In 1909 Robert Millikan carried out experiments to determine the magnitude of thecharge on an electron.His experiments involved the motion of small, electrically charged droplets of oilbetween two charged metal plates.Some students carried out a similar experiment in a school laboratory.(a) The terminal velocity v of an oil droplet was measured as it fell a known distancein air when the plates were uncharged. Stokes’ law was then used to determine theradius r of the oil droplet. Upthrust was ignored.(i) Show that r = 92ηvρgη = viscosity of airρ = density of oil
Question
In 1909 Robert Millikan carried out experiments to determine the magnitude of thecharge on an electron.His experiments involved the motion of small, electrically charged droplets of oilbetween two charged metal plates.Some students carried out a similar experiment in a school laboratory.(a) The terminal velocity v of an oil droplet was measured as it fell a known distancein air when the plates were uncharged. Stokes’ law was then used to determine theradius r of the oil droplet. Upthrust was ignored.(i) Show that r = 92ηvρgη = viscosity of airρ = density of oil
Solution
The question is asking to derive the formula for the radius of an oil droplet given by Stokes' law. Stokes' law states that the drag force F on a small spherical object moving through a viscous fluid medium is given by:
F = 6πηrv
where: η = viscosity of the fluid r = radius of the spherical object v = velocity of the spherical object
When the oil droplet is falling at terminal velocity, the drag force equals the weight of the droplet. The weight W of the droplet can be given by:
W = 4/3πr^3ρg
where: ρ = density of the oil droplet g = acceleration due to gravity
Setting these two equations equal to each other gives:
6πηrv = 4/3πr^3ρg
Solving for r gives:
r = sqrt((9ηv)/(2ρg))
However, the question asks to show that r = 92ηv/ρg. This seems to be a mistake, as the derivation from Stokes' law does not yield this result. The correct formula derived from Stokes' law should be r = sqrt((9ηv)/(2ρg)).
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