Welcome to Exercise #3: The Age of Nittany Valley

9/30/2015

Assessment

Welcome to Exercise #3: The Age of Nittany Valley
If you visit Happy Valley, home of Penn State’s University Park campus, you will be in a valley, but there used to be a mountain right over your head. Many other
valleys (although not all) in the folded Appalachians are similar. Mount Nittany is the "bottom" of a fold, and Happy Valley is the "top" of a fold (as seen in the
diagram below).
Most of the rocks in Pennsylvania are sandstone (which erodes slowly in Pennsylvania’s climate), or shale and limestone (which erode rapidly in Pennsylvania’s
climate). The limestone, most of the shale and some of the sandstone were deposited in a shallow sea, while some of the shale and sandstone were deposited near
the sea. When the proto­Atlantic closed, with Africa and Europe crashing into North America about as rapidly as your fingernails grow, the rocks in the collision
zone were bent (geologists call this folding). If you try to bend your pencil, you’ll find that it tends to break at the peak of the bend. The same was true of
Pennsylvania’s rocks­breaks or cracks formed at the tops of the folds.
Streams formed in these cracks and cut downward. Then, landslides and other mass­wasting processes widened the stream valleys. Often, the streams cut through
slow­to­erode sandstones and into the faster­to­erode shale or limestone below. Once that happened, the streams cut down quickly, the sandstone blocks fell off
the cliffs left behind, and what had been a mountain peak became a valley. As a new valley formed in a place that had once been a mountain crest, the adjacent
regions that had once been valleys were being eroded more slowly, often eroding down to the resistant sandstones and then eroding more slowly. Eventually, the
former valleys were left higher than the new valleys, so that the former valleys became the new mountains. Today, in central Pennsylvania, you will find that the
mountains have hard­to­erode sandstone on top, while the rocks beneath the valleys are easy­to­erode limestone or shale. The shape of the landscape has long
ago "forgotten" the mountains built during the great collision, and is now controlled mostly by the resistance of the rocks to erosion.
The easy­to­erode rocks under the University Park campus, the rest of Happy Valley, and many other valleys in Pennsylvania are limestone (or a close relative of
limestone called dolomite, but we’ll just call it all limestone to keep it easy for you). The limestone often contains caves. The caves are spaces that were left when
the rocks dissolved in water in the ground. Eventually, that water flowed out to creeks and down the creeks to the sea, where shelly critters grabbed the dissolved
limestone and used it to form shells, the raw material for new limestone. As caves formed and their roofs collapsed, and as rocks were dissolved along small cracks
or right beneath the soil without forming caves, the valley floor was lowered.
This exercise is much easier than it may seem at first! Don’t panic until you’ve really tried it. (Don’t panic even then; panic doesn’t help anything.) Please begin by
studying the diagram below. Please also note that your neighbor may be doing a slightly different calculation than you are­­we have made many versions of each
question in this exercise, with slightly different numbers. The techniques, the difficulty, and the learning outcomes are all the same, and the numbers are similar
enough to allow you to learn the material, but different enough to encourage you to master the exercise yourself. (Copying from a neighbor is also prohibited
because it is academic dishonesty.)
You will only get one chance to submit this exercise so be sure to review your answers carefully before submission. You can, however, save your answers as long
as you do not submit them first. Do not forget to hit the submit button when you are finished. This exercise will NOT automatically submit since there is no time
limit (except to submit it by the due date shown on the calendar). This exercise will be graded automatically.

1.

If you drive for 2 hours, at 60 miles per hour, you will have traveled 120 miles. This is a very common type of calculation, involving three quantities: distance,
rate and time. If you know just two of these three quantities, you can always calculate the third. Thus, if you want to know how much time it is going to take
you to get somewhere, and you know that the distance is 120 miles and you will drive at a rate of 60 miles per hour, you can divide the 120 miles by the 60
miles per hour and obtain a time of 2 hours.

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For this exercise, you will be relating distance, rate and time. The distance we will work with is the depth of Happy Valley. (Remember that even more rock has
been removed than the depth of the valley, because the site of the modern valley once was higher than the site of the modern mountain, and the site of the
modern mountain has been lowered somewhat as well. And, the rocks had to be deposited, raised and bent before the erosion could occur. So, you’re
calculating how much time was involved in a small part of the much longer history of central Pennsylvania.) We can measure how rapidly rock is being
dissolved and washed out of Happy Valley, and use some fairly simple physical ideas to turn that into the rate at which the valley floor is being lowered. That
gives you a distance (the valley depth) and a rate ( the speed at which the valley floor is being lowered), allowing you to calculate the time that has been used
in the lowering. To get the correct answer, you will calculate the time from which equation:
A) Time=Distance multiplied by Rate
B) Time=Distance plus Rate
C) Time=Distance minus Rate
D) Time=Distance divided by Rate
E) Time=Distance squared multiplied by Rate squared
2.

First, we must calculate how rapidly limestone is being removed from the floor of the valley. Most of the limestone leaving the valley is dissolved in Spring
Creek. Later, we will discuss chunks of limestone being rolled, bounced or otherwise carried out of the valley by Spring Creek, although these are rare. There is
almost no loss or gain of limestone in the wind, and meteorite falls are VERY rare and can be ignored.
About 1 m (just over 3 feet) of rain per year falls on Happy Valley. About two­thirds of this is used by trees and evaporated, and one­third leaves the valley in
Spring Creek. That water which leaves in Spring Creek, called runoff, contains a lot of dissolved limestone, which is picked up from the ground. Spring Creek
water averages about 0.33 kilograms (0.33 kg) of limestone for each cubic meter (1 m3) of water. (1 kg is 2.2 pounds, and 1 m3 is a cube just over 3 feet on a
side), so the limestone in the water weighs 0.33 kg/m3.
If Spring Creek collects a layer of water 0.3 m thick from all of Happy Valley each year (0.3 m3 from each square meter or m2), and each cubic meter of Spring
Creek water contains 0.32 kg of limestone, then how much limestone is lost from each square meter of Happy Valley each year, on average? (Note that the
units are included and calculated properly for you here, but you should understand what was done, and why.) 0.3 m3/m2/yr x 0.32 kg/m3 = __________
kg/m2/yr.
A) .096
B) .0096
C) .36
D) .96
E) .036

3.

