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M2 Elasticity Question watch

1. Hey, can someone explain where I'm going wrong here? I'm getting different answers with different methods. I hoped I would find my problem during the writeup but I haven't spotted it. Sorry for the bad formatting. Crossposted from the physics forum.

A particle, of mass 5kg, is attatched to one end of a light elastic string of natural length 0.6 metres and modulus of elasticity 150N. The other end of the string is fixed to a point O.

Find the extension of the string when it hangs in equilibrium at point A below O.
By forces:

At A,

By energy:

At O, taking A as the zero-line for GPE:

At A:

Unfortunately, I don't know who I am any more.
3. The problem is how you're using the energy equation.

The energies summing to 0 isn't what you want, it's the change of potential energy with respect to distance (in this case e) that we want to equal 0.

Differentiate with respect to e and set equal to 0, and you get the answer you got to part one. However, I'm pretty sure this stuff is M4 - the force balancing is probably the way to go.
4. This is a duplicate thread and has been resolved on the physics forume.
5. Thanks ghostwalker, I did mean to post that here this morning but was in a bit of a rush. The other thread is here:

http://www.thestudentroom.co.uk/show....php?t=1590729

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Updated: March 31, 2011
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