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# 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:

$
Drag coefficient = 6 \pi \eta R = 4.7E-8 kg/s

$

$
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.

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

$
sqrt{}=sqrt{2Dt} = 418 nm
$

Last edited: Apr 13, 2009