In
1935, Charles Richter established the original “Richter
Scale” for
measuring earthquakes, defining the magnitude of an earthquake
as M = log10(d),
where d is the maximum horizontal movement in micrometers at
a distance of 100 km from the epicenter. For example, a movement
of 1 mm (1000 micrometers) corresponds to a magnitude 3 earthquake.
Modern standards for the design of buildings, dams, power plants
and other structures now use a different system based on the
maximum
acceleration
of the ground, not the maximum movement, but the Richter scale
is still widely used in reporting the strength of earthquakes.
In
this classroom activity, Students design and test
the mathematical functions which convert magnitude into a
scaled linear movement. In trials, "earthquakes"
are produced by voltages ranging from -9V to +9V, corresponding
to earthquakes
from an undetectable magnitude -9 to a catastrophic
+9.
Math
students in particular can be challenged to make the
calculation more efficient by combining the functions into
a single expression.
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