In the same Singh article in the Guardian that I mentioned in the previous post, there is a quiz. Nice to see. I’m not really sure what its purpose is, but it does not have to have one. Why not have a go at it yourself?
It is entitled “Do you know your Newton from your neutrons?”:
1. A metal plate is heated to 200C with a bunsen burner. It subsequently cools by emitting what kind of radiation?
a) Ultraviolet waves b) Gamma rays c) Infrared rays d) Radio waves2. You’re in the back of a stationary car with a helium balloon. When the car accelerates, which way does the balloon move?
a) Forwards b) Backwards c) Up d) It doesn’t move3. What two properties of a particle does Heisenberg’s uncertainty principle say you can’t measure at the same time?
a) Energy and mass b) Position and momentum c) Position and mass d) Momentum and velocity4. A skater is spinning on a spot with her arms outstretched. What happens when she pulls her arms in?
a) Nothing b) She changes direction c) She spins more slowly d) She spins more quickly5. A big wooden ball and a small ball bearing sit at the top of a slope. When they are released, which reaches the bottom first?
a) The wooden ball b) The ball bearing c) They both get there at the same time d) Depends on the masses of the balls and the angle of the slope6. If the Sun were to disappear right now, how long would it be before we noticed?
a) Straight away b) About 8 minutes c) Just over an hour d) Almost a day
So, how many did you get right? Do you care? I’m sure we can all discuss the answers if you’re interested…..
(Answers at end of the article at source.)
-cvj
November 22nd, 2005 at 12:52 pm
and if the wooden ball is hollow?
November 22nd, 2005 at 1:00 pm
I just stumbled upon your blog and took the test. I missed #2 only I guess some of the things I’ve learned over the years have stuck around.
November 22nd, 2005 at 1:35 pm
I have a question on #5. First, I assume that the usual caveat of really occurring in a vacuum applies to this one to so we can ignore air resistance. But even then, it is not at all clear to me that the the different rates of rotation and masses won’t accelerate down the slope at different rates. What is the simplifying assumption or what “always sums to zero” in this case that lets us treat these as basically point masses sliding down a frictionless incline.
I am not saying it isn’t so I just wonder why it is a gimme.
November 22nd, 2005 at 1:55 pm
taalinukko,
I presume air resistance should be neglected. If there is no friction then they will be just like point masses, you are right. You do need friction for them to roll, but ignore any energy losses due to that friction, since they are not skidding or sticking (say).
In that case, they are not going to get down the slope at the same time as a point mass would. Their rolling means that you have to take into account moment of inertia of a sphere because energy needs to be put into making it turn about its axis in addition to its center of mass moving down the slope (yes, the factor depends upon whether it is hollow or not, see commenter #1, but the radius drops out of the computation). This gives an extra dimensionless (i.e. purely numerical) number in the answer for the time taken. But the numerical factor is the same for objects of the same geometry (irrespective of relative radius). If they are both solid spheres, then same factor, so same time.
-cvj
November 22nd, 2005 at 2:00 pm
#5: it is not at all clear to me that the the different rates of rotation and masses won’t accelerate down the slope at different rates.
Well, assuming that they are solid balls, their moment of inertia is proportional to their masses (I = 2/5 MR^2, or something similar). Now, the loss in potential energy between the top and bottom (= mgh) equals the gain in kinetic energy (1/2 MV^2 + 1/2 I w^2) where w = v/R, and so the mass cancels out.
And if they end with the same velocity at the end, it is “trivial” to demonstrate that they must have taken the same time down the slope, eh?
November 22nd, 2005 at 2:54 pm
5 of 6. Does that get a passing grade?
Elliot
November 22nd, 2005 at 3:08 pm
#2 is misleading and poorly written – in fact the classic example of the poorly written physics questions: it needs to specify the observer viewpoint, do they mean whether the balloon moves relative to “you in the car” or a person outside the car in an inertial frame; and they need to specify whether they mean the transient motion of the balloon or the asymptotic motion.
Fortunately it is subject to experimental testing…
November 22nd, 2005 at 3:21 pm
Aha… so I’m to guess you got that one wrong then, Steinn Sigurdsson?…
kidding!
-cvj
November 22nd, 2005 at 3:48 pm
I don’t think #2 is misleading at all. The only logical choice of observer is the person in the car. It’s actually quite a cute question to relate acceleration to density like that. I had to think for a second before I realised “helium” was the key word.
November 22nd, 2005 at 3:57 pm
Clifford and SC,
Thanks for the explanation that is crystal clear.
