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A spring is stretched by distance x and ...

A spring is stretched by distance x and then compressed to same distance from its original length. The work done by the spring force is (k=spring constant)

A

Zero

B

`1/2kx^2`

C

`3/2kx^2`

D

`-1/2kx^2`

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In the previous illustration. Consider the situation when the string is completely compressed. Then it begins to relax and will come to its original length. a. What is the work done by the spring during the period? b. Is the work done by the spring positive or negative?

Knowledge Check

  • A spring of force constant K is first stretched by distance a from its natural length and then further by distance b. The work done in stretching the part b is

    A
    `(1)/(2)Ka(a-b)`
    B
    `(1)/(2)Ka(a+b)`
    C
    `(1)/(2)Kb(a-b)`
    D
    `(1)/(2)Kb(2a+b)`

  • An elastic spring of unstretched length L and force constant k is stretched by a small length x. It is further stretched by another small length y. The work done in the second stretching is

    A
    `1/2 ky^2`
    B
    `1/2 k(x^2 + y^2)`
    C
    `1/2 k(x + y)^2`
    D
    `1/2 ky (2x + y)`

  • Two equal masses are attached to the two ends of a spring of spring constant k . The masses are pulled a part symmetrically to stretch the spring by a length x over its natural length. The work done by the spring on each mass is.

    A
    `(1)/(2) kx^(2)`
    B
    `-(1)/(2) kx^(2)`
    C
    `(1)/(4) kx^(2)`
    D
    `- (1)/(4) kx^(2)`

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    Assertion :- When a spring is elongated work done by spring is negative but when it compressed work done by spring is positive. Reason :- Work done by spring is path dependent

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