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A steel wire 4.0m in length is stretche...

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

Text Solution

Verified by Experts

(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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