1. Nov 11, 2004

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, where V-volume
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?

Last edited: Nov 11, 2004
2. Nov 11, 2004

Staff: Mentor

I can't quite figure out what you're doing with energy and volume. But I suspect that your mistake is in treating the rod as if the tension were the same throughout, which is not the case.

3. Nov 11, 2004

Yegor

Ok. In final moment Energy is equal U=V*(E*ε ^2)/2=V*(σ*ε/2),
where σ-stress (tension), (σ=F/S=E*ε (Hook's law)
But the "tension is not the same throughout".
It changes from 0 to P/S.
What I should do?

4. Nov 11, 2004

Staff: Mentor

The stress ranges from 0 (at the bottom) to P/S at the top. So the average stress is 1/2 P/S. Thus the overall strain is P/(2 E S), where E is Young's modulus.