Friday, March 11, 2005

Answers to "How Things Work" test.

1. Could someone invent an air-breathing engine that burns water?

(o) Yes.
(o) There's no way to know until it's tried.
(o) No, because water puts out fire.
(x) No, because water won't chemically react with oxygen.

"Burning" means the chemical combination of a substance with free oxygen (O_2). Water (H_2O) is what you get by burning hydrogen (H_2). You can't burn what's already burnt!


2. In the drawing below, a rock on a string is being whirled around counter-clockwise in a circle. If the string suddenly breaks, what path will the rock take?

(o) A
(x) B
(o) C
(o) None of the above.

The string is keeping the rock going in a circle. If the string breaks, the rock will just continue in the same direction it was going in just before the string broke. This is Newton's Second Law of Motion.

Interestingly, Aristotelian physics, i.e. the physics widely accepted in Europe from the time of the late Roman Empire until about the 1500s, would predict something like path C (a path that continues curving for a while). The reason is this: Aristotelian physics says objects have "natural" tendencies, which can be subverted by "impulses" (roughly what we mean by force multiplied by how long the forces is applied). When an impulse is applied to an object, it follows the forced motion, and when the impulse is exhausted, the object relaxes to its natural state.

So you could say the rock's natural motion is to fly away from the hand, but the impulse the string gives it keeps it in a circle. If the string breaks the rock continues in a circular way until the impulse is exhausted.

Studies have shown a substantial fraction of 21st century people still believe intuitively in Aristotelian physics. But they're not very good at softball or darts.


3. Can blood clot underwater?

(o) No, it can't dry out.
(x) Yes, the chemistry still works.

The clotting of blood is not just simply drying out, it's a complex cascade of biochemical reactions. That's why it doesn't do a haemophiliac any good to dry the blood off -- in his case, the chemistry is not working. The chemistry obviously works under water, because it works in a wet wound!


4. Why is the sound that bats emit to locate their prey in the dark at such a high frequency, so high it can't be heard?

(o) So the prey can't hear them coming!
(o) No reason. They could use any frequency, really.
(o) They need a really high repetition rate to track rapidly moving targets.
(x) They get more precise information about the prey's location with higher frequency sound.

When you "see" things by reflecting some kind of wave off them, you always get sharper "pictures" with shorter wavelength, or equivalently higher frequency, waves. The reason is, essentially, that only features in your target that are the same size or larger than the wavelength of your wave will perturb it. (Think of boats and waves: the boat will greatly perturb small ripples, or waves up to roughly their size, but a boat won't alter a giant wave at all.)


5. Not long ago the press reported that the Human Genome Project had finished determining "the" DNA sequence of human beings. But don't we each have our own unique set of genes?

(o) Yes, but our DNA sequence is all the same.
(x) Yes, but most of our DNA sequence is all the same.
(o) Yes, but the HGP didn't study the DNA in genes.
(o) No, but our interaction with the environment during growth and development makes us unique.

It's a bit of an error to say they sequenced "the" genome -- they sequenced "a" genome, literally. But the differences in DNA from one person to another are a very, very small fraction of the total DNA, so they do practically know the entire genome. Individual variations are "clean-up" work. Actually, we share most of our DNA with all higher animals. One of the reasons we can share so much DNA with animals
that are nothing like us is that most of our DNA is not used, it's just junk that we carry around.


6.How many bits per pixel are necessary to store an image with a
maximum of 255 colors?

(o) 7
(x) 8
(o) 32
(o) 255

A "pixel" = "PICTure ELement" is the smallest dot in a picture, and if there are 255 colors you need to be able to store 255 different numbers for each pixel, to label the color it might be. A "bit" = "BInary digIT" is a single digit in base 2. So we need as many bits as we need binary digits to store the numbers between 0 and 254.
11111110 in binary is 254, and it has 8 digits, so we need 8 bits.


7. When you throw a ball into the air, it falls back to the ground. So why don't the molecules that make up the Earth's atmosphere all fall to the ground? What keeps them up there?

(x) They do fall, but bounce back up, over and over, forever.
(o) They're so light they fall undetectably slowly.
(o) They're stacked up, higher molecules resting on those lower down.
(o) Wind keeps them stirred up, like bits of paper in a breeze.

Gravity certainly affects air molecules like it affects any other object thrown into the air. So air molecules will fall under the influence of gravity, just like a ball tossed up, and eventually hit the ground (although they may well ricochet off many other air molecules on the way). What's strange to our "common sense," however, is that they then always bounce up again. We might believe they could bounce a few times, but in that case we'd expect them to bounce lower and lower, eventually coming to rest on the Earth's surface.

So why don't they? The key difference between a ball that might bounce on the ground a few times, only to come to rest quickly, and the air molecules is that the ball has about a trillion trillion possible modes of internal vibration. These possible tiny wiggles and jiggles represent places to which the energy of the ball initially found in the bouncing motion can and does disappear. That is, the ball may start out with most of its energy in the bouncing motion, but very quickly this energy wanders off into the bazillions of internal jiggling and wiggling motions. Since there are so many of these internal vibrations, practically any amount of energy you initially give the ball (by throwing it higher and higher) will be quickly absorbed, much as water is absorbed by sand. Furthermore, the amount of energy that ends up in each wiggling motion is so very small (because it's divided among zillions of them) that the amplitude (size) of the wiggling will be imperceptibly small. In short, it will look as if the energy of the bouncing has vanished.

In the case of air molecules, there are at most 2 or 3 internal vibrations, so there really isn't anywhere for the bouncing energy to go. So it doesn't go anywhere, and the air molecules bounce up and down again, forever.


8. What determines the lowest frequency sound your stereo speakers can produce?

(o) The diameter of the speaker cone.
(o) The stiffness of the speaker cone material.
(o) The quality of the speaker cables.
(x) Nothing, there is no lower frequency limit.

