Typically when we describe falling objects in a physics class, we say \"ignore r
ID: 1772571 • Letter: T
Question
Typically when we describe falling objects in a physics class, we say "ignore resistive forces". In this problem, we'll estimate which resistive force dominates for different objects. If we have a sphere moving in a fluid of density, dauid, and the object has a radius, R, then it will experience two resistive forces, drag and viscosity as given by the equations: drag viscouS For air and water, here are the values of the parameters that occur in these equations. Density (d) 1.2 kg/m3 1.0 x103 kg/m3 Drag coefficient (C) 0.20 0.25 Viscosity (H) 2.0 x 10-5 N-s/m2 0.8 x 10-3 N-s/m2 Air Water Since we are only interested in the approximate scale of the forces, we will model our objects by spheres, even though they are not really spherical. (Corrections can be expected to be less than a factor of 10.)Explanation / Answer
A)
Ratio= Fdrag/Fviscous
Ratio = CdfluidR2v2/6µRv
Ratio = CdfluidRv/6µ
Plugging given values,
R=0.0003, v=0.002m/s, m=0.0003 kg, dfluid=1000kg/m^3, µ=0.0008Ns/m^2 , C=0.25
Ratio = (0.25*1000*0.0003*0.002)/(6*0.0008)= 0.03125
Fdrag/Fviscous = 0.03125
Fdrag < Fviscous
Thus Fviscous is more important for passive sinking of larva.
B)
Ratio= Fdrag/Fviscous
Ratio = CdfluidR2v2/6µRv
Ratio = CdfluidRv/6µ
Plugging given values,
R=0.15, v=0.50m/s, m=0.200 kg, dfluid=1.2kg/m^3, µ=0.00002Ns/m^2 , C=0.20
Ratio = (0.20*1.2*0.15*0.50)/(6*0.00002)= 0.03125
Fdrag/Fviscous = 150
Fdrag > Fviscous
Thus Fdrag is more important for passive sinking of larva.
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