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Solutions to 2010 Monthly Questions
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October 2010: From Sunrise Difference to Intercity Distance
This problem is from the book of puzzles Mad About Physics by Jargodzski and Potter.
Wiley & sons. 2001. To fully appreciate it:
(1) make a prediction with some rationale
(2) try it to see what really happens
(3) understand what happened.
Three holes are drilled into a metal can the size of a 1 kg package of infant formula. The
first hole is halfway between the bottom of the can and the water level, which is kept
constant by adjusting the flow from a faucet. The other two holes are, respectively, ¼ and
¾ of the distance from the can’s base.
The question is: predict how far the water will fall from each hole. In other words, predict
s (see diagram) for each hole.
Extra Question
I’ve had a prior question similar to this one, but I love to solve for several unknowns, so here is a balancing question.
Balance
N2 + CaC2 + H2O àNH3 + CO2 + CaO
ANSWER
We’ll balance by solving for each of the unknown coefficients:
a N2 + b CaC2 + c H2O àd NH3 + e CO2 + f CaO
Atom to be balanced
Equation to balance the number of that atom
N
2a = d
Ca
b = f
C
2b = e
H
2c = 3d
O
c =2e + f
Starting with the simplest equation involving
calcium, let b = f =1.
For carbon: 2b = e,
So e = 2(1) = 2.
For oxygen: c =2e + f
c = 2(2) + 1 = 5
For hydrogen 2c = 3d
2(5) = 3d
d = 10/3
For nitrogen 2a = d
2a =10/3
a = 5/3
5/3 N2 + 1 CaC2 + 5 H2O à10/3 NH3 + 2 CO2 + 1 CaO or multiplying through by 3:
5 N2 + 3 CaC2 + 15 H2O à10 NH3 + 6 CO2 + 3 CaO
Solution to February 2010 Question of the Month
This chemical storage cabinet is full of rust. What is the cause of the corrosion? Why is it concentrated along the edges of the cabinet? Why is most of it above the level of the top shelf?
ANSWER
Corrosion of metal involves the loss of electrons. In most cases it first occurs at stress points, where electrons concentrate themselves and leak off more easily. That's why it appears along the edges of the cabinet's doors and walls. One type of chemical that catalyzes oxygen's "theft" of electrons from metal is acid. Acids should be stored in wooden cabinets; otherwise, if acid containers are not properly sealed or if a minor spill occurred on the side of the bottle, acidic vapours will promote rusting of metal.
In the bottom shelf of the cabinet I found a bottle of glacial acetic acid. Its vapours are not only corrosive but flammable, which explains why it was placed alongside alcohol,sodium and other combustibles. Because of its acidic properties, however, acetic acid should not be in a metal cabinet. But unless the bottle was originally on the top shelf, if glacial acetic acid was mainly responsible for the rusting, why would the vapours emanating from the bottom shelf only attack at the level above the top shelf, especially when the density of CH3COOH vapour is higher than that of air?
Another possibility is that at one point in time other acids were stored on the top shelf. A third hypothesis comes to mind if you notice the test tubes to the right of the picture. They contain solid iodine. To the right of those test tubes(out of the picture range) is an old bottle with blackened plastic underneath the lid. The discoloration strongly suggests sublimation, the process by which solid iodine becomes corrosive iodine gas, which likely rusted the edges of the metallic cabinet.
Solution to March 2010 Question of the Month
A sugar cube was placed in a candle flame for about eight seconds. It did not ignite, but it did turn black. With a separate pair of tongs some cigarette ashes were placed in a second candle flame. The ashes did not ignite, as expected. But when the cube was coated with ashes it burst into flames in less than eight seconds. Why?
ANSWER
Cigarette ash contains metals and metal oxides that act as catalysts for the combustion of sugar.
The tobacco plant preferentially absorbs other harmful metals such as Cd(linked to pancreatic cancer). Another reason not to smoke!
Solution to April 2010 Question of the Month
What chemical am I?
See how many clues you need before you are convinced of being correct.
1. I am a large molecule detected in the vomeronasal (Jacobson's) organ of snakes, giraffes and other animals. In mammals the sensory data from the base of the nasal cavity then travels directly to the brain's amygdala, one of the centers of emotional learning.
2. Writing for the Smithsonian, Jennifer Margulius does not mention this molecule directly, but it's what male giraffes detect in the urine of females if they subsequently engage in a slow neck-rubbing foreplay and prompt humping.
3. With an identical alpha subunit to that of the follicle stimulating hormone, it contains 92 amino acids in the human version but 96 in almost all other vertebrate species.
