Experiments using \"optical tweezers\" measure the elasticity of individual DNA

Question

Experiments using "optical tweezers" measure the elasticity of individual DNA molecules. For small enough changes in length, the elasticity has the same form as that of a spring. A DNA molecule is anchored at one end, then a force F of 1.5nN (1.5*10^-9 N) pulls on the other hand, causing the molecule to extended by 5.0 nm (5.0*10^-9 m), as shown in the figure. (p.s. The source of the external force is the laser beam that traps and moves the polystryene bead in the horizontal direction.)

(a) Find the spring constant of this DNA molecule. What is the direction of the restoring force when the DNA molecule is stretched?

(b) The DNA molecule is now suppressed by the laser trap. Find the magnitude and direction of the restoring force while this DNA molecule is suppressed by 7.0 nm.

Explanation / Answer

Given

DNA molecule anchored at one end and other end is force applied

F = 1.5 nN = 1.5*10^-9 N

the molecule extended by a distance x = 5.0 nm = 5*10^-9 m

we know that the force F = -k*x ===> k = F/x = 1.5*10^-9 /(5*10^-9) N/m = 0.3 N/m

The direction of the restoring force is in the opposite direction of the force applied that is in the -ve x direction

b)

now the DNA is suppressed by Laser trap so that suppressed through 7.0 nm the restoring force is  

F = - K*x

F = 0.3*7*10^-9 = 2.1*10^-9 N

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