Confounding Physics puzzler (infamous paper 5)

ifconfig

Recently I remembered a confounding question on our final paper at TCD/Physics. The famous "Paper 5" (I'm sure they still run this paper at TCD) contained multiple choice questions with conundrums, puzzling questions where the answers could be deduced using basic physical principles, back of envelope calculations/formula rejigging, etc.

The question as I recall was:

If all automobiles on the earth conformed to driving on the right side of the road would the length of the day
(a) increase
(b) decrease
(c) be unchanged

I remember comparing notes with colleagues after the exam finished and there seemed to be a consensus that the problem was related to moments of inertia and angular velocity. I can't remember what the consensus answer was but I know the reasoning was based on angular momentum conservation and moments of inertia for rigid bodies. I remember I was sound on angular momentum conservation so long as the assumptions were simple. This was a bit of a "curve ball" as Americans might say....

Anyone recognise this problem or have an idea how to formulate an answer ?

More generally is there anyone here still at TCD. Do they still run Paper 5 ?
I'd love (in my dotage.. I'm now 40) to have an archive of the questions
just for posterity sake and maybe have a go at tackling them now to keep my grey matter ticking over a bit )

-ifc

Professor_Fink

ifconfig wrote:

The question as I recall was:

If all automobiles on the earth conformed to driving on the right side of the road would the length of the day
(a) increase
(b) decrease
(c) be unchanged
...
Anyone recognise this problem or have an idea how to formulate an answer ?

Maybe I'm missing something, but shouldn't the length of the day be unchanged, since you have cars going both directions on the road anyway.

Unless a car took to driving continuously around the planet, when you go home you would undo what ever difference you made driving to work etc.

ifconfig

Professor_Fink wrote:

Maybe I'm missing something, but shouldn't the length of the day be unchanged, since you have cars going both directions on the road anyway.

Unless a car took to driving continuously around the planet, when you go home you would undo what ever difference you made driving to work etc.

Hi Prof Fink - Yes that sounds about right .. Looking back it seemed like a cheeky little question more to do with common sense than physics.
I'd say I've thrown out the original paper. It was 1988/BA Mod/Physics/TCD
That ages me
Most of the other answers to questions on that paper could be deduced
using dimensional analysis, a few lines of rejigging fundamental formulae
and basic understanding of classical and quantum physics principles
and maxims. They did have a tendency to throw in a few "quack" teaser
questions as well. Someone else who posted on this forum mentioned
paper V. I must see if he/she has any of the past papers.

David19

Here's past physics papers in TCD. They're under Science. It seems that they still have this paper 5.

http://www.tcd.ie/Local/Exam_Papers/summer_nonTSM.html

ifconfig

David19 wrote:

Here's past physics papers in TCD. They're under Science. It seems that they still have this paper 5.

http://www.tcd.ie/Local/Exam_Papers/summer_nonTSM.html

David - thanks a million.
I've downloaded 8 years worth of paper5 for posterity sake !
Handy link !

-ifc

dudara

We had a similar paper in UCC, and it could be so much fun! I always enjoyed sitting it, just for the challenge alone.

ifconfig

Good stuff Dudara.
Do you know if the UCC Physics past examination papers are available
to download from the UCC website ?
It was nice to be able to fetch 8 yrs worth of them from the TCD site.
Those exams bring back memories.

-ifc

dudara

I can't access them from outside UCC, and my password has expired as I'm no longer a student. Maybe someone else here can get them for you.

dudara

ApeXaviour

Damn only saw this thread now cos was away. Yes infamous paper 5, I shall be sitting it in 9 months time. Looking forward to it a little actually. The schol papers have a section of a similar ilk if you're looking for a couple more questions. It's usually paper 2 section D. In that link David gave ya, on the top of the page is a link to foundation scholarship past papers. Under science again.

There was a good one from this year actually, it was part a) of a 2 part question. I remember it cos I got it out but part b) was lost on me

Anyway here it is:
You have two identical sealed containers. One contains most air, the other dry air. They are both at the same temperature and pressure.

Which one is heavier? (ya obviously have to explain why too )

fluppet

I'm surprised TCD allows external access of its past exam papers...

