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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

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Here , l=4.0 m , `Deltal=2xx10^(-3)` m , `a=2.0xx10^(-6) m^2 , Y=2.0xx10^11 N//m^2`
(i) The energy density of stretched wire
`u=1/2` x stress x stain
`=1/2 x Y x "(strain)"^2`
`=1/2xx2.0xx10^11 xx(2xx10^(-3))//4)^2`
`=0.25xx10^5 = 2.5xx10^4 J//m^3`
(ii) Elastic potential energy = energy density x volume
`=2.5xx10^4xx(2.0xx10^(-6))xx4.0J = 20xx10^(-2)` = 0.20 J
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