Large objects have inertia and tend to keep moving-Newton\'s first law. Life is

Question

Large objects have inertia and tend to keep moving-Newton's first law. Life is very different for small microorganisms that swim through water. For them, drag forces are so large that they instantly stop, without coasting, if they cease their swimming motion. To swim at constant speed, they must exert a constant propulsion force by rotating corkscrew-like flagella or beating hair-like cilia. The quadratic model of drag of the equation given below fails for very small particles. Instead, a small object moving in a liquid experiences a linear drag force, D? = (bv, direction opposite the motion), where b is a constant. For a sphere of radius R, the drag constant can be shown to be b=6??R, where ? is the viscosity of the liquid. Water at 20?C has viscosity 1.0

Explanation / Answer

Answer for A: 100 micrometer swimming at 1mm/s

A: 9.4 x 10^(-10) N   use D=bv (this is given)      b=6(pi)(n)R where R = 100 micro meters (100/1000000)/2 and n= .001 N s/m^2 (this is given)

                                              6(pi)(.001)(.00005) = b   then b(v) = b(.001 m/s) (v is given a 1 mm/s convert to m/s)

Answered B for 2.0 micrometer swimming at 22 micrometers/s

B: 4.1 x 1-^(-13) N same formula as in A but with different R and v

C: 1.8 m/s^2                           V=(4/3)(pi)(r^3),     m = V(density) = V(1000 kg/m^3) now you have mass

                                              F=ma so a=F/m   use your F rom part A and the mass you just calculated

D: 99 m/s^2    same as part C but different R and F(use the ones from part B)

                                   You have a lot of really small numbers to work with so pay careful attention

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