Work of a spring

[Electro]

Hello everyone!
The problem I have is really easy, but something is confusing me.

A spring with spring constant 24 N/m is stretched 0.24 m from its equilibrium position. How much work must be done to stretch it an additional 0.072 m?

I used the formula : W = (1/2)*k(Xf^2 - Xi^2), (it came out negative) but the answer I get is not the correct one. For Xf I used 0.24+0.072 since that's the distance from the equilibrium position.
Can you please give me a hint?

[Diane_]

What did you use for xi?

[Electro]

Hi Diane,
For X1 I used 0.24 and as I said for Xf i used 0.24+0.072. I think that the work should be negative since the spring goes toward positive x-axis.
I am not really clear with the work on a spring because the chapter on the book was very brief and that other books I have used are really messy. So I think this should be easy. Thus I just applied the formula I first posted.

[Electro]

Anyone can give a hint?

[Doc Al]

Your method seems correct to me. Why do you say it comes out negative? You are finding the work done to stretch the spring: the force and the displacement are in the same direction, so the work is positive.

Perhaps you are making an arithmetic mistake.

[Electro]

Thanks Doc Al,
I apologize, the work is really positive. That's how I solved it.
I have to solve the exercise and submit the answer online. I have only 7 chances. So I tried for the first time using the formula and the distances I wrote on the first post. It said "Incorrect"; than I thought maybe work is negative (I knew it was positive) but still I tried once more and I came out
"Incorrect" again. Then I just considered the first position as 0 and I applied the formula W=-.5 *k*X^2 but I falied again.
I don't know what is wrong with this!

[Doc Al]

Are you stating the problem exactly as given? Are you using proper units in reporting your answer? Show your arithmetic and we can check it over for silly errors.

[Electro]

Thank you for the time Doc Al,

I wrote the problem exactly as written on the paper. k is 24 N/m and it is stretched 0.24 m from equilibrium. Then the question is; How much work must be done to stretch it and additional 0.072m? (Answer in J)
so : W = 0.5*24([0.24+0.072]^2 - 0.24^2)
W = 12 (0.312^2 - 0.24^2)
W= 12(0.097344 - 0.0576)
=12* 0.039744 = 0.476928 J
This is what I think it should be (which in fact it isn't).

[Doc Al]

Your answer looks correct to me. (I'd round it off, though.)

[Electro]

:cry: I realized that on Friday night the server had failed because I entered the same answer this morning and amazingly it said "Correct". I don't know what happened; probably a server break down.
Anyway thanks a lot for the help.