I don't think the latest Schol papers are online yet. I was one of the lucky people who sat it, and I remember that question about the dry/wet air, but I can't remember what I came-up with for it.

ApeXaviour

fluppet wrote:

I'm surprised TCD allows external access of its past exam papers...

What's the harm? They're obviously proud of how difficult they are

fluppet wrote:

I don't think the latest Schol papers are online yet.

Neither are the latest annuals, they won't be til around november afaik.

fluppet wrote:

I was one of the lucky people who sat it, and I remember that question about the dry/wet air, but I can't remember what I came-up with for it.

Care to try an attempt now? I admit it's more of question that suits students who did mcp (maths, chem, physics in science) or advanced materials than tps. Was chattin to lunney (head of school) and he said not many people got it out.

Professor_Fink

ApeXaviour wrote:

Care to try an attempt now? I admit it's more of question that suits students who did mcp or advanced materials than tps. Was chattin to lunney (head of school) and he said not many people got it out.

Surely it's a relatively simple statistical mechanice question. The partition function for the two are different, since the components of air (like O2, N2, and CO2) are distinguishable from the water component.

ApeXaviour

Professor_Fink wrote:

Surely it's a relatively simple statistical mechanice question. The partition function

lol.. I love TP's! "Surely it's a simple case of <insert something complicated>"

So do you know the answer prof?

enda1

I'll go out on a lmb here and say wet air one is lighter.
Reasoning: Water molecule is lighter than average air molecule.

Is this silly reasoning?

(dont just say yes )

ApeXaviour

enda1 wrote:

I'll go out on a lmb here and say wet air one is lighter.
Reasoning: Water molecule is lighter than average air molecule.

Is this silly reasoning?

(dont just say yes )

Excellent well done! It's a simple problem with a simple solution. Physics ain't (well, at least it tries not to be) about over-complication.

For the benefit of others I'll explain in a bit more detail. It just requires the ideal gas law classical approximation. This states that the volume a gaseous material takes up is not based on the nature of the material but the amount of particles it contains.

i.e. pV=NkT=nRT. So if pressure, volume and temperature are equivalent, then the number of particles (molecules) are also the same. Since gaseous H20 is lighter than N2 or O2. Then the dry air container is heavier.

Professor_Fink

ApeXaviour wrote:

Excellent well done! It's a simple problem with a simple solution. Physics ain't (well, at least it tries not to be) about over-complication.

For the benefit of others I'll explain in a bit more detail. It just requires the ideal gas law classical approximation. This states that the volume a gaseous material takes up is not based on the nature of the material but the amount of particles it contains.

i.e. pV=NkT=nRT. So if pressure, volume and temperature are equivalent, then the number of particles (molecules) are also the same. Since gaseous H20 is lighter than N2 or O2. Then the dry air container is heavier.

I've PDFed the rigorous derivation here.

Sorry I was just trying to upload it when you posted an answer.

ApeXaviour

Professor_Fink wrote:

I've PDFed the rigorous derivation here.

And rigorous it is (fair play by the way). Statistical thermodynamics is amazing like that, I've no doubt it can be applied to every single classical thermodynamics question and wield the same results, more accurate approximations of figures and more.

However for a classical problem is it not better to use a classical approximation? When doing calculus you don't differentiate all the time by first principles do ya

Note: I may be slightly biased as I really dislike stat therm, well the concept I like it's the study thereof I've taken a regretful aversion to. So I can follow your derivation but wouldn't have been able to replicate it. There's a video somewhere of me burning my stat therm notes last may after the exam.

Professor_Fink

ApeXaviour wrote:

However for a classical problem is it not better to use a classical approximation? When doing calculus you don't differentiate all the time by first principles do ya

Note: I may be slightly biased as I really dislike stat therm, well the concept I like it's the study thereof I've taken a regretful aversion to. So I can follow your derivation but wouldn't have been able to replicate it. There's a video somewhere of me burning my stat therm notes last may after the exam.

It's not exactly the same thing. When we apply identities we already know doing calculus we the exact solution. Using classical approximations give you approximate answers.

Also in this case you can't directly apply PV = NRT since there are several different gases present.

For what it's worth, I was never much of a fan of statistical mechanics, but I had to teach it last year, so I've had to brush up.