Physics 101 was too long ago…
-t
November 22nd, 2005 at 3:58 pm
#2 was the one I got wrong – presumably the balloon has floated to the ceiling and is thus in contact with the car as it accelerates. I thought that I, a passenger in the back of the car, would see the balloon tipping backwards (at least at first), in the same way that I, the passenger, would feel pushed back into my seat when the car accelerates. Why is my intuition wrong (as it so often is)?
November 22nd, 2005 at 4:01 pm
Thanks dampt_dweller! Of course, it is all due to density differences!
November 22nd, 2005 at 4:29 pm
The balloon experiment is something you can easily observe. I once took a helium balloon inside a bus. When the bus took a left (right) turn I could clearly notice the balloon moving to the left (right).
November 22nd, 2005 at 4:35 pm
Stein: ”#2 is misleading and poorly written – in fact the classic example of the poorly written physics questions: it needs to specify the observer viewpoint, do they mean whether the balloon moves relative to “you in the car” or a person outside the car in an inertial frame; and they need to specify whether they mean the transient motion of the balloon or the asymptotic motion.”
So, you can either make ”correctly formulated” questions for lay persons or for physics graduates, but not for both.
November 22nd, 2005 at 4:51 pm
I had seen #2 before, and it annoyed me then.
So not I did not “get it wrong” in that I knew the answer expected.
Plus the local supermarket gives free balloons to kids (Wegmans, fiendishly clever), this experiment is done twice per week.
If you really want to annoy the questioner, ask whether the head of the passenger is in contact with the seat and head rest, or is free to move.
It is an imprecisely worded question designed to trick people (or to make them think if you want to be charitable), and is therefore not useful for testing general understanding of physics.
November 22nd, 2005 at 5:04 pm
Steinn Sigurdsson, I very much agree that these kinds of questions should be carefully worded. I was just teasing a little in my earlier comment. Hope you don’t mind….
Thanks,
-cvj
November 22nd, 2005 at 6:39 pm
#2 may be subject to experimental testing, but #6 is not. This should be made crystal clear! Nobody knows the answer to #6. Just because the whole world believes it’s true, doesn’t make it so.
Doug
November 22nd, 2005 at 6:53 pm
I have to say these questions make physics seem awfully boring. Maybe we should have a contest to come up with interesting everyday-physics quiz questions? Here’s a quick stab:
Which of these is not an example of the same underlying physical phenomenon?
a) heat from a radiator
b) music from a violin
c) radio waves from a broadcast tower
d) light from an incandescent bulb
Obviously there’s some room for interpretation, but that’s not necessarily a bad thing — nobody is getting a grade here.
November 22nd, 2005 at 6:59 pm
Doug…… what?!
With respect, that is simply wrong on a multitude of levels. But I should maybe wait to find out exactly what you mean before saying why..in case you’re making a really subtle point that I’ve missed.
-cvj
November 22nd, 2005 at 7:23 pm
Number 6 is perhaps the question which needs to be phrased most carefully. The answer to the question “If the Sun were to disappear right now, how long would it be before we noticed?” is not (a), (b), or ( c) but “We wouldn’t notice it because, according to general relativity, such things are forbidden by conservation of energy-momentum.”
November 22nd, 2005 at 7:35 pm
Sean,
(a) is the odd one! It delivers energy by convection and radiation. (and conduction, when I lean my fat arse against it).
(b) is the odd one! The energy radiates in a longitudinal wave. (radiative only).
(c) is the odd one! It passes an electric current from one conductor to another over an air gap
(d) is the odd one! The current in the conductor doesn’t vary directly with voltage. (OK, that was a bit desperate)
Apologies,
Chaz
November 22nd, 2005 at 7:37 pm
and, of course, they are all examples of energy being transferred by waves….
November 22nd, 2005 at 8:31 pm
Hmmm – Six is actually interesting. If the Sun disappeared right now, I probably woudn’t notice until I heard about it on TV. One the other hand, if it “disappeared” in the daytime while I was outside, it would only take me a few milli-seconds to notice. If, on the other hand, it left our universe abruptly, I probably wouldn’t get the message until aout 8 more minutes of comoving time had elapsed.
November 22nd, 2005 at 8:49 pm
Actually don’t Doug and CIPig bring up an interesting question. While EM radiation would take 8 minutes 93,000,000/c, is there definitive scientific proof that the “speed” of gravity is also c? I seem to remember this is still an open question.
Elliot
November 22nd, 2005 at 8:49 pm
1) At 473K, the peak of the radiation cure is a few microns, so that’s mostly IR.
5)SC and Cliff – mass and the R^2 factors cancel.
November 22nd, 2005 at 8:51 pm
CapitalistImperialistPig: Yes…as I said…. but the geometrical factors from the moment of inertia do not. There will be 2/3s and 5/7s and things like that, depending upon the shape.
