A wire of area of cross section `3.0mm^2` and natural length 50 cm is fixed at one end and a mas of 2.1 kg is hung from the other end. Find the elastic potential energy stored in the wire in steady state. Young modulus of the material of the wire `=1.9xx10^11Nm^-2. Take g=10ms^-2`

Explanation

The volume of the wire is
`V=(3.0mm^2)(50cm)`
`=(3.0xx10^-6m^2)(0.50m)=1.5xx10^-6m^3`
Tension in the wire is
`T=mg`
`=(2.1kg)(10ms^-2)=21N`.
The stress `=T/A`
`=(21N)/(3.0mm^2)=7.0xx10^6Nm^-2`
The strain `stress/Y`
`=(7.0xx10^6Nm^-2)/(1.9xx10^11Nm,^-2)=3.7xx10^-5`
The elastic potential energy of the wire is
`U=1/2(stress)(strain)(volume)`
`=1/2(7.0xx10^6Nm^-2)(3.7xx10^-5)(1.5xx10^-6m^3)`
`=1.9x10^-4J`.