Work and force

  1. Hi,

    Could someone please help me with this problem?

    1. The problem statement, all variables and given/known data
    A spring has a natural length of 20 cm. If a 25 N force is required to keep it stretched to a length of 30 cm, how much work is required to stretch it from 20 cm to 25 cm?

    2. Relevant equations

    w=lim a to b f(x)dx

    3. The attempt at a solution

    int. from 0 to 10 kxdx=25N
    25=[1/2kx^2]0 to 10

    int. from .05 to .10 (.5)xdx

    Could someone please tell me if this is correct so far?

    Thank you very much
  2. jcsd
  3. No, its not right. You've almost hit it. You know [tex]F=kx[/tex] Now, you know 25N force is required to hold it at 30 cm. Plug these values in and find k from here. Be careful about the unit and convert everything to SI before plugging the values in.

    The second part asks you to find the work done, you know [tex]W=\int F(x)dx[/tex].
    This gives you [tex]W=\frac{1}{2}kx^2[/tex] Apply the limits as you did, and use the value of k found above, and you have your answer.
  4. Thank you very much

    Would the limit be from 0 to 10?

    Also, I was thinking that maybe I should have used the formulas f/d=k and w=1/2kd^2

    Would that also work, since the force isn't constant?

    Thank you very much
  5. Does this look right?



    w=int. .10 to .15(250xdx)

    Thank you very much
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