Elastic potential energy and natural length of a spring- relation?

[Stormzy67]

Homework Statement

The question states, a spring of length 0.5m is can be extended by 0.05m before fracturing, storing elastic energy ‘U’. Now, another spring of the same material but of half the length(0.25) is also stretched to its maximum extension.
What will be the new elastic energy in terms of ‘U’?

Relevant Equations

F=kx , E=1/2 kx^2, Young’s modulus?

I figured out that the spring constant is inversely proportional to the natural length, but there’s still an unknown change in a quantity( most likely extension).

 

[TSny]

Is there something that’s the same for both springs at the point where they break?

 

[Stormzy67]

The strain?

 

[Chestermiller]

The strain?

Yes. Also, the force.