A bit of trick question. Sound waves are longitudinal, meaning the air shakes back and forth. The size of the speaker has nothing to do with the wavelength it can produce, since it produces shorter or longer waves by moving frontwards and backwards faster or slower, and NOT by waving like a drumhead. So the lowest frequency it can produce is just the slowest it can move back and forth. Since, of course, it
can move back and forth infinitely slowly, there is no lower limit. The reason low-frequency speakers are larger than high frequency is because the human ear does not perceive long wavelengths well, so you need to make powerful waves when you make low frequency waves, i.e. move a lot of air back and forth.


9. If you drop a rifle bullet from your hand at the same instant, and from the same height, as you fire a rifle bullet horizontally from a rifle, which hits the ground first?

(o) the dropped bullet
(o) the fired bullet
(x) they both hit simultaneously

Classic Newtonian physics problem, just like the rock on a string. The truth is that the downward motion of the bullets is completely independent of the forward motion, so that the bullets, having both started with downward velocity of zero, and having the same distance to fall, will reach the ground at the same time. Of course, the fired bullet will reach the ground way far away, while the dropped bullet will reach the ground at your feet.

Folks who believe in Aristotelian physics get this wrong, too.


10. What's the most important reason HIV is hard to cure?

(x) The virus mutates frequently.
(o) HIV attacks the immune system.
(o) Very little is known about how HIV infects cells.
(o) You can't kill all HIV-infected cells without killing the patient.

To kill HIV you need to target some part of its genome that stays reasonably constant, and unfortunately it changes its genome very often. In fact, HIV would be an unimpressive virus, less dangerous that the cold, if it did not mutate so much. The immune system apparently has no trouble killing it initially, but it mutates so fast that before every bit is gone it has become something new, and the immune system must learn to recognize and kill the new version. Then it changes again. This arms race goes on for years if not decades, and AIDS only develops when (for reasons we don't yet know) the immune system exhausts its repertoire, and the virus finds a form that the immune system will no longer recognize and kill.


11. Why is there almost no hydrogen in Earth's atmosphere?

(o) It's a rare element, there's not much anywhere.
(o) There wasn't any in the part of the primordial cloud that condensed to form the Earth.
(x) Earth's gravity is too weak to hold it.
(o) It's so flammable it all burned up long ago to form water.

Most of the primordial cloud that formed the planets was hydrogen, and planets with a strong enough gravity like Jupiter and Saturn still have most of it. But it's a very light gas, and smaller planets like the Earth or Mars just don't have enough gravity to hold onto it.


12. In the device sketched below, water falls, turning a waterwheel, which then drives a bucket chain lifting the water back up. The wheel also supplies power. This device. . .

(o) is a Ptolemaic water wheel, used for irrigation
(x) is a perpetual motion machine of the first kind
(o) was used in ancient Egypt to irrigate fields

This device is impossible. A little thought should convince you that just as much energy is required to lift the water back up as is released by the water falling onto the water wheel. If the water wheel *also* supplies energy, then energy is being created out of nowhere. This violates the First Law of Thermodynamics, the principle
of Conservation of Energy ("energy is never created or destroyed"). It's called a perpetual motion machine of the first kind because, first, if it existed it would run forever (since it needs no energy to run), and, second, because it violates the First Law. Machines that violate the Second Law of Thermodynamics (the one about entropy) are called perpetual motion machines of the 2nd kind, and have more subtle flaws. You can find very respectable-looking companies offering to sell you shares in a perpetual motion machine of the 2nd kind all over the Web.


13. Why are fluorescent light bulbs more energy-efficient than regular light bulbs?

(o) They extract a higher percentage of the energy in electricity.
(x) They don't produce as much heat.
(o) They have a lower electrical resistance.
(o) They flicker, i.e. they're only really on about 50% of the time.

Regular light bulbs actually emit *most* of the electrical energy they consume as heat. (That's why they get so hot.) Fluorescent bulbs do a much better job of turning the electrical energy into visible light, not heat. (That's why they are cool to the touch.)


14. Mr. Wonka has hidden 5 golden tickets in a million candy bars. Charlie wants to find one. Charlie's Uncle Olaf buys 100 candy bars before Charlie gets to the store. Charlie's chance of finding a gold ticket has just. . .

(o) Increased, since there are fewer tickets left.
(o) Decreased, since Uncle Olaf might have found a ticket or two.
(x) Stayed the same. Uncle Olaf has had no effect.

Consider the first ticket Uncle Olaf buys. The probability of Charlie finding a ticket is now the probability Uncle Olaf *found* a ticket (5/1,000,000) times the probability that Charlie's ticket is one of the 4 remaining (4/999,999) plus the probability that Uncle Olaf did *not* find a ticket (1 - 5/1,000,000) times the probability that Charlie's ticket is a winner (5/999,999). Perhaps surprisingly, the result is 5/1,000,000, which is the same result as if Uncle Olaf had bought no tickets.

Another way to look at is this: whether the ticket is in Uncle Olaf's hands or still at the shop, or in someone else's hands, can have nothing to do with Charlie's chances of winning. It doesn't matter where the tickets that Charlie doesn't buy are!


15. The red color of blood has the same chemical source as the color of. . .

(o) poinsettia leaves
(x) rust
(o) red algae
(x) Mars

Both blood and Mars are red because it's the color of iron atoms when they are bound to oxygen. In essence, blood "rusts" in the lungs, to pick up oxygen, and then "unrusts" (gets reduced) in the capillaries to deliver oxygen to cells.


16. Why aren't birds electrocuted when they perch on power lines?

(x) They aren't also touching ground.
(o) The power lines are insulated.
(o) They're too light to make good contact with the electricity.
(o) They're smaller than the wavelength of the electricity.

Power lines are rarely insulated except by the air around them, because it would make the lines too heavy. But electricity cannot flow unless there's a place to flow to. Since the birds only touch the power lines, there's no place for the electricity to go.


17. Imagine a ball is dropped inside a box with perfect insulation. No energy can escape this box! How long will the ball bounce?

(o) Forever!
(o) Longer than when it's outside the box.
(x) Exactly the same time as when it's outside the box.
(o) Not at all.

