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

Answer

`2.5 xx 10^4 J m^(-3) ; 0.2 J`

Explanation

Energy density, `u = (1)/(2) "stress "xx "strain"`
` =(1)/(2) Y xx ("strain")^2 =(1)/(Y) Y = ((Delta l)/(l))^2`
`(1)/(2)xx 2xx10^(11) [(2xx10^(-3))/(4)]^2`
`= 2.5 xx10^4 J m^(-3)` Elastic potentail energy`. U = `Energy density `xx `volume ` = uxx A xxl`
`2.5 xx10^4 xx(2xx10^(-6))xx 4.0 = 0.2 J`