# The natural length of a spring

1. Oct 26, 2015

### astrololo

1. The problem statement, all variables and given/known data

A block is fixed on the extremity of a mobile ideal spring that is horizontal and which has the other side of it fixed (Non mobile). When the lenght of the spring is 50 cm, the block has a force of 5 N on the right; When the lenght of the spring is 80 cm, the block has a force of 10 N vers the left. What is the natural lenght of the spring and what is the spring constant?

Image of the situation : http://imgur.com/RN7Hv3T
2. Relevant equations
e=L-Lnat
F=k*Absolutevalue(e)

3. The attempt at a solution
I know that the natural lenght is going to be between 50 and 80 cm and that the natural lenght is going to be closer to 50 cm because the force is 5 N which indicates that we don't put a lot of pressure on it. Other than that, I have no idea where to go next.

2. Oct 26, 2015

### Student100

Whats the work done for each displacement?

3. Oct 26, 2015

### astrololo

You mean what have I done so far ? Nothing....

4. Oct 26, 2015

### Student100

No I mean what's the work required to compress the string to 50 cm or stretch it to 80 cm?

5. Oct 26, 2015

### astrololo

Oh, I guess that if we want to maintain it stable, then it's going to be -5 N on the left and 10 N on the right. So it's the inverse.

6. Oct 26, 2015

### Student100

Remember that work is $w=\vec{F}\cdot\vec{R}$, one dimensional (this problem) we can write $w=F_xR_x$

The spring is compressed in the first case from some natural length, and stretched in the second. We can write work in terms of some variable, L.

7. Oct 26, 2015

### astrololo

Sorry but we didn't see this yet. Also, my problem sindicates that this exercice's solution doesn't any complex/hard algebra or a calculator.

8. Oct 26, 2015

### Student100

Then the rabbit hole I'm going to lead you down probably isn't the easiest way to do this problem. If no one else has responded when I get home I'll take a second look.

9. Oct 26, 2015

### astrololo

Thank you, I got some other things to do so I'm patient with this.

10. Oct 26, 2015

### Nathanael

Use your "Relevant equations" to write a system of two equations for the forces. It will involve two unknowns, the spring's constant and the spring's rest length.

11. Oct 26, 2015

### astrololo

Thank you ! I didn't realize that it was a system of equation. The worse is that I was able to get the two equations previously but I didn't realize that I had a system ! Thank you again !