One is tempted to think that, in general, the ball bounces lower and lower and then stops because its energy escapes. If so, then preventing the escape of the energy will prevent the ball from stopping, and the correct answer would be "Forever!" or at least "Longer than when it's outside the box."

But this understanding is false. What actually happens to make the ball stop bouncing is that the energy initially in the bouncing motion of the ball "gets lost" by spreading out into the zillions of tiny internal wiggling and vibrating motions of the ball, which are too small to see. You might say the bouncing turns into heat, in some sense. But in any sense, the energy does not really leave the ball so much as it's just that organized motion (bouncing) turns into unorganized motion (microscopic wiggling) that is too small to see. So insulating the ball will actually have no effect at all on its behaviour.


18. Suppose you accelerate in the passing lane on the Highway to Hell (which begins in Los Angeles but passes mostly through outer space) until your '56 Corvette is going 299,792,457 meters/second. (That's 1 m/s slower than the speed of light!) You open the window and throw an empty Bud can straight forward at 10 m/s. What do you observe?

(x) The can going 10 m/s faster than me. Duh!
(o) The can going 1 m/s faster than me. Can't go faster than light!
(o) The can going 0.14 m/s faster than me, roughly.
(o) The lights of a very angry cop in your mirror.

Most folks know that Einstein's Special Theory of Relativity predicts that nothing can go faster than the speed of light. But the more important prediction of his theory, relevant (ha ha) here, is that all physics experiments have to look the same no matter what "inertial" (not accelerating) reference frame you're in. That means anything you do while traveling steadily, even at an absurdly high speed, has to look exactly the same as it does when you are traveling at a safe and legal speed, or not traveling at all. Therefore, what you observe when you throw a beer can forward when you are not moving must be exactly what you observe when you throw a beer can forward when you are moving at nearly the speed of light.

But how does one reconcile the fact that, since you're traveling at 1 m/s less than the speed of light, the beer would now "seem" to be traveling 9 m/s faster than the speed of light? By realizing two things: first, and most important, this statement implies that we are talking about some "objective" beer can velocity that is "more real" than the velocity you report ("10 m/s faster than me"). For example, the velocity relative to some other observer. What does the cop at the side of the road see, in other words? Isn't the velocity he measures more "objective" than what you measure? Isn't that the "real" velocity? Well, no. Relativity says there are no privileged reference frame. The cop's measurement of velocity is no more "real" than yours (although you will not want to take this position in traffic court). The best the cop can say is "the can is traveling x m/s faster than me," where x is a number we would have to calculate.

Once you realize this, then we can set about calculating x, and it will turn out that, if we are to insist that (1) you see the can doing what it would do if you were stationary and (2) the policeman does not observe the can exceeding the speed of light, then we can't calculate the speed of the can from the point of view of the policeman by just adding 10 m/s to your speed. We have to do a more complicated calculation. It will also turn out that we need to allow you and the cop to disagree about the way time passes, too.

That's a lot to change about how we see things. Is it really required? Why can't you have a different experience throwing a can at nearly the speed of light than when stationary? Well, it simply turns out, that's the way the universe works. Experiments prove relativity is correct, and that's that.


19. Imagine one of those sleek glass-wall office buildings that looks in the daytime like a gigantic column of mirrors. You can't see in through the windows, but the people inside can see out. Why?

(o) The windows transmit more light inward than outward.
(o) The windows transmit more light outward than inward.
(o) The windows are polarized.
(x) It's usually darker inside than outside.

It's not possible for the windows, which are unpowered, to transmit more light in one direction than in the other. That would violate the Second Law of Thermodynamics (the one about entropy). One way to realize this is to realize that, if such a window could be devised, it could be used to construct a perpetual motion machine of the second kind, a way to recycle energy forever perfectly. (For example, you enclose whatever machinery you want to operate in a double-walled box made of these windows, set to pass energy only inwards. The waste heat from your machinery is trapped and concentrated by the box, and when the temperature inside your box rises higher than the temperature near your machinery, which it eventually must, you use the temperature difference to drive a steam engine that powers your machinery.)

The important fact here is just that it's normally darker inside the building than out. This has two effects: first, the light reflected from objects inside the building is much less than the light reflected from objects outside, simply because there's less light available. It is, of course, easier to see objects that are strongly illuminated than poorly illuminated. The windows magnify this effect, because they pass only a small fraction (say 5%) of the reflected light passing through them. However a brightly illuminated object (something outside) can easily afford to have 95% of the light reflected from it thrown away and still be visible, while a poorly illuminated object (something inside) might become completely undetectable if 95% of the light reflected from it is thrown away.

The other important effect is that your eyes, like a digital camera, adjust their sensitivity to the generally available light. In bright light, like outside, they become less sensitive, not sensitive enough to see the dim objects inside the windows. Inside the building, your eyes are more sensitive.

20. In Star Trek IV, Scotty tells a 20th century Earth firm the secret of transparent aluminum. What, theoretically, could produce a form of aluminum that conducted electricity but was perfectly transparent?

(x) Nothing. A perfectly transparent conductor is impossible.
(o) Treating aluminum at very high (currently impossible) pressures.
(o) Chemically combining aluminum with the right mix of other elements.
(o) Doping the aluminum with positive charge carriers.

Alas, Scotty discovery is not possible even in principle. To be transparent, a material must absorb no visible light. However, to conduct electricity a material must have free (mobile) electrons, and anything with mobile electrons can absorb light. A good way to understand this is to realize that light is a form of electromagnetic radiation, like radio waves. An antenna is something that can absorb electromagnetic radiation, and any conductor can be used to make an antenna.

The front of your LCD computer display is coated with conductor, however, and yet you can see through it. How is t his possible? The most important reason is that the layer is very thin, so that it need not be perfectly transparent.

21. If you are a normal healthy woman, you can be sure your body does
not contain. . .

(o) The genes that cause hemophilia.
(o) The genes for a penis.
(o) Both of the above.
(x) Neither of the above.

It's important to remember that genes need not be expressed (cause the
effects they are designed to cause).


22. When are you most likely to see a meteor?

(x) Just before dawn.
(o) Just after dusk.
(o) Midnight.
(o) During a lunar conjunction.

