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

[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
but the answer is wrong

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

 

[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.

 

[Sneakatone]

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

 

[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.

 

[Sneakatone]

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

 

[DTM]

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

 

[DTM]

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

 

[tms]

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

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

 

[Sneakatone]

is it stretched by 0.21 m?

 

[DTM]

You got it.

 

[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.

 

[tms]

They mean 0.3 of the relaxed length.

 

[Sneakatone]

would the relaxed length be .21/2=0.105

 

[Sneakatone]

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

 

[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.