An uncharged molecule of dna is 2.11 micrometers long. The ends of the molecule become slightly ionized so that there is a charge of -1.6 E -19 C on one end and 1.6 E -19 C on the other. The helical molecule acts like a spring and compresses 1.2% upon becoming charged. The value of Coulomb's constant is 8.98755 E 9 N-m^2/C^2 and the acceleration due to gravity is 9.8 m/s^2. Find the effective spring constant of the molecule. Answer in units of N/m.
I have struggled with this for like the whole weekend. Please Help!
2007-01-07 09:52:25 · 5 answers · asked by Brown Nymph 07 3 in Science & Mathematics ➔ Physics
I am sure the acceleration due to gravity is a red herring, so this is my answer:
Hooke's law (for the spring) is:
F = k dx
where F is the force, k is the spring constant (what you want to find) and dx is the change in length of the spring (the stretch or compression, the sign indicates which).
You will also need to know the coulombic force:
F = kc q1 q2 / r^2
Where F is the force, kc is the coulomb connstant, q1 and q2 are the two charges and r is the radius (the distance between the two charges).
You can equate these two:
k dx = kc q1 q2 / r^2
and rearrange in terms of the spring constant:
k = kc q1 q2 / (r^2 dx)
Now, simply plug in your numbers:
k = 8.98755E9 * 1.6E-19 * (-1.6E-19) / ((2.11E-6 ^ 2) * 0.012 * 2.11E-6)
(remember, dx will be 1.2% of 2.11E-6 metres, or 0.012 * 2.11E-6)
Plug these numbers into your trusty calculator to get:
k = 2.04E-9 N/m
I am sure this is right. Can I have 10 points please?
2007-01-07 10:28:33 · answer #1 · answered by Mawkish 4 · 0⤊ 0⤋
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2007-01-07 10:03:21 · answer #2 · answered by closetmeateater 2 · 0⤊ 1⤋
I can probably do this with some simplifying assumptions. If calculus is introduced it gets a bit more complex and I doubt that that's a factor. I teach physics.
Email me a short message, I'll work on it, and get the answer back to you later tonight or early in the morning. My email address is
fortitudinousskeptic@yahoo.com
- kevin
I need to work it out on paper, scan it, and attach it to an email to send back to you.
I worked it out and my preliminary answer is 5.04 x 10 ^-11 N/m
Yes, the acceleration of gravity is a red herring
If you wish to see my paper answer worked out in detail, email me, I'll scan it, and send it back via email attachment
2007-01-07 10:02:15 · answer #3 · answered by Anonymous · 0⤊ 1⤋
Yes.
2007-01-07 10:00:05 · answer #4 · answered by Bobbi 5 · 0⤊ 1⤋
I dont understand this language.
2007-01-07 09:56:08 · answer #5 · answered by Anonymous · 0⤊ 1⤋