Just before dawn, you are facing forward in the Earth's orbit if you
look up in the sky. It's like looking out the windshield of a
speeding car -- you'll get a lot more bugs splatted on the windshield.
At dusk you're looking out the "back window", facing back along the
Earth's orbit, and meteors have to be able to catch the Earth (which
is moving at 18 miles/second) to hit it.


23. Which gear below will turn faster (more revolutions per minute)?

(o) The big one.
(x) The small one.
(o) They turn at the same rate.

This is why gears are useful, they can change the rate of rotation of
shafts without any loss of power.


24. Which is the main reason a hybrid car gets better gas mileage?

(x) The engine does not idle (run when the car is stopped).
(o) Regenerative braking. (The energy of the car is stored, not thrown away, when you brake.)
(o) During steady high speed driving the electric motor does most of the work.
(o) Because the engine is smaller the car is much lighter.

Typical stop-and-go driving wastes a tremendous amount of fuel idling
at stop lights and so forth. Remember, you get zero MPG under those
conditions, which really drags the average down. If you spend half
your travel time stopped at stop lights (not uncommon in a city) your
average MPG would be half what it is when you do not spend any time
stopped. A hybrid turns off the engine when the car is stopped, so
you never have to average in any zero MPG time.


25. Suppose you join an online bulletin board or website like OkCupid, and suppose they state in their advertising that anybody can join, and can post whatever they like. Suppose you make a few unpopular posts, and then the operators start deleting all your posts as soon as you write them. Have your First Amendment (free speech) rights been violated?

(o) Yes!
(o) Yes, as long as your posts were not hate speech.
(o) No, unless you paid to join the site.
(x) No.

OK, this is not about scientific principles at all, but it's still about important principles of everyday life.

Many folks have a vague impression that the First Amendment to the United States Constitution says that each of us has "the right to free speech," and that, therefore, anything anyone does that interferes with our saying what we please is an infringement of that right.

This is not correct. The text of the First Amendment reads in the relevant part: "Congress shall make no law...abridging the freedom of speech...." Hence, the shortest explanation for the answer to this question is that, since the operators of the bulletin board or website are not Congress, there is no Constitutional restriction whatsoever on their actions.

It is an important general principle of life in our Republic that the Bill of Rights restricts only the actions of the government, not those of our fellow citizens in their private capacity. For that reason, no property owner is required by the Constitution to allow any form of speech at all on his property. An oil refinery, for example, is under no obligation to allow peaceful protesters in their lobby, even if the lobby is commonly used by the public to transact business with the refinery.

And, to get back to this case, the private operator of a website is under no obligation to allow any speech on his website. He can accept or reject posts for any reason, including the vilest personal prejudice, or for no reason at all.

Armed with this understanding, you can make short work of First Amendment conundrums such as these:

  • Can a newspaper refuse to print letters to the editor that criticize the paper, or which take positions the editors don't like? You bet.
  • Does the FA mean a reporter must present all sides of a story? Or that a newspaper is forbidden from "slanting" the news it reports? Nope.
  • Can a billboard owner refuse to run an advertisement for Planned Parenthood on his bulletin board? Yes.
  • Do I have the right to yell "Fire!" in a crowded movie theater? No.
  • Do I have the right to yell "This movie sucks!" in a crowded movie theater? No!


26. Is the product of two prime numbers also prime?

(o) Always.
(x) Never.
(o) Sometimes.

A prime number is a number that has no factors (numbers that divide it
evently) other than itself and 1. Clearly a number N that's the
product of primes A and B has A and B as its factors! So N can't
ever be prime.


27.When you're prescribed antibiotics, why are you supposed to finish all of the prescription, even if that means you're taking pills long after you're cured?

(o) So the bacteria can't come right back.
(o) Because it's dangerous to leave the drugs lying around.
(o) So the drug companies make more money!
(x) So bacteria don't become resistant to the drug.

It's inevitable that some bacteria will be better able to resist the chemical attack of the drug. When you first start taking the drug, there will be very few of these. But of course, they are the only ones that will succeed in surviving long enough to reproduce. (Bacteria reproduce very fast, as often as every 15 minutes.) Hence soon enough most of the bacteria left alive in your body will be pretty resistant to the drug, since they will all be descendants of the very few who were initially resistant to the drug.

Now, if you continue the chemical artillery in an overwhelming amount and for an extended time, then even these tough guys will succumb and die, and all is well. But it is worth noting that some of them will survive long past the time when you have no more symptoms. (At that point, they are so few they no longer cause symptoms.)

What you don't want to do is quit the fight and let these last few very tought battle-hardened villains escape. Not for your own sake -- chances are you're immune to them now anyway -- but because you will loose them on the wide world. That means the next person who gets the disease, from descendants of your escaped POWs, will have to cope with bugs that are already pretty resistant to the antibiotic that helped you out.

When this process goes on for a decade or so (practically forever on the bacterial time scale) you can get major strains of bacteria which can't be killed by any known antibiotic. Which is trouble for all of us.


28. Why are there two prongs on an electrical plug?

(o) Because household electricity is AC (alternating current).
(x) Because electricity always needs a return path to the generator.
(o) Tradition.
(o) One for the positive charge, one for the negative.

Electricity is the flow of electrons, to have a flow you always need a
source and a sink, just like to have a flow of water you need a tap
and a drain. Hence all electrical circuits require two lines to the
power source: one that provides the electrons and one that takes them
back after they've flowed through the circuit.


29. If you're sitting in an airplane flying at 500 MPH in level
flight, and you throw something exactly straight up, where will it
fall back down?

(o) Slightly behind my hand (towards the back of the plane).
(o) Slightly ahead of my hand (towards the front of the plane).
(x) Exactly into my hand.
(o) Into my gin and tonic.

Very like the bullet question. You might think the motion of the
airplane affects the motion of the object. Nope. You might also
think the object, once free of contact with the airplane, starts to
slow down. Nope again. There's no force to slow it down. If the
object were outside the plane, i.e it were thrown out the window, then
of course it would slow down, because of the tremendous air
resistance. But inside the airplane, because the airplane carries all
the air with it, there's no air resistance, so the object does not
slow down.


