Ballistic vs Hydrodynamic Damping Time
Consider a small spherical particle of mass m, initially at rest, which is acted on by a
constant force F turned on at t = 0. Solve the equation of motion for this particle, which
is F - fv = m dv/dt, where v is the velocity. Show that the particle approaches a constant
velocity vmax = F/f. If the particle is spherical, of radius 100 Å, and of density 1.5 g/cm3,
calculate the time required to attain 99 percent of the final velocity in water ( = 1
centipoise). (At times shorter than this, the molecule has a ballistic type of motion-otherwise, it is heavily damped by viscous drag). Hint: I don't just make up problems
like this; someone else does.