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1. 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
2. (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.
3. (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.
4. how did you prove [email protected]@

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