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What is energy density of a stretched wi...

What is energy density of a stretched wire?

Text Solution

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Elastic potential energy stored in the stretched wire per unit volume
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What is elastic potential energy of stretched wire? Show that the energy density of a stretched wire is (Yl^2)/(2L^2) (symbols have their usual meanings).

The young modules of an wire of length ‘L’ and cross sectional area alpha is y The wire is extended in length within elastic‘limit with a stress's’. Calculate the energy density stored in the wire.

Knowledge Check

  • Potential energy per unit volume of a stretched wire is

    A
    `1/2 (Stress)/(strai n)`
    B
    `1/2 (stress)/(strai n)`
    C
    `1/2 ` Young modulus `times strai n^2`
    D
    `1/2 times` Young modulus `times` strain

  • A uniform wire of cross-sectional area A and Young's modulus Y is stretched within the elastic limit . If S is the stress in the wire , the elastic energy density stored in the wire in terms of the given parameters is

    A
    `S/(2Y)`
    B
    `(2Y)/S^2`
    C
    `S^2/(2Y)`
    D
    `S^2/Y`

  • A wire of initial length L and area of cross section A has Young's modulus Y of its material. The wire is stretched by a stress 5 within its elastic limit. The stored energy density in the wire will be

    A
    `5/(2Y)`
    B
    `(2Y)/5^2`
    C
    `5^2/(2Y)`
    D
    `5^2/Y`

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    What will be the change in temperature of a stretched wire if snaps suddenly?

    Find an expression for the potential energy in a stretched wire. (Similar question : Find out an expression for the work done by a force in stretching a length of a wire with respect to strain produced in the wire.

    Initial length of a wire is L and its area of cross section is A. The wire is elongated by applying a stress tau within its elastic limit. Prove that the potential energy density in the wire due to elongation is (tau^2)/(2Y) [Y=Young's modulus]

    One end of an aluminium wire whose diameter is 2.5 mm is welded to one end of a copper wire whose diameter is 2.0 mm. The composite wire carries a steady current of 6.25A. What is the current density in each wire ?

    A wire of resistance 4Omega is stretched to twice its original length. The resistance of stretched wire would be

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