30. It says right here that your brain begins to die after 6 minutes
without oxygen. But Tom Sietas of Germany, world record holder, has
held his breath for almost 9 minutes. What gives?

(o) Mr. Sietas is now brain-damaged, poor soul.
(o) Your brain can last longer without oxygen if you deep breathe first.
(x) You can get oxygen from the air trapped in your lungs, if your heart is still beating.
(o) 6 minutes is just an average, some folks can go longer.

Lungs don't take nearly all the oxygen out of the air. That's why CPR
works. It's really the failure to get that oxygen up to the brain
that is the problem.


Blogger Terralthra said...

In response to the "bullet fired/bullet dropped" question:

The bullet fired has also gone a significant distance...on a curved earth. It has further to fall, at the same acceleration, therefore, the one you drop will hit the ground first.

1:16 PM  
Blogger Joe said...

Um, Question 2; Shouldn't you state that there's no gravitational field in the plane of the image (which is implicit otherwise)

5:33 AM  
Blogger Joe said...

Other annoyances...
Q8: It's not sound if it's not audiable, If it's within the audiable frequency range but you can't hear it, it's a problem with the maximum power output. You need to increase the swept volume of your drivers; typically the diameter.

Q9 just doesn't work generally, the dynamics of a rifle round have lots to do with precession & aerodynamics that the question doesn't have scope to touch upon.

Q24 - Amn't sure if your stated answer is correct, but your explanation is definately overly confusing. "If you spend half
your travel time stopped ... your average MPG would be half what it is..." Makes the (ridiculous) assumption that fuel consumption is the same in an idling engine as in an engine driving a moving car.
The reason stop & go driving wastes so much fuel is that you're often accelerating to get up to cruise speed, which takes a lot more torque (.'. fuel) than either idling or cruising. I'd suggest then, that on cars that have it, an efficient regenerative braking saves a lot more fuel than re-starting the fuel engine all the time (which they only do rarely, for obvious reasons)

5:48 AM  
Blogger Carthoris said...

terralthra: Well, you seem to be assuming the bullet flies horizontally, which it would not -- it would execute an elliptical orbit around the Earth's center. But it's an interesting subtlety. I did a simple computer simulation of the actual answer, and for a 0.22 fired at 1.0m above the ground, the dropped bullet hits in 451.5 milliseconds and the fired bullet about 0.5 ms later. You may be right. But on the other hand this tiny difference may be swamped by differences in how one treats air resistance (I used a very simple v^2 model), local variations in wind, gravity, etc. Not to mention the bullets are only 2mm apart vertically when the first one hits, and the Earth is hardly spherical to within 2mm over a distance of several hundred meters. Interesting point, albeit a quibble. Thanks.

12:31 AM  
Blogger Carthoris said...

joe: Mmm, actually all I need to do is assert that the gradient of the gravitational potential in the plane is small compared to the curvature you can detect by eye in the lines. Which is pretty obvious, I'd say, unless one assumes the experiment might be being done close to the surface of a neutron star or black hole.

12:34 AM  
Blogger Carthoris said...

joe: Q8. Nope, I don't agree. There's nothing about audibility in the definition of "sound." For example, you've no doubt heard of "ultrasound" (sound of frequency too high to hear, used by bats to echolocate, or to take pics of babies in utero). This would just be "infrasound," such as elephants use to talk to each other.

Q9: I disagree. The effects you mention may perturb the trajectory by inches over a flight of a few hundred meters, but that means only a very small difference in the arrival times (see my comment above, where the difference due to curvature of the Earth amounted to only 0.1% or so). This is quite small enough to establish the basic point, since many people wrongly believe there is a substantial e.g. 25% difference in arrival times. We've got to distinguish between the big picture here and minor details. You'd probably argue a Flat Earther is wrong to deny that the Earth is "spherical," despite the fact that there are minor variations away from a perfect sphere, because the big picture is correct.

Q24: Well, I think your arguments are more substantial here. You're right the car idling uses less gas per minute than the car cruising, but if the difference were as large as you suggest ("ridiculous"), then hybrids would not bother to turn off the engine while stopped. They do (at least the Prius does). Hence, the (Toyota) engineers, who know for sure, have concluded you save a substantial amount of gas by avoiding any idling. Yes, accelerating takes more fuel per unit time than idling or cruising, but you are going somewhere, not standing still. No matter how little the engine uses while idling, it's still getting 0 MPG. The general difficulty here is converting between the various usages per unit time and the resulting average usage per unit mile. The typical velocity profile figures prominently. If you want to ponder some numbers, here's a guy who fiddled with the numbers a bit, and under the most optimistic possible assumptions (100% recovery, although Toyota itself only claims "up to" 30%) he estimates the Prius boosts gas mileage by about 3% by using regen braking and maybe 15% by turning off the motor and using a smaller engine with better optimization of its typical operating range. You may be right, but so far I am not convinced.

1:21 AM  
Blogger opelfruit said...

in relation to your comment on question 8: "Note 2: Acoustic waves audible to the normal human ear are termed sound waves" There is a limit to lowest tone audible by the human ear, if it is not udible then it is an acoustic wave and not a "sound" wave. If the diameter of the cone were larger the volume of the sound can be increased making the lower waves more audible but there will still be a point where they become inaudible and are no longer termed as "sound" therefore the answer to question 8 is "a" - but only due to the change in volume levels that this would bring.

5:33 AM  
Blogger An Jiaoshi said...

Q29 is problematic because you specify that the object is thrown straight up. In a moving plane, throwing an object straight up would mean that, from your point of view, you were throwing it backward, so it would land behind you. What looks "straight up" to you is actually throwing the object up and forward at the same horizontal velocity as you and the plane.

1:44 PM  
Blogger 4sonnets said...

Question 26. The answer sound be SOMETIMES. One (1) is a prime number. Therefore, anything multiplied by one would still be a prime number.

