Finding the value of k (spring constant)

[p0ps1c1e]

During a test experiment, the engineer finds an ideal very light spring has already been stretched 1.4m from its original length. He also finds that he needs to perform 100J of work to further stretch this spring an additional 1.5m. What is the value of the spring constant for this spring?

Homework Equations

W = F*d

F = -kx

So I wrote out that F₁ = -kx to stretch the spring the initial 1.4m and then to stretch it the additional 1.5m it would take:

F₂ +F₁ = -2.9*k

I also wrote out:

F₁ = -1.5k

Then I used 100 = F₂*1.5

so F₂ = 66.67 although I'm not sure if you can use this equation for a spring

Then 66.67 -1.5k = -2.9k and I tried solving for k but that didn't work so I'm not sure what else to try.

 

[haruspex]

Then I used 100 = F₂*1.5

There are two problems with that approach. First, your F₂ is the additional force to get the extra 1.5m extension, but while extending it that 1.5m the total force applied is between F₁and F₁+F₂. Therefore F₁is an important part of the work done.
Secondly, the force only reaches F₁+F₂ at full extension, so neither can you write 100 = (F₁+F₂)*1.5.

In terms of k, what work was done to stretch it 1.4m? What total work was done to stretch it 1.4+1.5m?

 

[p0ps1c1e]

So W₁ = 1/2k*(1.4)^2 = 0.98k
W₂ = 100
Work_Total = 1/2k(2.9)^2 = 4.205k

Then I put it together 4.205k = 0.98k + 100J

so k = 31 N/M ?

Also, I thought 1/2kx^2 was for potential energy of a spring. So I'm kind of confused about the difference between the two now

 

[haruspex]

so k = 31 N/M ?

Looks right.

I thought 1/2kx^2 was for potential energy of a spring.

The work done to stretch a spring (from slack) equals the potential energy stored in the spring (assuming no losses). Where's the confusion?

 

[p0ps1c1e]

Thanks. I guess I just need to review this chapter some more