-cvj
November 22nd, 2005 at 8:56 pm
Who cares which way the balloon moves? I only care if the helium is in a cylinder where I can mix it with oxygen in another cylinder to help an asthmatic patient breathe better.
Tammy, R.N.
November 22nd, 2005 at 9:46 pm
I give problems like this in class and have found that for problems like #5 it is very helpful to allow for a little error in the “same time” answer. E.g. “They both get there at the same time, to within 5%.” This prevents hair splitting, but it is also important. In the context of a class we have trained the students to pay attention to some things, but to ignore others. The general population hasn’t been told what to ignore, so we shouldn’t say they “got it wrong” if they decided to account for friction.
I don’t quite know what Doug’s point is, but I also was a bit concerned with question 6. It is the only question of the form “If [something totally impossible], then…?” If the sun disappeared it would violate local energy conservation, one the basic results of general relativity. If general relativity is wrong it is difficult to say how long it would take for us to find out about it without know what the new theory is that we are supposed to use. For example, if the sun disappeared “right now” because the solar system was tunneling to a new vacuum, then we might know about it “straight away,” except we’d all be dead.
None the less, I think it was a fun quiz. If it gets people talking about physics, that is great.
My nomination for a question: Which is bigger, a drop of water or a drop of vodka?
Gavin
November 22nd, 2005 at 9:59 pm
No offence Cliff, I am not that sensitive, most of the time.
And it is a nice question on the principle of equivalence, if you consider the local effective “gravitational acceleration” when you add the acceleration vectors, and then consider that the balloon is buoyant and moves opposite the local effective gravity.
But, it is still a gotcha, it is not a “do you understand physics” for the man on the Clapham omnibus, at the level the ice skater question is, or Galilean physics. It is a question which invites the “intuitive” answer which is wrong. Q
Arguably the “Sun disappearing” question is a trick question (it depends on what “now” is, one could make a perfectly good case for the time being zero, since “now” at the Sun is the now a light travel time ago [cf how we talk about a supernova happening "now" when we see it a light travel time later]), but at least in that case the default assumption of the pundit is the “correct” one, and the right answer is the proper distance divided by the speed of light.
Ah well, we all have our obscure little buttons which set us off.
November 23rd, 2005 at 2:11 am
I scored 100%. I guess this means I’m ready for my qualifier!
November 23rd, 2005 at 9:09 am
damtp_dweller: ”Number 6 is perhaps the question which needs to be phrased most carefully. The answer to the question “If the Sun were to disappear right now, how long would it be before we noticed?” is not (a), (b), or ( c) but “We wouldn’t notice it because, according to general relativity, such things are forbidden by conservation of energy-momentum.” ”
Couldn’t the Sun theoretically vanish in a theory with infinite extra dimensions?
November 23rd, 2005 at 9:20 am
Couldn’t the Sun theoretically vanish in a theory with infinite extra dimensions?
I don’t know. GR is my area of quasi-expertise so I’d feel nervous about commenting on theories outside that. There are two important points to note however. Firstly, regardless of how many dimensions a theory requires one would assume that it must still obey the usual sanity requirements associated with “ordinary” theories. The most important of these is that the energy of a system must be conserved in some sense. I’m unable to see how going to extra dimensions would allow one to dispense with energy conservation. Even if you take the string theorists viewpoint that the energy may “leak” away into a brane instead of actually disappearing I think I’m correct in saying that you still need to ensure that energy is conserved regardless. Presumably, (n->oo)-dimensional models should still contain some conservation laws that prohibit such things occurring.
Secondly, show me a working theory of gravity coupled to matter fields in infinite dimensions.
November 23rd, 2005 at 9:52 am
While some might of thought it “dreamy,” there is a direct physics correlation to that leaking in the collider. Although it is encompassed, like you said.
So where did it go, and how is “it” encompassed?
November 23rd, 2005 at 10:07 am
Sean,
I’ll make a stab at answering your quiz: my choice is (b) music from a violin. The key word as I see it, is *music*. Now if you had used the word “noise” instead, I would not have selected it. There is no physical principle that I know of, categorizing certain kinds of noise as music.
November 23rd, 2005 at 10:12 am
Oops .. correction to post #34.
There is no physical principle that I know of, categorizing certain kinds of SOUNDS as music and others as mere noise.
November 23rd, 2005 at 11:28 am
To Sean’s question:
I’m hoping it’s fairly obvious that the primary difference between (b) “music from a violin” and the other choices is that the medium of propagation for sound (compression of the atmosphere, to put it simply) is different than for the other choices (wave propagation of electromagnetic). In space, no one can hear you play Vivaldi.