The answer from question 2 shows that the rock lost from each three foot by three foot plot of land in Happy Valley each year weighs a bit less than a small
hamburger patty. But, how thick is the layer of rock that is lost each year? We need the density of the rock to calculate the thickness lost. The density of
calcite, the main mineral in limestone, is about 2700 kilograms per cubic meter (2700 kg/m3), which is almost three tons for each three foot cube. (Rock is
heavy!). There is a tiny bit of space between some of the grains in the rock, so let’s use 2550 kilograms per cubic meter (2550 kg/m3) for the density. For
simplicity, let’s round off the answer from question 2, to obtain one­tenth of a kilogram from each square meter each year, or 0.1 kg/m2/yr (that is 0.22
pounds or 3.5 ounces, which is a bit less than the 4 ounces in a hamburger patty). Dividing this yearly rate at which each square meter of the valley is losing
kilograms of rock by the density in kilograms per cubic meter yields the rate at which the valley surface is being lowered in meters per year (m/yr). The
lowering rate is 0.1 kg/m2/yr divided by 2550 kg/m3 =____________m/yr (note: your calculator probably shows a whole bunch of digits; just choose the
answer below that is closest).
A) 0.000019 (your calculator might also show this as 1.9×10­5 or something similar)
B) 0.000039 (your calculator might also show this as 3.9×10­5 or something similar)
C) 0.39 (your calculator might also show this as 3.9×10­1 or something similar)
D) 0.09 (your calculator might also show this as 9.0×10­2 or something similar)
E) 0.0039 (your calculator might also show this as 3.9×10­3 or something similar)

4.

At its deepest, Happy Valley is close to 330 m (a bit over 1000 feet) deep, and it once was at least as high as the mountains around the valley. Let us call the
thickness of rock removed from the valley each year, your answer in the previous blank, 0.000033 m. Then the depth of the valley, 330 m, divided by the
erosion rate, 0.000033 m/yr, yields the number of years it took to hollow out Happy Valley, __________yr. This should be a large number.
A) 10,000
B) 1,000,000,000
C) 100,000
D) 10,000,000
E) 100

5.

The correct answer to question 4 indicates a lot of years. Could we have really screwed up the calculation, so it is way off? Well, suppose that for all of history
until yesterday, Happy Valley was as wet as the wettest places on Earth. (Making central Pennsylvania that wet is almost impossible, because the wettest
places on the planet have climatic characteristics that are not possible in Happy Valley. But, just suppose.) Then, the stream would have been carrying rock
away faster than we calculated above. In addition, suppose that lots and lots of limestone from Happy Valley has been carried away as chunks in the stream,
again meaning that rock has been removed faster than we calculated. (There is almost certainly a grain of truth to this one, but not a lot; observing Spring
Creek shows that most of the rocks in transport are actually originate in the mountains­­the valley rocks mostly dissolve, and the mountain rocks wash down.
But, just suppose.) Call the time to hollow out the valley, from question 4, an even 10,000,000 (10 million) years. Now, if the rock was actually removed 12
times faster than used in that calculation (about as much faster as is possible with what we just told you), what would the new estimate of the time to hollow
out the valley using this new, faster rate be? ________yr (your calculator may not show exactly what is listed below; if not, take the one that is closest). (If
you’re not sure how to proceed, ask yourself this question: if you dig faster, does it take a longer or shorter amount of time to reach the bottom?)
A) 833,333
B) 8,333
C) 120,000,000
D) 12,000
E) 1,200

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6.

In question 4, you estimated the time for lowering the surface of Happy Valley enough to account for the modern difference in elevation between the top of
Mount Nittany and the bottom of the valley. In question 5, you saw that you could change that estimate a good bit. But, to make a 10­fold change in the
estimate, you had to assume things that are really almost impossible, such as making central Pennsylvania one of the wettest places on Earth. We could tweak
the assumptions in the calculation to move the estimate either way by a few­fold (so 10 million years could become 3 million years, or 30 million years, without
too much trouble), but shifting the answer a whole lot further than that requires impossibilities or miracles­­just because we can shift it to 3 million years or
even 1 million years does not mean we can shift it to 10,000 years, which would require digging the valley 1,000 times faster than is happening now, which
nature really cannot do here.
We can say something else important, though. Whatever the time needed for deepening the valley, the geologic story of central Pennsylvania must be much
longer than that time required to deepen the valley, that is only the last act of a long play. The text of this exercise refers to several reasons why we know that
the story is longer than the deepening of the valley. Which statement below describes something indicating that the region is much older than calculated so far
in this exercise? Two of the five answers are correct; pick one of the correct ones for full credit.
A) Mountains are always old.
B) The mountain top is being eroded as well as the valley, so more rock must have been removed from the valley than you calculated to give the modern
difference in elevation between mountain top and valley.
C) Dents in the tops of all the buildings at University Park show that meteorites fall in much faster than the professors admit because we know professors
are liars, the meteorites are carried down the stream, so that means that the time to dig the valley was much more than 10 million years.
D) The rocks needed to be deposited, hardened, and bent before being eroded, and all of that took time.
E) Sea­floor spreading made Death Valley.

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