- #1
sarmar
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Homework Statement
Calculate the terminal velocity for a pollen grain falling through the air using the drag force equation. Assume the pollen grain has a diameter of 7 µm and a density of 0.3 g/cm3.
Homework Equations
Vterm= sq.rt of 2mg/pA
Volume= 4/3pi*r^2
Density = m/v
The Attempt at a Solution
I am given the answer but need to show how to get there.
Here is what I have, can someone point out where exactly I am going wrong?
Thank you!
Vterm= sq.rt of 2mg/pA
p= air density of 1.3kg and
A = cross section of the pollen grain
A= 7µm = 0.000007m
To find mass of pollen grain:
radius= 1/2diameter
= 1/2(0.000007)
= 0.0000035m
Volume= 4/3pi*r^2
= 4/3pi(0.0000035)^2
= 5.13x10^-11 m^3
Density = m/v
m=DV
=0.3g/m^2 (5.13x10^-11 m^3)
= 1.54 x10^-11g
to kg = 1.54 x10^-14 kg
So, Vterm= sq.rt of 2mg/pA
Vterm = sq.rt. of 2(1.54 x10^-14 kg)(9.8m/s^2) / (1.3kg/m^2)(0.000007m)
=0.0018m/s
But I know this is wrong since I am given the final answer, which is 0.145m/s
I've worked it out so many times and I'm stuck. Please help.