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Chain and Elastic string problem

  1. Jul 13, 2014 #1
    1. The problem statement, all variables and given/known data

    A uniform chain of length L hangs from an elastic string of natural length L. The upper end of the string is connected with the ceiling .When the system is in equilibrium , the string stretches by an amount L .At what distance from the lower end of the chain ,the chain should be cut so that upper end of chain just strikes the ceiling?

    2. Relevant equations



    3. The attempt at a solution

    'k' is the force constant of the string and m is the mass of the chain.

    From equilibrium condition kL = mg → k=mg/L

    Suppose the chain is cut a distance 'x' from below .

    Applying COE , (1/2)kL2 = (m/L)(L-x)g(2L)

    This gives x= (3/4)L .

    Is it right ?

    Many Thanks
     
  2. jcsd
  3. Jul 14, 2014 #2

    Simon Bridge

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    You have argued that the energy stored in the string needs to be enough to throw the remaining mass through a height 2L ... that is well reasoned, well done.
     
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