Question

a steel wire of 4m is stretched through 2mm the cross sectional area of wire is 2mm*2 and young modulus of steel is 2×10*11 <br />find the energy density of the wire<br />b the elastic potential energy stored in a wire​

Answer 1

Here, l=4.0m;Δl=2×10  

−3

m;a=2.0×10  

−6

m  

2

,Y=2.0×10  

11

N/m  

2

 

(i) The energy density of stretched wire

u=  

2

1

​  

× stress × strain

=  

2

1

​  

×Y×(strain)  

2

 

=  

2

1

​  

×2.0×10  

11

×(2×10  

−3

)/4)  

2

 

=0.25×10  

5

=2.5×10  

4

J/m  

3

.

(ii) Elastic potential energy = energy density × volume

=2.5×10  

4

×(2.0×10  

−6

)×4.0J=20×10  

−2

=0.20J.

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