Can the spring constant k be negative ?

[idir93]

Can the spring constant "k" be negative ?

Hi,
I found a difficulty when solving this problem from my textbook :

In the arrangement of Figure 7-11 (which is basically a standard block attached to spring resting horizontally), we gradually pull the block from x = 0 to x = +3.0 cm, where it is stationary. Figure 7-36 gives the work that our force does on the block. We then pull the block out to x = +5.0 cm and release it from rest. How much work does the spring do on the block when the block moves from xi = +5.0 cm to (a) x = +4.0 cm, (b) x = –2.0 cm, and (c) x = –5.0 cm?

So I found the spring constant k:
W = -0.5kx2
0.9 = -0.5k(0.03)2
k = -2000 N/m ? of course it's wrong (the correct answer is 2000 N/m) but i couldn't find my mistake.
Please help me :)

 

[Doc Al]

So I found the spring constant k:
W = -0.5kx2

Why do you have a minus sign? The work done (by you) when stretching a spring is positive.

 

[idir93]

Why do you have a minus sign? The work done (by you) when stretching a spring is positive.

We are talking about the spring's work, if it was our work, does human being have a spring constant ? :

W=F.d.cosθ / θ=180°
So it will be negative

 

[Doc Al]

Sure, the spring's work will be negative. So what? The spring constant is still positive.

What makes you think that that is a diagram of the spring's work? It looks like the positive work that you do in stretching the spring.

 

[idir93]

ok right so how would you answer to the problem ?

 

[idir93]

ok thank you i found my mistake, thank you very much
Kf - Ki = Wa + Ws

since it goes from rest to rest then Kf - Ki = 0j so Wa = -Ws ;)