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

In summary: That means the distance over which the spring acts is also reduced, to 1.09% less. So you need to multiply your force by (1 - 0.0109) before setting it equal to kx. That will give you the correct answer for the spring constant. In summary, the effective spring constant of a molecule of DNA that is 2.10 μm long and becomes singly ionized at its ends, compressing 1.09%, can be determined by using Coulomb's law to get the force and then multiplying it by (1-0.0109) before setting it equal to kx.
  • #1
jybe
41
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?
 
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  • #2
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?
 

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

1. How does DNA act like a spring?

DNA is a double-stranded molecule that can coil and uncoil, similar to a spring. This coiling and uncoiling is due to the twisting of the two strands around each other, creating tension and elasticity in the molecule.

2. What causes DNA to act like a spring?

The twisting of the two strands of DNA around each other is caused by the hydrogen bonds between the nucleotides. These bonds create a helical structure that allows DNA to behave like a spring.

3. What is the significance of DNA acting like a spring?

The spring-like behavior of DNA is essential for many biological processes, such as DNA replication and protein synthesis. It also helps to protect the genetic information stored in DNA by keeping the molecule tightly coiled and compact.

4. Can DNA behave like a spring in both directions?

Yes, DNA can act like a spring in both the clockwise and counterclockwise direction. This is due to the complementary base pairing of nucleotides, which allows for the same twisting and coiling in either direction.

5. Is the spring-like behavior of DNA affected by external factors?

Yes, the elasticity of DNA can be affected by changes in temperature, pH, and the presence of certain chemicals. These external factors can alter the strength of the hydrogen bonds between nucleotides and, in turn, affect the spring-like behavior of DNA.

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