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    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,
    m g = \frac{\lambda e}{l}

    (5) (9.8) = \frac{150 e}{0.6}

    e = 0.196m


    By energy:


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

    Energy = GPE = m g h = 49 (0.6+e)

    At A:

    Energy = EPE = 49 (0.6+e) = \frac{\lambda e^{2}}{2 l}

    49 (0.6+e) = \frac{150 e^{2}}{1.2}

    29.4+49e-125e^{2} = 0

    125e^{2}-49e-29.4 = 0

    e = \frac{49 + (49^{2} - (4) (125) (-29.4))^{0.5}}{250} = 0.719m
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    I had a look at this, thinking I could help you.
    Unfortunately, I don't know who I am any more.
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    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.

    125e^2-49e-24.9=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.
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    This is a duplicate thread and has been resolved on the physics forume.
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    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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