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Chapter 7: Problem 18

A biophysicist grabs the ends of a DNA strand with optical tweezers and stretches it \(26 \mu \mathrm{m}\). How much energy is stored in the stretched molecule if its spring constant is \(0.046 \mathrm{pN} / \mu \mathrm{m} ?\)

Short Answer

Expert verified
The energy stored in the stretched DNA molecule is approximately \(1.495 pJ\).

Step by step solution

01

Convert pN to N

Given, spring constant, \(k = 0.046 pN/渭m\). We need to convert it in standard units, which is N/m. We know that \(1pN = 10^{-12}N\) and \(1渭m = 10^{-6}m\). Therefore, the spring constant, \(k = 0.046 * 10^{-12}N/10^{-6}m = 0.046 N/m \)
02

Convert 渭m to m

In addition, also convert the stretched distance in meters. Hence, \(26渭m = 26 * 10^{-6} m\)
03

Calculate stored energy

The formula for stored energy in a spring is given by, \(E = (1/2)kx^2\). Substituting the given values, we get \(E = (1/2)*(0.046)*(26*10^{-6})^2\)
04

Solving the equation

The equation simplifies to \(E = (1.495x10^{-3})*10^{-12} Joules = 1.495 pJ\)

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Most popular questions from this chapter

A particle slides back and forth on a frictionless track whose height as a function of horizontal position \(x\) is \(y=a x^{2},\) where \(a=0.92 \mathrm{m}^{-1} .\) If the particle's maximum speed is \(8.5 \mathrm{m} / \mathrm{s},\) find its turning points.

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The force on a particle is given by \(\vec{F}=A \hat{i} / x^{2},\) where \(A\) is a positive constant. (a) Find the potential-energy difference between two points \(x_{1}\) and \(x_{2},\) where \(x_{1}>x_{2} .\) (b) Show that the potential energy difference remains finite even when \(x_{1} \rightarrow \infty\)

How much energy can be stored in a spring with \(k=320 \mathrm{N} / \mathrm{m}\) if the maximum allowed stretch is \(18 \mathrm{cm} ?\)
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