2:23 AM  
Blogger Carthoris said...

opelfruit, thanks for the interest, but you're just wrong.

an jiaoshi, you assume a privileged frame of reference, to which I refer when I say "straight up." Sorry, I believe in relativity, which means there are no privileged frames, which means the only "straight up" I could have meant was in the frame of the person on the plane.

4sonnets, the number 1 is not a prime number. Consult a good mathematics text, or

7:26 PM  
Blogger A. Poutanen said...

Q24: While regenerative braking, shutting down the gasoline engine at idle, etc. all contribute to the efficiency of a hybrid car... as far as I know the major difference is the inefficiency of an internal combustion engine designed to run over a broad RPM range (1000-6000 or so in a family car).

By using the gasoline engine primarily to aid/charge the electric system, it's required RPM range is substantially reduced, and the cam profiles, fuel injection, etc. will all be optimised for that more narrow RPM range, resulting in a more efficient engine.

So a non-hybrid car has to make a compromise between efficiency and the need for a wide rev range.

A hybrid will use the stored electrical energy to get the vehicle to normal operating speeds, and then at those higher speeds the internal combustion engine is running in it's optimum rev-range, more efficiently moving the car at the same time as recharging the batteries.

9:32 PM  
Blogger Carthoris said...

poutanen, it's an interesting theory, but I think you're wrong. The gas engine in hybrids does not shut off when the car is accelerated hard, i.e. when the gas engine goes above its optimal RPM range. And that's precisely where running the gas engine outside of its most efficient range wastes the most gas.

Since the engineers didn't bother to make the gas engine shut off when it goes above the optimal RPM range, but did design it to shut off when the car is motionless, I conclude the former gives less gas savings than the latter.

3:52 AM  
Blogger A. Poutanen said...

A quick glance at....

Will reveal that hybrids tend to use an Atkinson or Miller cycle engine rather than otto cycle. The cam profiles are designed for efficiency (about +15% from otto cycle) rather than power.

Also this excerpt from the first reference kinda sums up what I said in my last post:

"The internal-combustion engine in a hybrid vehicle is much smaller, lighter, and more efficient than the one in a conventional vehicle, because the engine can be sized for slightly above average power demand rather than peak power demand. The power curve of electric motors is better suited to variable speeds and can provide substantially greater torque at low speeds compared with internal-combustion engines."

I'd be curious to see what the Toyota engineers put together for the theoretical savings from each 'feature' of the system (regen braking/engine off at idle/more efficient ICE)...

Though I'm sure that if you consider a Prius gets much better mileage than a much smaller, lighter Echo when crusing at highway speed... (
you'll see how the efficiency of the cars internal combustion engine *could* be the single largest factor in it's improved mileage.

Anyway, to each his own, I just think that 'Higher Volumetric Efficiency of the onboard Internal Conbustion Engine' should be a possible multiple choice answer in your test.



4:25 PM  
Blogger Carthoris said...

poutanen: Nah, still don't buy it. The Wikipedia citation (for what it's worth, by the way -- Wikipedia is not what I'd call a professional-quality resource) just argues that the engine is tuned for efficiency. Well, of course. But this says nothing about the relative contributions of engine tuning, cutting out the idle, etc., to the higher gas efficiency of the hybrid over the conventional drivetrain.

Another argument that you've sussed this out wrong is that the gas engine gets its best mileage on the highway, but the Prius gets better mileage in the city, when there's lots of stop-and-go driving. In fact, the Prius highway mileage isn't much better than that of any other small car (with an engine tuned for efficiency, as they mostly are). Where it really shines is in the city. Because, as I said, you cut out all the 0 MPG time idling.

8:58 PM  
Blogger pde said...

Conductors can theoretically be transparent in the visible spectrum range -- provided there are other (higher or lower energy) electron transitions possible to move charge around. Apparently tin oxide can do this.

5:26 AM  
Blogger pde said...

I was also thrown by the question on how molecules in the atmosphere stay up. The answer is a combination of bouncing off the ground and bouncing of (ie being supported by) lower molecules. At STP, the mean free path of oxygen is only ten to the minus seven meters, so the "stacked up" explanation seemed overwhelmingly more accurate.

5:32 AM  
Blogger Karl said...

On question 21, small disagreements mainly with how I read the question but first there isn't really a gene that causes hemophilia, it is normally caused by the abscence of a protein which is cause by a genetic mutation within a gene, secondly and this is the part I actually missed is that the formation of the actual testes in the male reproductive system is actually found on the Y chromosome, so where as the differentiation of cells to form the penis might be correct in saying that encoding might exist I think its a question that is can be read different ways. Otherwise it was a really good test

5:25 PM  
Blogger Phil said...

Joe is right about Q9. A spinning bullet actually creates lift, which of course will keep the bullet airborne longer. Yes, it may only equate to a millisecond or so when dealing with an initial height of 1 - 2 meters. But the question doesn't specify an initial height, nor does is say "approximately" the same time. And physics deals with precision, not "close enoughs".

I'd suggest using the old "penny & a feather in a vaccum" or otherwise changing the question to discount aerodynamic forces.

5:07 PM  
Blogger 11 73 3 33 said...

About the questions about the plane and the bullet - You assume there's no friction with air, while actually you haven't told it exactly.
As all of us know, friction grows linearly with the speed.

1:05 PM  
Blogger druberego said...

The question on antibotics is incorrect. The lifespan of the bacteria and the medicine's effectiveness are both half-life predictable with the blood serum concentration being the primary variable. Prescribing doctors are more concerned about the re-establishment of the original bacterial colony following a shortened course than they are about breeding resistant bugs.

While I would agree that there is some merit to your answer in that the release of a super-bug is possible. (Which is possible with or without antibotics and during the normal course of healthy human life anyways.) The belief that this is the reason for encouraging a full course of antibotics is primarily amongst germaphobic people who incorrectly believe that antibotics are causing resistant bugs. They aren't. Such bugs always came into existence and we are now able to properly detect and categorize them.

