# Homework Help: Terminal Velocity In Glycerin 2.10 in Classical Mechanics

1. Sep 17, 2011

### thomaslanny

Terminal Velocity In Glycerin 2.10 in "Classical Mechanics"

1. The problem statement, all variables and given/known data
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 flin = 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 vter. 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 flin = 3*pi*n*D*v and fquad=kpAv2 (p being density) with k = 1/4 and compute fquad/flin at the terminal speed

2. Relevant equations
v(t) where t = characteristic time = 0.63vter
vter = g*t
0.95vter = 3t where t = characteristic time
Fbouyancy = (pi/6)d3p*g (p being density of fluid)

3. 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.

2. Sep 17, 2011

### rude man

Re: Terminal Velocity In Glycerin 2.10 in "Classical Mechanics"

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

3. Sep 17, 2011

### thomaslanny

Re: Terminal Velocity In Glycerin 2.10 in "Classical Mechanics"

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