What is the effective spring constant of a charged DNA molecule?

  • Thread starter Thread starter jybe
  • Start date Start date
  • Tags Tags
    Dna Spring
AI Thread Summary
The discussion revolves around calculating the effective spring constant of a charged DNA molecule, which is 2.10 μm long and compresses by 1.09% when ionized. The user attempts to apply Coulomb's law and Hooke's law to find the spring constant but receives feedback indicating their answer is incorrect, albeit within 10% of the correct value. A key point raised is that the distance used in Coulomb's law should account for the compression of the DNA molecule, suggesting it should be slightly less than 2.10 μm. This adjustment is crucial for accurately determining the effective spring constant. The conversation highlights the importance of considering physical changes in the system when applying theoretical equations.
jybe
Messages
41
Reaction score
1

Homework Statement


A molecule of DNA (deoxyribonucleic acid) is 2.10 μm long. The ends of the molecule become singly ionized: negative on one end, positive on the other. The helical molecule acts like a spring and compresses 1.09% upon becoming charged. Determine the effective spring constant of the molecule.

Homework Equations



Q = 1.9 E-19

F = KQ^2/r^2

F= kx

The Attempt at a Solution



F = KQ^2/r^2

F = ((8.99E9)*(1.6E-19)^2)/(2.1E-6)^2

F = 5.224489796E-17 N

F = kx

k = (5.224489796E-17)/(0.0109*2.1E-6)

k = 2.282433288E-9 N/m

This is the answer I get but the software keeps saying my answer is wrong BUT within 10% of the correct answer. I've done it about 10 times now and don't understand. Can anybody see anything wrong?
 
Physics news on Phys.org
jybe said:

Homework Statement


A molecule of DNA (deoxyribonucleic acid) is 2.10 μm long. The ends of the molecule become singly ionized: negative on one end, positive on the other. The helical molecule acts like a spring and compresses 1.09% upon becoming charged. Determine the effective spring constant of the molecule.

Homework Equations



Q = 1.9 E-19

F = KQ^2/r^2

F= kx

The Attempt at a Solution



F = KQ^2/r^2

F = ((8.99E9)*(1.6E-19)^2)/(2.1E-6)^2

F = 5.224489796E-17 N

F = kx

k = (5.224489796E-17)/(0.0109*2.1E-6)

k = 2.282433288E-9 N/m

This is the answer I get but the software keeps saying my answer is wrong BUT within 10% of the correct answer. I've done it about 10 times now and don't understand. Can anybody see anything wrong?
Almost good.

When you use Coulomb's law to get the force, the distance between charges is reduced to slightly less than 2.10 μm. Right?
 

Thread 'Errors and significant figures'

I multiplied the values first without the error limit. Got 19.38. rounded it off to 2 significant figures since the given data has 2 significant figures. So = 19. For error I used the above formula. It comes out about 1.48. Now my question is. Should I write the answer as 19±1.5 (rounding 1.48 to 2 significant figures) OR should I write it as 19±1. So in short, should the error have same number of significant figures as the mean value or should it have the same number of decimal places as...
View full post »
Thread 'Collision of a bullet on a rod-string system: query'

Thread 'Collision of a bullet on a rod-string system: query'

In this question, I have a question. I am NOT trying to solve it, but it is just a conceptual question. Consider the point on the rod, which connects the string and the rod. My question: just before and after the collision, is ANGULAR momentum CONSERVED about this point? Lets call the point which connects the string and rod as P. Why am I asking this? : it is clear from the scenario that the point of concern, which connects the string and the rod, moves in a circular path due to the string...
View full post »
Thread 'A cylinder connected to a hanging mass'

Thread 'A cylinder connected to a hanging mass'

Let's declare that for the cylinder, mass = M = 10 kg Radius = R = 4 m For the wall and the floor, Friction coeff = ##\mu## = 0.5 For the hanging mass, mass = m = 11 kg First, we divide the force according to their respective plane (x and y thing, correct me if I'm wrong) and according to which, cylinder or the hanging mass, they're working on. Force on the hanging mass $$mg - T = ma$$ Force(Cylinder) on y $$N_f + f_w - Mg = 0$$ Force(Cylinder) on x $$T + f_f - N_w = Ma$$ There's also...
View full post »

Similar threads

Calculating the Effective Spring Constant of a Charged DNA Molecule
Replies
3
Views
2K
Spring constant formlula for Force and Work Done
Replies
12
Views
2K
Energy stored in a double spring system
Replies
17
Views
1K
Find spring constant k using an electrical circuit
Replies
10
Views
2K
What is the Relationship Between Force and Spring Constant?
Replies
14
Views
3K
What Is the Effective Spring Constant of a Charged DNA Molecule?
Replies
1
Views
9K
Problem with solving for force constant k of spring?
Replies
3
Views
2K
Two point charges repelling, stretching a spring
Replies
14
Views
2K
How Do You Calculate the Spring Constant of a Charged DNA Molecule?
Replies
4
Views
14K
What is the Spring Constant of a DNA Molecule?
Replies
2
Views
5K

Hot Threads

Recent Insights

Back
Top