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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 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}=kpAv^{2}(p being density) with k = 1/4 and compute f_{quad}/f_{lin}at the terminal speed

2. Relevant 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)d^{3}p*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)d^{3}p*g

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

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# Terminal Velocity In Glycerin 2.10 in Classical Mechanics

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