Further. While the generation breeding cycle of bacteria can be fast. The danger is not in mutation, which has a rare chance of success but in the rate that an infection can spread. Starting with a single, wimpy, non-superbug bacterium... if it splits once and then each result splits and so and so on (think Clariol hair commercial here) you only need to split 30 times to wind up with 1 BILLION bacterium. (Ignoring the bacterium deaths that occur during this time.) As you mentioned this can happen in only 2.5 hours. Now which are you more afraid of? The rare chance of a superbug (which has very little precedence of occuring in medicine) or the single nearly harmless bug that generate a billion friends in no time at all (and this has tons of precedence in medicine.)

You are correct in your explanation of "so they are ALL wiped out" but you are incorrect in assuming that it is due to fear of super-bugs. We just don't want the original to be given a chance to make a come back given the ability of exponential growth rates in a short period of time.

Sorry the answer is A) So they won't come back.

4:51 PM  
Blogger Carthoris said...

pde, thanks for the link. Most interesting article about tin oxide...however, a material that loses 3% of visible light per micron of thickness (as it says in the article) strikes me as "transparent" only in a very limited sense of the word. A mere 1mm thick window of tin oxide would transmit only (0.97)^(1000) = 0.000000000001% of incoming light. I'd say that qualifies as opaque by any normal standards.

What you are talking about in general is materials that are "transparent" when they are applied as very thin coatings on microelectronics. I'm aware these exist, of course. However, this is not at all the same as the sturdy but transparent building materials Scotty imagined in Star Trek IV.

On the second question I think you've made a definitional quibble. Whether the force from the ground is transmitted directly through a bounce or indirectly via bouncing off other molecules that have bounced off the ground seems a bit irrelevant. Think of the other molecules as force carriers, eh? However, the "stacking" explanation is wholly incorrect, because it suggests static forces between molecules are supporting the atmosphere. This is absurd, because, while (as you note) the mean-free path of molecules in the atmosphere is small by human standards -- it is enormous by atomic standards. It's several thousands times the diameter of each molecule. Hence in no meaningful sense of the word can they be said to be "stacked" on each other.

Another way to put it is this: if "stacking" were a "more accurate" description of the situation, as you suggest, then nothing would change if the temperature were lowered to 0K. After all, stacking is stacking, right? Why should the temperature matter? But of course you know if the temperature were lowered -- if the dynamic aspects of the situation were cancelled, the molecules would all "fall down" and form a thin layer on the Earth's surface.

7:38 PM  
Blogger Carthoris said...

Phil, physics in fact does not deal in "precision" to the absurd, attention-deficit personality degree you suggest. That's, mathematicians, let's say. Or computer programmers. And barely sane ones at that.

Get yourself a copy of Feynman's autobiography, or Consider a Spherical Cow, and learn how essential to the practise of good physics is knowing what are the important aspects of a problem -- and what are ignorable second-order trivial corrections.

7:43 PM  
Blogger Carthoris said...

drubergo, you're full of shit. Go ask your physician next time you see him. Thanks for playing.

7:45 PM  
Blogger Michael M. said...

Your explanation of electrical prongs in question 28 needs improvement. The wires are there to transmit energy, not so much the electrons themselves. With AC, the electrons in the wires wiggle back and forth a tiny, tiny distance; they do not undergo net motion.

7:46 PM  
Blogger Carthoris said...

michael, thanks for the comment, but you're wrong. You don't need a return path to merely transmit energy. Think of a shotgun; the pellets don't need a return path to transmit energy from the gun to the target, right? You can transmit energy via light (think of a laser beam) and you don't need a return path. What you're missing is the fact that electricity is the movement of electrons, and that transmits energy, but the movement is not itself energy. Don't confuse the thing that moves with the motion. A car is not its kinetic energy.

The fact that the electrons move back and forth instead of only in one direction is not relevant to the fact that you still need a source and a sink to have electrons moving through a circuit. All you're saying is that in an AC circuit, which prong is the source and which is the sink switches every 1/60 of a second. Doesn't change the essential nature of the answer.

10:53 PM  
Blogger Fred said...

I agree with Joe on Question 2; If your questions said what "vector" does the ball begin heading in, you would be correct. But unless you said you were weightless in space, gravity is relatively strong on the surface of the earth and the straight line forward is impossible. Instead you asked "What path does the ball follow" and clearly it follows a curved path to the ground, anywhere but in space. In other words the ball is subject to 2 vectors, the straight ahead AND a smaller gravity vector, combining to make a curve to the ground. In fact this is the same as the bullet question. By your logic the bullet would continue straight ahead forever heading in a straight line out into space.

11:08 AM  
Blogger Carthoris said...

fred, taking the size of the hand in the image as indicating the scale of the drawing, and assuming a reasonable velocity for a rock being whirled on a string (say 45 MPH), why don't you calculate the deviation from a straight path that could be expected in the Earth's gravity? If you manage to show it would be detectable by eye (e.g. more than 10 pixels) then I'll admit you have a point. Good luck.

Really, you might as well complain that resistance from air currents, or turbulent forces from the rock's tumbling will probably affect the rock's path as well.

Maybe you just got the question wrong and are hoping to find some tiny defect in the wording that would let you believe you got it wrong because you know too much rather than too little?

5:49 PM  
Blogger Bob said...

I had three main issues. I certainly understood the issues with the bullet, but I thought the question was pretty clear in intent.
7.When you throw a ball into the air, it falls back to the ground. So why don't the molecules that make up the Earth's atmosphere all fall to the ground? What keeps them up there?

(x) They do fall, but bounce back up, over and over, forever.
(o) They're so light they fall undetectably slowly.
(o) They're stacked up, higher molecules resting on those lower down.
(o) Wind keeps them stirred up, like bits of paper in a breeze.

