Terminal Velocity In Glycerin 2.10 in Classical Mechanics

[thomaslanny]

Terminal Velocity In Glycerin 2.10 in "Classical Mechanics"

Homework Statement

For a steel ball bearing (diameter 2mm and density 7.8g/cm3) dropped in glycerin (density 1.3g/cm3 and viscosity 12 N s/m2 at STP) the dominant drag force is linear drag given by f_lin = 3*pi*n*D*v where D is the sphere's diameter, v is velocity, n is the viscosity of the fluid
a) Find the Characteristic time and terminal speed v_ter. Include Archimedes buoyant force as a 3rd force.
b) How long after it is dropped from rest will the ball bearing have reached 95% of its terminal velocity
c) Use f_lin = 3*pi*n*D*v and f_quad=kpAv² (p being density) with k = 1/4 and compute f_quad/f_lin at the terminal speed

Homework Equations

v(t) where t = characteristic time = 0.63v_ter
v_ter = g*t
0.95v_ter = 3t where t = characteristic time
F_bouyancy = (pi/6)d³p*g (p being density of fluid)

The Attempt at a Solution

So far I've gotten for part a)
(3.2672x10^-8 kg)*9.8m/s = 3.202E-7 N (for gravitational force)
3*pi*n*D*v = 3.202E-7N - (pi/6)d³p*g

Is this correct? Solve for v above and that's terminal velocity? if so I'm good for the rest of the problem.

 

[rude man]

Looks A-OK. I did not check your gravitational force number.

 

[thomaslanny]

Yeah it's actually 3.2019E-4 N for the F... my mistake