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

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SUMMARY

The effective spring constant of a charged DNA molecule, measuring 2.09 µm in length and compressing by 1.13% when ionized, can be calculated using the equations F=kx and F=ke. The compression distance (x) is determined to be 2.3617x10^-8 m. The force (F) is derived from Coulomb's law, utilizing the charges of a proton and an electron (1.6x10^-19 C). The final calculation yields the effective spring constant, confirming the DNA's behavior as a spring under electrostatic forces.

PREREQUISITES
  • Understanding of Coulomb's law and electrostatic forces
  • Familiarity with spring mechanics and Hooke's law
  • Basic knowledge of DNA structure and ionization
  • Ability to perform calculations involving scientific notation
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  • Explore the implications of spring constants in biological molecules
  • Learn about the effects of ionization on molecular stability
  • Study advanced applications of Coulomb's law in biophysics
  • Investigate the mechanical properties of other biomolecules
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Biophysicists, molecular biologists, and researchers interested in the mechanical properties of DNA and its interactions under electrostatic conditions.

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

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