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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)`,Find:
(a) the enrgy density of wire,
(b) the elastic potential energy stored in the wire.

Text Solution

Verified by Experts

Here, `l=4.0m , Delta l= 2 xx 10^(-3), a=2.0 xx 10^(-6)m^(2), Y=2.0 xx 10^(11)N//m^(2)`
(i) The energy density of stretched wire
`u=1/2 xx "stress" xx "strain "= 1.2 xx Y xx ("strain")^(2) = 1/2 xx 2.0 xx 10^(11) xx (2 xx 10^(-3)//4)^(2)`
`=0.25 xx 10^(5) = 2.5 xx 10^(4) J//m^(3)`
(ii) Elastic potential energy = energy density `xx` volume `= 2.5 xx 10^(4) xx (2.0 xx 10^(-6)) xx 4.0 J`
`=2. xx 10^(-2) = 0.20 J`.
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