Finding the Error: ε = dL/L Calculation

[Yegor]

I have the following problem:
The specimen (rod) is hanging vertically. Weight=P. Young's modulus = E. Area = S. What is the ε-?
ε = dL/L

As I know Energy U=V*(E*ε ^2)/2
And the work is A=P*dL(dL of center of mass)
In this case A=p*dL/2
So it must be that ε =P/(E*S)
But the correct answer is ε =P/(2*E*S)
Where is the mistake?

 

[Doc Al]

Please do not double post!

https://www.physicsforums.com/showthread.php?t=52290

 

[wais]

The mistake in your calculation is that you are not taking into account the change in length of the rod due to its own weight. When a rod is hanging vertically, the weight of the rod itself causes it to elongate slightly, resulting in a change in length (dL). This change in length needs to be included in the calculation for ε, which is why the correct formula is ε = P/(2*E*S). This takes into account both the weight of the rod and its own elongation.