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I am still really stuck with this M3 elastic springs question- please help :) watch

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    A light elastic string has natural length L and modulus (lamba). One end is fixed to a point A on a ceiling and a particle P of mass m is attached to the other end. P is held vertically below A so that AP=2L and then released. P has speed v when the extension of the string is x. Show that, while the string remains taut,

    1/2mv^2 = L/2 ( (lamba) - 2mg ) + mgx - (lambda)x^2 / 2L

    I have completed that part

    I am stuck with this part:

    By considering the speed of P when x=0 show that the string will never become slack provided 2mg > (lamba)

    Thank you
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    (Original post by sulexk)
    A light elastic string has natural length L and modulus (lamba). One end is fixed to a point A on a ceiling and a particle P of mass m is attached to the other end. P is held vertically below A so that AP=2L and then released. P has speed v when the extension of the string is x. Show that, while the string remains taut,

    1/2mv^2 = L/2 ( (lamba) - 2mg ) + mgx - (lambda)x^2 / 2L

    I have completed that part

    I am stuck with this part:

    By considering the speed of P when x=0 show that the string will never become slack provided 2mg > (lamba)

    Thank you
    This has really been answered on your other two threads. All that is left is to sum it up with something like:

    For the string to become slack it must pass through the point specified by x=0. At this point, if 2mg > lambda then the square of its velocity will be less than zero, which is not possible. Hence if 2mg > lambda then it cannot pass through the point speified by x = 0, and consequently the string cannot become slack.
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    (Original post by ghostwalker)
    This has really been answered on your other two threads. All that is left is to sum it up with something like:

    For the string to become slack it must pass through the point specified by x=0. At this point, if 2mg > lambda then the square of its velocity will be less than zero, which is not possible. Hence if 2mg > lambda then it cannot pass through the point speified by x = 0, and consequently the string cannot become slack.
    Thank you


    I really appreciate it.
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