+ 0 1 points | Prev ous Answers ColPhys2016 5.2.WA-032. Find the terminal speed

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+ 0 1 points | Prev ous Answers ColPhys2016 5.2.WA-032. Find the terminal speed of a bacteria (size 6 m) falling in water. The drag force for a small object like a bacteria is given by Farag-Crv where C = 0.02 is the drag coefficient, r is the radius and v is the speed. Take the density of the bacterium to be 1100 kg/m3. (Assume the bacteria is spherical.) 2.032e-5 X What is the acceleration of the object at terminal speed? Express the mass in terms of volume and density. um/s Additional Materials

Explanation / Answer

at the terminal speed

Drag force is balanced by the weight of the body

Fdrag = m*g

C*r*Vt = (rho*V*)*g

Vt is the terminal speed

rho is the density of the body

V is the volume of the body = (4/3)*pi*r^3

C*r*Vt = (rho*(4/3)*pi*r^3*g

0.02*(3*10^-6)*Vt = (1100*(4/3)*3.142*(3*10^-6)^3*9.8)

Vt = 2.03*10^-5 m/sec = 20.3*10^-6 m/sec = 20.3 um/sec is the required terminal speed

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