November 23rd, 2005 at 11:35 am
I think “the sun disappeared” should be interpreted as “sun stopped radiating in the optical frequencies”. This would not violate general relativity
November 23rd, 2005 at 12:42 pm
my answer is b) music.
the others are all examples of electomagnetic waves: radio waves, visible light, infra red (radiators really heat rooms by convection, but the radiator will lose some heat in the form of infra red radiation, no?).
–Q
November 23rd, 2005 at 1:20 pm
“Electromagnetism” was the common phenomenon I was looking for, and “heat from a radiator” was a really bad example; should have picked something where the heat was more purely radiative and not convective.
But there are different answers one could plausibly defend, and that’s okay. It’s not about getting a grade, it’s about understanding the unity of disparate natural phenomena.
November 23rd, 2005 at 4:29 pm
I prefer to interpret “the Sun disappeared” as “the Sun no longer appeared,” that is, stopped being visible. One way this could happen without violating many popular physical theories would be if somebody (Vogons perhaps) inserted a moderately large sheet of non transparent material (aluminum foil, say) between us and the sun.
November 23rd, 2005 at 6:24 pm
I have to make another attempt at Sean’s challenge of coming up with a brief but thought provoking question. This one is related to the other physics education post:
When you look at a rainbow you see the arcs of color, often against a dark backdrop of clouds. You also see the grayish mist of the falling rain. Where does the mist appear brighter?
a) inside the rainbow
b) outside the rainbow
c) the brightness is the same inside and outside
d) it varies
To find the answer, use google to search for images of rainbows. If the background sky is bright you can’t see the effect, but if the rainbow is bright and the background is dark, the effect is quite striking, I think. I’ve also seen this first hand, which is why started thinking about it. What is going on? (I think I know, but I haven’t seen it described anywhere.)
Gavin
November 23rd, 2005 at 10:37 pm
I understood 6 as “If the sun stopped radiating / burnt out / no more nuclear power generation”. Which is a wonderful question, because a good way to model it is to consider photons moving through a cloud of electrons as behaving the same as perfume moving through a room. The answer: tens of thousands of years.
November 23rd, 2005 at 11:07 pm
Gavin-
You might enjoy watching MIT professor Walter Lewin lecture on the rainbow. He explains what’s going on.
Tom
November 23rd, 2005 at 11:14 pm
????
November 24th, 2005 at 1:46 am
I actually got #5 flat-out wrong because, off the cuff and it having been a while since I was a freshman class TA, I misremembered how moment of inertia entered into it and thought the density of the ball might make a difference there. (But it is true that you have to assume they’re rolling ideally, that there’s no sticking resistance or air resistance to consider and that the balls are both solid and of constant density inside.) Had I not been over-thinking it I’d have gotten it right.
The answer to #1 could be “all or several of the above”, right? I mean, sure, most of the radiation is infrared but it’s probably some sort of continuous spectrum. If it’s an ideal blackbody, then all frequencies are emitted to some degree.
For #3, the most obvious answer is (b) but you could probably come up with situations under which (c) and (d) are correct as well if you squint hard enough. I suppose it depends on how you define, say, the velocity operator in the theory you’re considering (which is a tricky issue in itself), and what definition of mass you use. They just have to be noncommuting. (…unless *Heisenberg’s* uncertainty principle is specifically the p/x one, I suppose.)
And, yes, I had the same objection several other posters did to #6, specifically because I’ve participated in a million frustrating Usenet arguments with Tom van Flandern about the speed of gravity in which the role of conservation conditions in general relativity turned out to be very important to the question. If it had only asked “if the sun stopped shining…” it would be much easier to answer. Though, come to think of it, you could still have lots of fun arguing about what “right now” means in this context.
November 24th, 2005 at 2:01 am
I had the exact same reaction to #6. And don’t mention his name. He might google….
(#3 skirts very close to the usual misunderstanding of Heisenberg, but I guess it’s still legit.)
November 24th, 2005 at 11:30 am
I guess one had to encompass “all the thinking” and show what existed beyond this?
November 25th, 2005 at 5:38 pm
If nothing else, I m good at these multiple choice tests. So 6 out of 6 to go with 990 on the Physics GRE, nearly 4 decades ago. Of course the wooden ball would break the plane first because it is bigger. But I know not to worry about such stuff, or friction etc. in the made of world of these tests. But Clifford, they aren’t point masses at all.
November 25th, 2005 at 5:43 pm
Ned Wright: True, they’re not point masses. I agree, and hence my explanation involving moments of inertia and friction and rolling, etc. I only brought up poiint masses in response to an earlier questioner. (#3)
Cheers,
-cvj