All of these answers are deceptive, so what is the best? Consider a molecule of air 10 meters off the ground (where the ball is at it's highest when you tossed it). It was swept there by the macroscopic wind currents, it bounces up, down, side to side, and every which way, off all the adjacent molecules, and is more or less kept where it is by adjacent air molecules that are bouncing around in a microscopic sense, but more or less static in a macroscopic sense. Does this particular molecule ever bounce off the ground (as the question asks)? Someday it might, but not any time soon. That's not why it stays were it is. Weight has no bearing on gravitational acceleration, so that one is wrong. They are not stacked up, but as a rudimentary analogy that I would use to explain to my 5 yr old, it's a good start. And the wind does indeed greatly influence their position, on a macroscopic sense (the butterfly that flaps it's wing in Beijing affects our weather much faster because of air currents than because of actual molecular diffusion).

17.Imagine a ball is dropped inside a box with perfect insulation. No energy can escape this box! How long will the ball bounce?

(o) Forever!
(o) Longer than when it's outside the box.
(x) Exactly the same time as when it's outside the box.
(o) Not at all.
In any other area, some energy is transferred to the impacting surface. You like to discuss all the micro vibrations as the end location of this energy (in essence, heat), but with a box that has perfect insulation, this energy doesn't get transferred. You still have reduction in velocity due to normal air friction (you don't say it is a vacuum), and some lost in the inefficiency of the rebound, but there is one less energy sink to absorb that energy.

22.When are you most likely to see a meteor?
(x) Just before dawn.
(o) Just after dusk.
(o) Midnight.
(o) During a lunar conjunction.
Seeing a meteor is different from having the most meteors hit the atmosphere. One prefers a darker sky to 'see' meteors (they hit all throughout the day as well, but we rarely see them). Also, there is an additional issue that most of the meteors are either coming or going across our elliptic path on their own elliptic path around the sun. As we have already cleaned up most of the meteors that are in our own rough orbit, we are intersecting those on convergent but different orbits (none are just floating there, all are moving fast). The speed issue is more similar to having a bullet hit a cannonball in mid air. Both of the vectors are equally important. Simple logic would support your conclusion, but there are many reasons why that is not the whole story as well.

6:35 PM  
Blogger googlethis said...

Did the question say that the rock was spun on a string in a plane perpandicular or parralell to earth's surface? no. no part of the description adressed that. AND its an arguement for arguement's sake, i.e. not relavant. I got this one right.
whatever. we are all smart enough to take the test and think about this stuff. kudos to us. Carthoris, thanks for the test. we dont have to agree with all of your answers do we? Not even if you did get a nobel prize. This type of thought is about the consideration. our scientists had all thier answers hundreds of yrs ago for us to reconsider.
again, thanks, and nice job

7:02 PM  
Blogger daedalus2u said...

the answer you have to question 15 is incorrect.

Blood is red from oxyhemoglobin. That is O2 coordinated to ferrous heme. Ferric heme as in methemoglobin doesn't coordinate O2, but is quite different in color, brown, not the same shade of red as O2 heme.

Carboxyhemoglobin, CO coordinated to ferrous heme is red, but a different shade than O2 heme.

Oxy heme, carboxy heme and deoxy heme all have ferrous iron. Metheme has ferric iron, the same Fe3+ that gives rust its red color. Fe3+ is not what makes oxyhemoglobin red because there is no Fe3+ in it.

2:09 PM  
Blogger Carthoris said...

bob, thanks for the comments. I have to begin by noting that in every case the answer for which I'm looking is the one that captures the essence of the subject, the key effect or cause. I'm not trying to trick anyone by posing oddball questions that have nonobvious answers where subtle and rare effects dominate. This seems to be an issue for a lot of OKC people, who, I dunno, are ADHD types who focus like a laser on minor details instead of grasping the big picture. Weird, that.

Anyway, the most important effect keeping the molecules of the atmosphere up is the fact that they have no internal degrees of freedom into which the bouncing energy might flow and "get lost," which is what happens with a macroscopic bouncing ball. The fact that they bounce off their neighbors on the way to and from the ground is quite interesting but not especially important. The effect these ricocheting collisions have is to just to greatly lengthen the timescale for the "bouncing" of the molecules on the Earth's surface, and change their motion from purely ballistic to diffusive in a field.

Perhaps it would help to imagine replacing the molecules with basketballs. Hopefully you can see that a bazillion bouncing basketballs ricocheting off each other will still come to rest, in a way the atmosphere doesn't. That tells you that the ricocheting is not the key to understanding why the molecules in the atmosphere don't fall to the ground.

I'm not sure I understand your objection to (17). It's the same thing as the bouncing molecule, however. In each case I'm testing to see whether you truly understand the nature of entropy and the Second Law of Thermodynamics. It's a tough law, and a subtle principle.

As for 22 -- again, bob, I'm looking for the most important effect, and, indeed, as a little googling will tell you, there are more meteors hitting the Earth faster at dawn than at dusk or midnight. More meteors going faster means more brighter meteors that you can see.

3:32 PM  
Blogger Carthoris said...

googlethis, the question also did not specify that the rock was being swung in air, instead of (say) under liquid iron, so that the bouyancy of the rock can safely be ignored.

You're expected to make the most reasonable assumptions about facts not explicitly stated, and the most reasonable in this case are that gravity is not important.

3:39 PM  
Blogger Carthoris said...

daedalus2u, you're wrong. In the first place, even you won't deny that the red color of blood come from the iron atom. (It sure as heck doesn't come from the protein, right?) That's the same place the red color of Mars and rust comes from. Furthermore, you will admit that the red color comes specifically from an iron atom bonded to oxygen in all three cases. Granted, the bonding is much more complicated in oxyhemeglobin, but this is minor detail.

About the only thing you can say is that maybe my crude explanation here (that blood "rusts" in the lungs and gets reduced in the cells) is not quite right. I agree the exact oxidation state of the iron in oxyhemoglobin is not easy to assign. (The Wikipedia article on hemoglobin flatly asserts it's +3, for what that's worth.) Nevertheless, surely we need to assign it something higher than +2, since when the O2 binds some electron density has got to move towards the O2 and away from the Fe. In any event, the color will come from the ligand field splitting of the d-orbitals, and probably doesn't depend on the oxidation state much. What matters is only that the crystal field in oxyhemoglobin is, apparently, much like that in solid Fe2O3. Which we can tell from the color.

4:01 PM  

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