Question

Coasting at Low Reynolds The chapter asserted that tiny objects stop essentially at once when stop pushing them. Let's see. a. Consider a bacterium, idealized as a sphere of radius 1 um, propelling itself at 1 ums-1. At time zero the bacterium suddenly stops swimming and coasts to a stop, following Newton's Law of motion with the Stokes drag force. How far does it travel before it stops? Comment. b. Our discussion of Brownian motion assumes that each random step was independent of the previous one; thus for example we neglected the possibility of a residual drift speed left over from the previous step. In the light of (a), would you say that this assumption is justified for a bacterium?

Answer 1

ANSWER;

(a) From the given data, proportional to the viscous drag force is velouty of the object FL-v F =-&v means) == &v both side amplying integration JA -- ) ** v = vo Exp (- + 2 ) de l = vo Exp(-42) x = 9 vo tept-HB) at --0 - No Chere & = 6nr, m= 4 Tv 3p)

- ( 9 Tr 3p) vo 67 nr = 2 g2 pro 9n 2 (100m) ² (103 kg / m3) (10 m/s) 91103 pais) na 2x 10m (b) It we consider P bacterium & Pwaters to ignore the Brownian motion of the bacterium from part (a), x (decaleration on distance) is very very short, from our model deceleration is not justified