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# A molecule of DNA (deoxyribonucleic acid) is 2.17 mm 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 1.00% upon becoming charged. Determine the effective spring constant of the molecule.

## 2.3$\cdot 10^{-9} \mathrm{Nm}^{-1}$

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##### Andy C.

University of Michigan - Ann Arbor

LB

### Video Transcript

{'transcript': "Okay, so for this case, we know the force is equal status. Spring constant has decompressed this. If we do some random year, we'll have the effects of spring. Constant is you go to force to a body compressed distance. And the force on this case is the ultra four spunk. The charge front, each case, the equivalent constant accused the charge Find Shane and distance between the charges. Our job going on that are is because the decision was compressed by 1%. So now the distance between two end is 99% of the original distance okay, and 9% in. That's a more representation. It's zero point on that. So the distance now between the two a zero point on our and then we put the square here and then we'll have the electric force. And just like what I said, it compresses is 1% of the original distance, which is 3.0 R. So if we're plugging all these write letters here back into the equation will have K wants UK queues were opened zero point no and I are into a part or two and then over 0.1 are and when OK was. This is a cool inconstancy time point. 0 10 Central Power nine. You're telling tens of meters squared booklet on sport and charge Q. Is, you know the 1.6 times 10 to a burning 19. Cool and the original distance all the land off the molecule is 2.17 my premiere, which is 2.17 times 10th of part of 96 meter every week we can plug in all these values. Speak into the equation here don't have K one, which is the fight of spring costume. Chemical, too. UH, nine point old times tensile pollen I Utah transmitters were cool on square N times 1.6 times Central Apartment in 19. Cool on nine square over zero point and I times 2.17 times 10 to the power of 96 meter Temple Square. Here over 0.0. Uh, times 2.17 kinds tend to apartment 96 meter, and it will give us the effective spring. Constant is about 2.3 times essential. Apart off neg night, Utah a meter"}

Georgia State University
##### Andy C.

University of Michigan - Ann Arbor

LB