4. Since humans have a difficult time detecting this molecule with their own senses, they rely on another chemical which makes the presence of this molecule visible. Most women are only interested in this molecule when trying to conceive. On a graph, its concentration peaks like a sole stalagmite only at the time of ovulation.
ANSWER
The molecule is the glycoprotein leuteinizing hormone (LH), produced by the anterior pituitary gland. In case you are wondering, the gene that codes for this protein(which also plays a role in male testosterone production) is found on the sixth chromosome. More interestingly the chemistry of ovulation kits is described in detail at the http://www.madsci.org/posts/1268094346.Ch.q.html by the biochemist Peter Hughes.
Solution to May 2010 Question of the Month
If water was the only matter absorbing heat on our planet, we receive enough energy to evaporate 10 m of H2O per year from its oceans. What three additional pieces of information do you need to calculate the number of joules received by the earth every year?
ANSWER
You need:
(1) the DH for H2O(l) = H2O(g) + 41 kJ at 10oC, the earth's average temperature.
(2) the earth's radius = 6378 km
(3) the percent of earth covered by water (70%)
Solution to June 2010 Question of the Month
When a lawn is left to fend for itself, dandelions and other so-called "weeds" take over. Dendelions, especially, seem to have such a marked advantage over grass. Why?
ANSWER
Part of the reason is that dandelions photosynthesize faster than Kentucky bluegrass, and they need less water. The reason is based on a combination of biochemical and anatomical differences. In bluegrass and other so-called C-3 plants, CO2 and O2 compete to bind with ribulose-1,5 diphosphate(RuDP), especially when we have normal high O2 to CO2 ratios. The problem with the competition is that when oxygen binds to RuDP, neither sugars nor ATP are produced.
The dandelion does not initially bind CO2 to RuDp; it uses the enzyme PEP carboxylase whose high affinity for CO2 allows leaf pores to remain open for less time, thus conserving water. PEP carboxylase also facilitates the formation of a four carbon compound which turns into two products that are then transported to a different part of the leaf, where concentration of oxygen is lower. CO2 is released from the C-4 compounds; it combines with RuDP and goes on to be part of sugars with far less wasteful competition from oxygen.
Dandelions also reproduce faster than grass. Although both grass and dandelions can grow from roots, a dandelion"flower" is really a composite of several miniature flowers, each of which turns into a seed that is transported to different lawns by a fluffy parachute-like attachment. These seeds are produced without pollination; they are are effectively clones of the mother. So if the mother was managing perfectly well in one environment, it guarantees that her daughters will fare just as well. Kentucky bluegrass takes longer to flower, and it requires pollination.
Source: Raven, Evert, Curtis. Biology of Plants. Worth. Second Edition
Solution to July 2010 Question of the Month
Use only earth's gravitational acceleration, the moon's period and earth's radius to calculate the distance to the moon.
Solution to August 2010 Question of the Month
Princeton University’s molecular biologist Bonnie Bassler has continued to reveal that nature is stranger than science initially supposes. She discovered that before bacteria conjugate, produce spores, form biofilms, cause disease or bioluminesce, they first take a “census of their population”. This is done by “quorum sensing” which involves the release and detection of signaling molecules. Surpassing the appropriate threshold concentration of these molecules activates genes responsible for a specific bacterial behavior. Prior to her work, it was never imagined that crucial bacterial functions were modulated by social interactions.
From a more meticulous point of view, another surprise to come out of her research is the chemistry of an autoinducing molecule for the bioluminescent bacteria Vibrio harveyi.
a) Looking at the structure below, what is unusual about this biomolecule, a furanosyl borate diester?
b) And here’s an even more interesting question: how can knowledge of quorum sensing potentially help us with the problem of antibiotic resistance?
ANSWER
a)Although boron is present in seawater, it was not known to be incorporated in biological molecules.
b) Antibiotics work by disrupting bacterial growth. The antibiotic molecules are usually mimics that compete with a bacterial building block. But the variants that have not been fooled by the mimic become increasingly more common through natural selection. These bacteria are no longer killed by say, penicillin. (In this specific case the resistant bacteria have enzymes that break down penicillin.)
But knowledge of quorum sensing can lead to the design of molecules that will interfere with autoinducing molecules. In other words by short-circuiting bacterial communication, the disease-causing effects of pathogenic bacteria will not materialize.
McKenzie, Kathleen M. and al. Chemical Communications 2005, 4863-4865
Bassler, Bonnie http://www.molbio.princeton.edu/index.php?option=content&task=view&id=27
Biodiversity DVD, Howard Hughes Medical Institute
http://en.wikipedia.org/wiki/Quorum_sensing#Anti-quorum_sensing
Solution to September 2010 Question of the Month
I was reading about Jack Tatum’s death when I noticed that a wasp had found a piece of my bitten, unripe pear on the deck. The fragment was about a centimeter in length but heavy enough to prevent the wasp’s takeoff. Instead the wasp dragged it across the floor for about two and a half meters until it reached the edge of the deck. Once off the edge, the wasp was able to fly away.
