Stretching DNA.
With its double-helix structure, DNA is coiled like a spring. A biophysicist grabs the ends of a DNA strand with optical tweezers and stretches it 26µm producing 1.2pN- tension in the strand.
What's the DNA's spring constant?
F=kx
F (tension of the strand)=1.2 pN
x (displacement)=26 µm
Solve for k, which is the spring constant. You may need to convert your unit measurements, as your answer's unit will come out in pN/µm instead of the standard N/m.
(I know this is a little late, but I wanted to post it up, in case anyone else needed it.)
To determine the DNA's spring constant, we can use Hooke's Law, which states that the force (F) exerted on an object is equal to the product of the spring constant (k) and the displacement (x) from its equilibrium position.
The equation for Hooke's Law is given by:
F = k * x
In this case, we are given the tension in the DNA strand (F = 1.2 pN) and the displacement (x = 26 µm = 26 * 10^(-6) m). We can rearrange the equation to solve for the spring constant (k).
k = F / x
Substituting the given values, we have:
k = (1.2 * 10^(-12) N) / (26 * 10^(-6) m)
Simplifying, we get:
k = 4.62 * 10^(-5) N/m
Therefore, the DNA's spring constant is approximately 4.62 * 10^(-5) N/m.
To determine the DNA's spring constant, you need to use Hooke's Law, which states that the force needed to stretch or compress an object is directly proportional to the displacement. The formula for Hooke's Law is F = k * x, where F is the force, k is the spring constant, and x is the displacement.
In this case, we have the force (tension) and the displacement, so we can rearrange the formula as k = F / x to find the spring constant.
Given that the tension in the DNA strand is 1.2 pN (piconewtons) and the displacement is 26 µm (micrometers), we need to convert the units before calculating.
1 pN = 10^-12 N, and 1 µm = 10^-6 m.
Converting the given values:
Tension (F) = 1.2 pN = 1.2 * 10^-12 N
Displacement (x) = 26 µm = 26 * 10^-6 m
Now we can calculate the spring constant:
k = F / x = (1.2 * 10^-12 N) / (26 * 10^-6 m)
Dividing these values, we get:
k = 4.62 * 10^-8 N/m
Therefore, the spring constant of the DNA strand is approximately 4.62 * 10^-8 N/m.