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Math Help - Why do I have to use energy conservation rather than using tension-extesion?

  1. #1
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    Why do I have to use energy conservation rather than using tension-extesion?

    One end A of a light elastic string of natural length a and modulus of elasticity 6mg is fixed at a point on a smooth plane inclined at 30 to the horizontal A small ball B of mass m is attached to the other end of the string. Initially B is held at rest with the string lying along the line of greatest slope of the plane, with B below A and AB =a. The ball is released and comes to instantaneous rest at a point C on the plane.

    Okay NOW It says I have to use a loss of GPE = EPE in the markscheme BUT WHY WHY WHY? Why cant I use

     Tension = \frac{\lambda x_{extension}}{x_{original length}}

    as the particle will stay be equilibrium when Tension balances the downward pull right?

    T = mgsin30
     Tension = \frac{\lambda x_{extension}}{x_{original length}} = mgsin30

      \frac{6mg x_{extension}}{a} = mgsin30
     \frac{6 x_{extension}}{a} = sin30
     x_{extension} = \frac{a}{12}

    therefore AC = a+a/12 = 13a/12

    which is wrong!

    Howcome????

    Thanks
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  2. #2
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    Quote Originally Posted by thomas49th View Post
    One end A of a light elastic string of natural length a and modulus of elasticity 6mg is fixed at a point on a smooth plane inclined at 30 to the horizontal A small ball B of mass m is attached to the other end of the string. Initially B is held at rest with the string lying along the line of greatest slope of the plane, with B below A and AB =a. The ball is released and comes to instantaneous rest at a point C on the plane.

    Okay NOW It says I have to use a loss of GPE = EPE in the markscheme BUT WHY WHY WHY? Why cant I use

     Tension = \frac{\lambda x_{extension}}{x_{original length}}

    as the particle will stay be equilibrium when Tension balances the downward pull right? right, but the position where the particle comes to rest is not the equilibrium position.

    T = mgsin30
     Tension = \frac{\lambda x_{extension}}{x_{original length}} = mgsin30

     \frac{6mg x_{extension}}{a} = mgsin30
     \frac{6 x_{extension}}{a} = sin30
     x_{extension} = \frac{a}{12}

    therefore AC = a+a/12 = 13a/12

    which is wrong!

    Howcome????
    .
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