Reif 2.9

[James Wine]

1. The problem statement, all variables and given/known data
Let a wire's tension increase quasi-statically from F_{1}\rightarrowF_{2}, with Young's Modulus Y, Cross-sectional Area A, and Length L. Find the work done


2. Relevant equations

F=\frac{YA}{L} *Delta L, tex having issues
W= Integral from L to L_2

3. The attempt at a solution

W = YA*Integral[dL/L]
W = YA ln(L_2/L)

Question is if the length changes then the cross-sectional area should also change and would require this to be a double integral, 2nd question would be if I even thought about the first integral in the right way.

[vela]

If you really need to take into account the effect of A changing, you could use the approximation that the total volume remains constant, or you could use Poisson's ratio (http://en.wikipedia.org/wiki/Poisson's_ratio).

Note your calculation assumes that F1=0 because you used L, the initial length of the wire, for the lower limit of the integral. Your work looks fine otherwise.