Can the spring constant k be negative ?

• idir93
In summary, the conversation discusses the problem of finding the spring constant "k" in an arrangement involving a block attached to a spring. The work done by both the force and the spring is considered, and the conversation ends with the realization of a mistake and the correct solution to the problem.
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.

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idir93 said:
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.

Doc Al said:
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

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.

ok right so how would you answer to the problem ?

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 ;)

1. Can the spring constant k be negative?

No, the spring constant k cannot be negative. It is a physical property that represents the stiffness of a spring and is always positive.

2. What happens if the spring constant k is negative?

If the spring constant k is negative, it would imply that the spring has a negative stiffness, which is physically impossible. The spring would not behave in the way we expect and may not return to its original position after being stretched or compressed.

3. Can the value of the spring constant k be zero?

Yes, the value of the spring constant k can be zero. This would indicate that the spring has no stiffness and would not resist any force applied to it. The spring would essentially act as a straight line.

4. What factors affect the value of the spring constant k?

The value of the spring constant k depends on the material of the spring, its dimensions, and the number of coils. It also varies with temperature, as the stiffness of a material changes with temperature.

5. Can the spring constant k have different values at different points along the spring?

No, the spring constant k is a constant value that remains the same throughout the length of the spring. However, in some cases, the effective value of k may vary due to factors such as the shape of the spring or external forces acting on it.

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