Calculations
of Plate Motions (15 points)
The goal of all science is to
understand the natural world. To do this, scientists frequently use
mathematical measurements and calculations. In this assignment, you’ll use
some simple math to calculate plate motions.
You will
need a calculator and a ruler to do this assignment.
Background
(Note: a forward slash (/) means
"divide," shown as ÷ on most calculators.)
The speed,
or velocity (V), of an object equals the distance (D) it travels divided by the
time (T) it takes to travel that distance: V = D/T (V = D÷T)
The equation shows that we can
solve for V if we know D and T. For example, if you drive a distance of
150 miles, and it takes you 2.5 hours to do it, your velocity is: V = D/T = 150
miles / 2.5 hours = 60 miles per hour.
The V = D/T equation can be
rewritten as D = VxT, which allows us to solve for D if we
know V and T. For example, imagine that you walk at a velocity of 2.3
miles per hour for a time of 3.5 hours. Your distance walked is: D = VxT = 2.3 miles per hour x 3.5 hours = 8.05 miles.
Similarly, the equation can be
rewritten as T = D/V,
which allows us to solve for T if we know D and V. For example, imagine
that a tectonic plate moves a distance of 140 miles at a velocity of 10 miles
per million years. The time it will take is T = D/V = 140 miles / 10
miles per million years = 14 million years.
Use the equations above to solve
the problems below. For each problem, think about what you are trying to
figure out: velocity (V), distance (D), or time (T), and use the appropriate
equation (V = D/T, D = VxT, or T = D/V).
Label your answers clearly (1a, 1b, etc.), and include only your answers in the
work you submit, not the question or problem. For all of your
answers, round to the
second decimal place (for example, 3.58, not 3.57692674).
1.
North Atlantic Widening
We might measure the speed of a
car in miles per hour,
or the speed of a wave in feet
per second. But the Earth’s plates move much more slowly than
cars or waves (although since the plates have been moving for millions of
years, they have still traveled great distances). It doesn’t make sense
to measure plate velocities in units like miles per hour or feet per
second. Instead, we use inches
per year or miles
per million years.
Geologic evidence indicates that
the North Atlantic Ocean began to open about 175 million years ago as
eastern North America broke away from Eurasia and Africa and sea floor
spreading began to form the Mid-Atlantic Ridge (see this figure). Today, the North Atlantic Ocean
basin is 2880 miles wide measured from the continental slopes on either
side. (The continental slope marks the boundary between continental crust
and the oceanic crust, as shown in this figure.) Using V = D/T, calculate the velocity at
which the North Atlantic is getting wider in:
1a. miles per million years
1b. inches per year (To do this second calculation,
take your answer in 1a and divide it by one million (1,000,000) to get miles
per year. (It
will be a very small number.) Then convert to inches per year by
multiplying that number x 12 (because there are 12 inches in one foot) and then
multiplying again x 5280 (because there are 5280 feet in one mile).
2.
Neighbor Cities along the San Andreas fault
San Diego lies on the Pacific
Plate, and San Francisco lies on the North American Plate. The two cities
are presently 470 miles
apart. However, the transform (side-by-side) movement of the two plates
along the San Andreas fault is carrying San Diego
closer to San Francisco at an average velocity of 2.0
inches per year. (See
this figure; San Diego (not labeled) is a bit south of Los Angeles.)
2a. Assuming a constant velocity of 2.0
inches per year, how
much farther apart, in feet,
were the two cities when the Egyptian pyramids were built 5500 years ago?
(Calculate the number of inches and then divide by 12 to get feet.)
2b. How much farther apart, in feet,
were the two cities when America declared independence in the year
1776?
2c. The velocity of 2.0 inches per year can
be converted to miles per
million years as follows: 2.0 / 12 inches per foot / 5280 feet per
mile x 1,000,000 = 31.6
miles per million years. Given that the two cities are
presently 470 miles apart, at this velocity (31.6 miles per million years), how much time (in millions of years) will it
take for San Diego and San Francisco to become neighbor cities?
3.
The Hawaiian Hot Spot and the Velocity of the Pacific Plate
This
figure and the associated text from chapter 2 in your book shows how the
Hawaiian Islands formed one after another, in sequence, as the Pacific Plate
slid northwest across a mantle
plume—a semi-stationary point source of magma welling up from the
mantle. Mantle plumes create localized areas of intense volcanism at the
Earth’s surface that we call hot
spots. The Hawaiian Hot Spot is a classic example, but there
are dozens of others, as this
figure shows. In general, we think mantle plumes stay in one place
while plates slide across them. However, some recent research questions this
assumption, as you’ll see in the last question.
Currently, the mantle plume
beneath Hawaii sits roughly beneath the big island, and lava erupts almost
constantly from Kilauea volcano, on the southeast side of the big island, as
well as from a small seamount called Loihi a few miles
southeast of there. We think all the volcanoes that make up the Hawaiian-Emperor chain formed
over the same mantle plume at different times, before being carried away by the
northwest-moving Pacific Plate. The map at this link shows the locations of the volcanoes
in the Hawaiian-Emperor chain, along with the geologic ages in millions of
years (MY) of some of them. Notice that the volcanoes get older as you
move northwest along the chain. This is what we would expect to see if
the Pacific Plate is moving northwest over a stationary mantle plume.
According to V = D/T, we can
calculate the velocity (V) of the Pacific Plate by dividing the distance (D)
between any of the islands (or seamounts) by their age-difference (T).
See the figure
at this link for the idea.
To do this exercise, print
out the map and table at this link, and follow the directions there.
Then come back and answer the questions below.
3a. From
Column 4, list, in order, the highest velocity, lowest velocity, and average
velocity of the Pacific Plate in miles
per million years. (To get the average, add up the five values in Col 4 and divide
by 5.)
3b. From
Column 5, list, in order, the highest velocity, lowest velocity, and average
velocity of the plate in inches
per year.
3c. Geologists have long assumed that
mantle plume that made the volcanoes in the Hawaiian-Emperor chain stayed in
one place as the Pacific Plate moved across it. This assumption may not
be correct (see the next question), but if it is, how must the direction of the Pacific Plate
have changed to create that “bend” in the chain that you can see on the
map? Approximately when (millions of years ago) did this probable change
in plate direction occur?
3d. Recent evidence may indicate
that the Pacific Plate did
not change direction to create the “bend.” If this is true, how else might the
bend be explained? Read the
short article at
this link before you write your answer.
***
Please clearly label all of your
answers (2a, 3b, etc.).
