Speed of swimming bacterium

Discussion in 'Physics' started by boks, Apr 13, 2009.

  1. boks

    Thread Starter Active Member

    Oct 10, 2008
    218
    0
    A bacterium with a diameter of 5 microns is able to generate a maximum force of 1000 pN. How fast will it swim in water at 293K where viscosity = 1*10^-3 kg/ms?

    Stokes:

    <br />
Drag coefficient = 6 \pi \eta R = 4.7E-8 kg/s<br />
<br />
<br />

    <br />
v_{drift} = \frac{f}{Drag coefficient} = \frac{1000E-12 N}{4.7E-8 kg/s} = 2.1 cm/s

    All too fast, isn't it?

    Calculate how far the same bacteria will travel in 1s due to Brownian motion.

    D=\frac{k_BT}{Drag coefficient}=8.7E-14 m^2/s

    <br />
sqrt{<x^2>}=sqrt{2Dt} = 418 nm<br />
     
    Last edited: Apr 13, 2009
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