Answered

Biophysicists use an arrangement of laser beams called optical tweezers to manipulate microscopic objects. In a particular experiment, optical tweezers exerting a force of0.373 pN were used to stretch a DNA molecule by 2.30 μm.What was the spring constant of the DNA?Express your answer with the appropriate units.

Answer :

Answer:

[tex]K = 1.622 * 10^{-7} \frac{N}{m}[/tex]

Hence, the spring constant is equal to [tex]0.1622[/tex] [tex]\frac{uN}{m}[/tex]

Explanation:

As we know that

[tex]F = Kx[/tex] ----------Equation (1)

Where F is the force

K is the spring constant and

x is the displacement of the spring on application of force F

Given

[tex]F = 0.373[/tex] pico Newton

[tex]F = 3.73 * 10^{-13}[/tex] Newton

Displacement  of the spring [tex]x = 2.30[/tex] micro meter

[tex]x = 2.30 * 10^{-6}[/tex] meter

Substituting the given values in above equation (1), we get -

[tex]3.73 * 10^{-13} = K * 2.30 * 10^{-6}\\K = \frac{3.73 * 10^{-13}}{2.30 * 10^{-6}} \\K = 1.622 * 10^{-7} \frac{N}{m}[/tex]

Hence, the spring constant is equal to [tex]0.1622[/tex] [tex]\frac{uN}{m}[/tex]

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