 10^(-3) m, ` `A = pi r^2 = pi (1 xx 10^(-3))^2= pi xx 10^(-6) m^2` The tension in the wire ` = 2.0 xx 10^11 xx 11 xx 10^(-6) xx pi xx 10^(-6) xx (30 - 20)= 69.14N`