Experimental Question 1
Terminal velocity in a viscous liquid
An object falling in a liquid will eventually reach a constant velocity, called the
terminal velocity
.
The
aim of this experiment is to measure the terminal velocities of objects falling through glycerine.
For a sphere of radius
r
falling at velocity
v
through a viscous liquid, the viscous force
F
is given by
F
= 6
πηrv
. Here
η
is a property of the liquid called the
viscosity
. In this experiment you will measure
the terminal velocity of metal cylinders (because cylinders are easier to make than spheres). The diameter
of each cylinder is equal to its length, and we will assume the viscous force on such a cylinder is similar
to the viscous force on a sphere of the same diameter, 2
r
:
F
cyl
= 6
πκηr
m
v
(1)
where
κ
= 1,
m
= 1 for a sphere.
Preliminary
Calculation of terminal velocity (2 marks)
If
ρ
is the density of the culinder and
ρ
0
is the density of the liquid, show that the terminal velocity
v
T
of the cylinder is given by
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 Spring '11
 NA
 terminal velocity, viscous force

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