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.

Explanation

Here, length of wire, l=4.0 m , `Deltal=2xx10^(-3)m`
Area, A `=2.0xx10^(-6)m^(2)`
Young's modulus , `Y=2.0xx10^(11)Nm^(-2)`
(i) The energy density of stretched wire
`U=(1)/(2)xx"stress"xx"strain"=(1)/(2)xxYxx("strain")^(2)`
`(1)/(2)xx2.0xx10^(11)xx[((2xx10^(-3))^(2))/(4)]=0.25xx10^(5)`
`=2.5xx10^(4) Jm^(-3)`
(ii) Elastic potential energy=energy density `xx` volume
`=2.5xx10^(4)xx(2.0xx10^(-6))xx4.0 J`
`=20xx10^(-2)=0.20 J`