The area of cross-section of railway track is 0.01 m^(2). The temperature variation is 10^(@)C. Coefficient of linear expansion of steel =10^(-5)//""^(@)C. (Young's modulus of steel = 10^(11) Nm^(-2)). Calculate the energy stored per meter in the track.

The area of cross-section of railway track is 0.01 m^(2). The temperat

1.	The area of cross-section of railway track is 0.01 m^(2). The temperature variation is 10^(@)C. Coefficient of linear expansion of steel =10^(-5)//""^(@)C. (Young's modulus of steel = 10^(11) Nm^(-2)). Calculate the energy stored per meter in the track.
Answer» Solution :LET `alpha`= Coefficient of LINEAR expansion. `:.` Elastic energy `=(1)/(2) xx "stress " xx "strain " xx "volume"` or `U= (1)/(2) xx (Y xx "strain") xx` strain `xx` volume or `U= (1 xx Y xx ("strain")^(2) xx "volume")/(2)` `alpha= (l)/(L xx t) = ("strain")/(t)` `:. alpha= ("CHANGE in LENGTH")/("original length" xx "temperature change")` or strain `= alpha t` `:. U = (Y xx alpha^(2) t^(2) xx ("AREA" xx "length"))/(2)` or `U= (10^(11)xx (10^(-5))^(2) xx (10)^(2) xx 0.01xx 1)/(2) = 5J` `:.` Energy stored `=5J`