We wish to find the speed of collapse (or fall by leaning) of a row of uniformly placed dominoes; see the
sketch below for a side view of the domino arrangement. The relevant variables are:
o
Variable
Symbol
Dimensions
m/s
<
m
Speed of collapse
Domino separation
Domino thickness
Domino height
Gravitation
ю
m
с
m
the
hali hemos
south of the
m/s2
Een
we het
(a) Using the variables given, indicate your repeat variables and determine all dimensionless groups.
(b) If << h, i.e. the dominoes are very thin, then we can neglect the influence of this o quantity and the PI
group involving the speed v can be written as a function of just one other group. If the ratio Nh is a constant,
then how will the speed of collapse vary with the domino's height h?
(c) If the same set of thin dominos, with << h, are set-up on the Moon (which has only 1/6 Earth's value
of gravity), then determine how the speed of collapse would change. Will this speed be faster or slower than
on Earth?
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