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Physics : Young's Modulus

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A mass m is attached to a weightless string of
length L, cross section S, and tensile strength ( the
maximum tension it can withstand ) T . The mass
is suddenly released from a point near the fixed
end of the string. What condition should be on the
value of Young's modulus Y so that the string
does not break?

  • Physics : Young's Modulus -

    The effective spring constant of the string is
    k = Y*S/L Newtons/meter

    When the mass m is dropped from the fixed end, the string will stretch a maximum amount dL, so that

    m g L = (1/2) k *dL^2 = (1/2)Y*S/L*dL^2

    dL^2 = 2 m g L^2/(Y*S)
    dL/L = sqrt[2 m g/(Y*S)]

    If the string is about to break at maximum stretch, the tensile stress will then be
    sigma = T = Y*(dL/L)
    T = sqrt[2 m g Y/S]

    Solve for Y. A larger value of Y will cause the string to break.

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