EPE problem

[GregA]

Hi folks...can someone tell me where I'm going wrong with this question, or back me up if I'm right?

A string of natural length 2a and modulus of elasticity b has its ends attached to fixed points A and B where AB = 3a. Find the work done when the midpoint C of the string is pulled away from the line AB to a position where triangle ABC is equilateral. My attempt to solve is as follows:

I ignore B and focus just on A and C
if the natural length of the string = 2a then the midpoint represents half this length and therefore = a
AB = 3a, and so AC = 3a/2... the extention x = a/2
AC when streched to the equilateral triangle = 3a and so...x = 2a
The question asks me how much work is done from pulling the midpoint from its initial position on the line AB to its final position

Surely I want to subtract the work taken to pull the string to from its natural length to AC1 from the work required to pull the string to AC2..using Work = (b(x)^2)/2a...
(b((2a)^2-(a/2)^2)/2a = 15ab/8.
The books answer is given as 4ab however....I've tried to find a problem with my working and cannot. :frown:

[GregA]

I think I have it...There are two tensions opposing the movement of that string not just AC but BC :redface:
If the question means how much work is done to extend from its natural length to its final position it is simply 2(b(2a)^2)/2a...=4ab