Determine the effective spring constant of the molecule

[Knfoster]

Homework Statement

A molecule of DNA is 2.17 micrometers long. The ends of the molecule becom singly ionized: negative on one end, positive on the other. The helical molecule acts like a spring and compresses 1.00% upon becoming charged. Determine the effective spring constant of the molecule.

Homework Equations

I need a spring constant equation... Is this what I use?
F=kx

The Attempt at a Solution

The distance is going to be .01(2.17), but I'm not sure where to go from there. Could you please point me in the right direction? Thanks!

 

[ideasrule]

Yes, F=kx is what you use.

What's the force compressing the molecule? Remember that the molecule is singly ionized.

 

[Matterwave]

Hooke's law gives F=-kx (note the negative).

Since you already know x in this situation, all you need is F. Where do you think the force of compression comes from, and what is that force?

 

[Knfoster]

WEll... Could I use Coulomb's Law?
I know it is compressing because the two charges would be attracted to each other and want to come closer... but I'm not really sure how to get the force from that.

 

[Matterwave]

Use Coulomb's law. F=-kQ1Q2/r^2 (note, this k is not the spring constant k, but a constant for Coulomb's law)

 

[Knfoster]

but it doesn't say how much my charges are ionized by... should I just say they are + and - 1 ?

 

[Knfoster]

And is r going to be 2.17 micrometers?

 

[Matterwave]

It does say that they are "singly ionized". Which means your charges are +1e and -1e. Your r is actually going to be .99(2.17) micrometers, since that's the final position. The force of the "spring" is the force applied in the final position, so the force of the charges should be the force applied in the final position as well, although I don't think this will affect your calculations much.