What Is the Effective Spring Constant of a Charged DNA Molecule?

[ccaramel]

A molecule of DNA (deoxyribonucleic acid) is 2.09 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 1.13% upon becoming charged. Determine the effective spring constant of the molecule.


equations that should be used are: F=kx and F=ke (Coulomb constant) q1q2 / r^2


you can find x, the distance the spring is compressed by multiplying 2.09x10^-6 x .0113 = 2.3617x10^-8 m

you can find the force by using coulomb's law; use have all the info to plug in except for the charges (q1 and q2). what are they? once you know the charges, you can solve for F and then plug into F=kx to solve for the spring constant. please help!

 

[ccaramel]

nvm... i figured out the answer. the charges used are that of a proton and electron (1.6x10^-19)

 

[ogb p]

I would first like to clarify that the content provided does not accurately reflect the properties of DNA. DNA is not electrically charged and does not act like a spring. It is a complex molecule that plays a crucial role in genetic information storage and transfer.

That being said, let's assume that this is a hypothetical scenario for the purpose of problem-solving. The length of the DNA molecule, 2.09 µm, is irrelevant to the problem at hand as it is not a factor in the equations provided. The key information we need is that the molecule compresses 1.13% upon becoming charged.

To determine the effective spring constant, we can use the equation F=kx, where F is the force applied, k is the spring constant, and x is the distance the spring is compressed. In this case, the force applied is the electric force, which can be calculated using Coulomb's law: F=ke (q1q2/r^2).

We know that the distance the spring is compressed, x, is 1.13% of the original length, which can be expressed as 0.0113 times the original length. We also know that the charges, q1 and q2, are opposite in sign and equal in magnitude, as the molecule is singly ionized with a negative charge on one end and a positive charge on the other.

Using these values, we can set up the equation F=ke (q1q2/r^2) = k(0.0113 x 2.09x10^-6)^2. Solving for k, we get k= 1.26x10^-18 N/m. This is the effective spring constant of the DNA molecule in this hypothetical scenario.

However, it is important to note that this calculation is based on a simplified model and does not accurately reflect the true properties of DNA. In reality, the forces acting on DNA are much more complex and cannot be accurately described using a simple spring model.