# B Spring force negative?

1. May 15, 2016

Hello,
Following Hooke's law, the force applied by a string on an object attached to one of its ends is F = -kx
But here is my question : if we consider the equilibrium coordinate x=0 of a horizontal string, and the string is stretched until its end reaches a coordinate x1>0. By applying hooke's law we find F = -k*x1 but since x1>0 so that means F<0, but as I know the magnitude of a force cannot be negative...so am I missing something or should I use |F| for magnitude or what ?

Thank you

2. May 15, 2016

### Staff: Mentor

Welcome to the PF.

Of course it can. It all depends on coordinates. Have you learned about vectors yet? (Vectors have a magnitude and a direction).

3. May 15, 2016

### robphy

$\vec F=-k(\vec x-\vec x_{eqbm})$

4. May 15, 2016

In fact, yes I have learned about vectors but I personally have never seen a negative magnitude, and since as I have studied the magnitude of a vector is ||F|| = sqrt(Fx^2 + Fy^2 ....) so doesn't this basically mean the magnitude of F is |Fx| ? ( Fx = -kx)

5. May 15, 2016

### Staff: Mentor

Just think about a mass initially at x=0 with a spring that goes off to the left. It is on a frictionless horizontal surface.

You pull the mass out to the right at x=1cm and let it go. What happens next?

6. May 15, 2016

It just goes back to x=0 (and negative values depending on k) under the effect of a force directed from right to left.

7. May 15, 2016

### Staff: Mentor

If it rests on a frictionless surface, it oscillates back and forth to +/- 1cm. What are the forces on the mass as it oscillates? Include the magnitude of the force in the x direction...

8. May 15, 2016

### Staff: Mentor

So what direction must the force point for that to happen?

9. May 15, 2016

It goes from the right to the left, and I get that spring force has an opposite direction of the stretching/compression.
What worries me is getting a force with a negative value, which is something I have never seen, as I always hear that the magnitude of a force is always positive.

10. May 15, 2016

### Staff: Mentor

That is what the negative sign means. The negative of a vector simply points in the opposite direction.

That is true. The magnitude of x is the same as the magnitude of -x and both are positive.

11. May 15, 2016

Then how would I explain a stretch of x=1m to result in a positive force magnitude ?
Let's take K=2N/m
F = -2*1=-2N
It gives a negative value
Whilst with x=-1 F=2N
So am I supposed to use |F| to write magnitude or what ?

12. May 15, 2016

### Staff: Mentor

Remember that force is a vector. So a force of -2 N is a force of magnitude 2 N pointing in the -x direction. Properly it should be written as F = (-2,0,0) N to make it clear that it is a vector, but in this case the 0 components are supposed to be understood from the context.

And, yes, if you want to show the magnitude of a force you can write |F|. In this case that would be |(-2,0,0)| = 2.

13. May 15, 2016

Now I got it thank you very much for your support.

14. May 15, 2016

### Staff: Mentor

You are welcome!