# How to find force of a spring given force constant and length

1. Feb 26, 2013

### Sneakatone

A spring with a constant force k=150 N/m has a relaxed length of 0.21 m.

a) what force must you exert to strength this spring to 2.0 times its length?
I used the equation F=kx
F=150(2*0.21)=63

b) what force must you exert to compress this spring to 0.30 its length?
F=150(0.3)
that is also wrong

2. Feb 26, 2013

### tms

First, the spring equation is $F = -kx$; the sign is important.

Second, the $x$ in the equation is not the length of the spring, but the amount by which it is stretched or compressed from its equilibrium point.

3. Feb 26, 2013

### Sneakatone

so how would I get a relaxed spring length into stretched length?

4. Feb 26, 2013

### tms

You are told the relaxed length. You are told the stretched length. How do you find the amount by which it has been stretched? The amount, not the ratio.

5. Feb 26, 2013

### Sneakatone

I would think you multiply relaxed by 2 to get stretched length.

6. Feb 26, 2013

### DTM

So what is the change in length between relaxed length and the length of interest?

7. Feb 26, 2013

### DTM

Try drawing a picture of the spring in its various conditions.

8. Feb 26, 2013

### tms

Right. Then by how much has the spring stretched, in absolute terms, not as a fraction of the relaxed length?

9. Feb 26, 2013

### Sneakatone

is it stretched by 0.21 m?

10. Feb 26, 2013

### DTM

You got it.

11. Feb 26, 2013

### Sneakatone

for the 1st part I did 150(.21)=31.5 N which is correct.
but for part b I tried to divide 2 by .21 to get compressed spring and multiplied by .3 but It dosent work.

12. Feb 26, 2013

### tms

They mean 0.3 of the relaxed length.

13. Feb 26, 2013

### Sneakatone

would the relaxed length be .21/2=0.105

14. Feb 26, 2013

### Sneakatone

never mind I did .3/2 to get relaxed length and then multiplied by 150,
Thank you !

15. Feb 26, 2013

### tms

You're given the relaxed length, just as in the first part. The compressed length is the 0.3 x 0.21 m. The amount of compression is then 0.21 - (0.3 x 0.21), or 0.7 x 0.21.