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A steel wire of 4.0 m in length is stret...

A steel wire of 4.0 m in length is stretched through 2.00 mm. The cross-sectional area of the wire is `2.0mm^(2)` if young's modulus of steel is `2.0xx10^(11)N//m^(2)` find (i) the energy density of wire (ii) the elastic potential energy stored in the wire.

Text Solution

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(i). The energy density of streched wire
`=(1)/(2)xx"stress"xx"strain"=(1)/(2)xxYxx("strain")^(2)`
`=(1)/(2)xx2.0xx10^(11)xx[(2xx10^(-3))/(4)]^(2)=2.5xx10^(4)J//m^(3)`
(ii). Elastic potential energy =energy density `xx` volume `=2.5xx10^(4)xx(2.0xx10^(-6))xx4.0J=20xx10^(-2)=0.20J`
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