Homework #1 Humphrey Geology 4880 Fall 2022
Some
notes on the questions and on the answers:
Question 4 is a great example of why you have to be careful when finding
“answers” on the Web. I generally assume
anything on the web is incorrect until checked by an independent means.
1 a)
area of continents ~ 1.5 x 1014m2, from taking 30% of
earths surface. Volume is that area
times 1 m thickness. Answer is this 1m
thickness volume, divided by (volume) output per time ~ 15,000yrs.
b) a little less than 0.1mm/year
c) from the USGS web page the
drainage area is about 4000 square miles.
The volume per year is just the depth times the erosion rate (all in the
same units). Change volume to mass,
using density. Answer on the order of 5
x 109 kg/year
d) Discuss in class, since the
answer is not obvious
2 a) For a block on a slope with no S,
incipient sliding occurs when pghsin(alpha)=pghcos(alpha)tan(phi),
cancelling pgh on both sides, and dividing thru by cos(alpha) gives: tan(alpha) = tan(phi),
or alpha = phi, or alpha = inverse tan(phi)
b)
discuss in class
c) note that ‘g’ cancels out on both
sides of the equation in 3a, therefore phi remains the same
3 for
plots see:
fig1 fig2 fig3 (also fig 4 gives
the relative shapes of 2 common curves.)
This exercise was for several
reasons. I wanted to check your graphing abilities, but I also wanted you to
think about the shape of some of the important curves we will be using. Finally I wanted you to see that the shapes
of curves vary hugely with the coordinate axes.
4
a) Chance
of an impact in one year is 1/75,000,000, assume you will live for 75 years
(makes the calculation easy), then your chances are about 1/1,000,000, or your
chance of dying by asteroid is about 1 in a million per lifetime.
b) There
are many ways to calculate your chance of dying by a landslide. One approach would be to note that the death rate
in the US is about 25 per year, this leads to a probability of 25/300,000,000
per year or less than 1/100,000 per lifetime.
Of course statistics are only as good as the data and interpretation. For example, I would suspect that the number
of deaths in Kansas from landslides is 0, so in Kansas you are much more likely
to die from a meteorite.
However, you should note that
probabilities of infrequent natural events are actually quite difficult to
estimate, and even common events such as river floods are much more difficult
to treat statistically than is commonly believed (and please don’t believe most of the numbers quoted by “media”
sources)
5 discuss in class