What do you infer from the above observations? Do birds have similar problems?ANSWER
By observing the wasp, I realized it needs a lot more of its own force to get off the ground than to propel itself in flight. (When flying, the motion of air molecules around its body and wings provide part of the upwrd force.) Here’s the abstract of a study done on the liftoff force generated by pigeons.
Measurements of the force generated by the legs of rock doves Columba
livia during vertical and near-vertical take-off showed that the birds were
able to develop an upward directed force of from 1-3 to 2-3 times their body
weight. This force resulted in an instantaneous acceleration of 15-63 ms~2at
maximum thrust. Motion pictures taken during the take-off showed that as
the birds' feet left the experimental perch, their wings were in the overhead
clap position. We suggest that the vertical take-off in birds is accomplished in
three stages; leg thrust, clap-and-fling and steady-state flight.
Dial, Kenneth B. J. exp. Biol. 176, 31–54 (1993)
I could not find anything on insects, but if wasps can also develop an upward force up to three times their body weight, it would have been up against a mass of somewhere between 0.6 and 1 gram(the pear is mostly water with a density of 1g/cm3). But the average mass of a wasp is only about 90 mg. Even if it could generate an upward force three or even five times its weight, it would still fall short of the force needed to directly takeoff with my pear. Since the 1960’s, it’s been difficult for engineers to successfully design vertical and/or short take-off and landing aircraft not because they have been trying to takeoff with my pears, but because the winged aricraft can’t generate the lift to overcome its own weight.
Solution to October 2010 Question of the Month
Use the following data to estimate the approximate aerial(direct)distance between the town of Gaspe and Montreal.
- We'll assume that they are both at a latitude of 47oN (almost true: 45.5o for Montreal and 48.8o for Gaspe)
- Sunrise for Gaspe on Aug 27h, 2010 : 5:27 AM
- Sunrise for Montreal on Aug 27th, 2010: 6:09 AM
- Radius of the earth(Re): 6378.1 km
- R = radius of circumference at latitude 47o(needed to calculate the speed of the earth’s rotation at that latitude)
ANSWER
r/Re = cos 47
r = Re* cos 47
=6378.1 km(cos 47)=
= 4349.85 km
The speed of the earth’s rotation at that latitude is:
2p(4349.85 km)/(24h*60min/h)=
18.98 km/min
There is a 42 minute difference in sunrises,
So 18.98 km/min(42 min) =797 km; with significant figures: 8.0 X102 km gap between Gaspe and Montreal
(accepted value = 782 km)
Solution to November 2010 Question of the Month
Here's a riddle. Consider an element in lamps and one in air. There's also nobelium and 5 others. From the symbols of the latter we can form a word describing humans. What is the word?
ANSWER
Na is in lamps. N2 is in the air. Nobelium' s symbol is No. Five other symbols of elements begin with "N": niobium(Nb), nickel(Ni), neptunium(Np), neon(Ne) and neodymium(Nd). With the 2nd letter of each symbol, we form the word biped, which describes humans.
Solution to December 2010 Question of the Month
I didn't have the answer to the question when I asked it, but Veronica C. untangled the mystery!.
Watch this video and try to figure out why so many colours are created by simply adding ZnO to burning methanol. Someone found it so incredulous that they thought my ZnO was contaminated with other substances. It's unlikely, but I'll check the hypothesis by using another source of zinc oxide to compare the results.
ANSWER
After a lot of research I found that ZnO has two distinctive colours, red and green. This explains the colours that are seen in the video, the blue is from the methanol. It produces two colours because when the powder hits the flame, it does so at different places and the temperature of the flame is different, so it produces a different colour depending on the temperature of the point of contact with the flame.To be more precise:
ZnO is red between 568 to 704 degrees Celsius
ZnO is green between 704 to 948 degrees Celsius.
A methanol flame's maximum temperature is 1152K which is about 880 degrees Celsius so this proves that this both colours could have been produced from the ZnO.
The sparks that are seen are ZnO particles that have fallen into the solution then were lifted with the flame, the methanol evaporated out of them and just like any dust particle they produced a spark.
I hope this explains it!
-Veronica Chudzinski
references:
Bulletin of the National Research Council Volume 5
If temperatures quoted seem high, they are in fact plausible; see: Flame Temperatures
Extra: Why time moves more slowly at high speeds.