A physics question...

[Shiver]

Not what you think - I don't have a question, I need one.

Simply put, I need one for a scene in a story I'm writing. It doesn't really matter what it's about, as long as it's something that would be very difficult to answer. Something the average advanced physics student would have trouble with.

Naturally, I'd also require the answer as well. Trick questions are fine, and it doesn't matter which subfield of physics it is - Particle, Biophysics or Astrophysics would be preferred, but any kind would work just as well.

Thanks in advance!

(Cross-posted in The Lounge)

One Edit I should specify what I mean by trick question. I mean a physics question designed to trick someone into doing a lot of unnecessary work to try and solve it, when the answer is actually a lot simpler than that.

[Bake]

1. A train leaves the station going west, accelerating at a variable rate

up to 60 mph. At the same time, another train leaves the same station going east, accelerating at a constant rate up to 50 mph.

When they crash, where do you bury the survivors?

Bake

[Greyskye]

3. You've got to state the rate of acceleration for both cases

And why would you bury the survivors? :shrug:


:evilgrin:

[Posteritatis]

21. Well, they're trapped in a word problem. Clearly they have no hope (nt)

[begin_within]

2. As the sun burns its fuel and loses mass, won't it's gravitational pull on the planets weaken,

to the point that the planets will fly away instead of orbiting?

[Shiver]

4. Hell if I know

I asked for the answer too, remember? :P

[begin_within]

6. It would, however the sun will turn into a red giant before that happens, and incinerate the planets

[caraher]

5. The old reverse sprinkler is always a good one

See, for starters, Wikpedia and links therein. The nice thing is that people still argue about the answer, and it's an easy question to understand.

[Shiver]

8. That's good, but

unfortunately not complicated enough....

Thanks though :)

[TlalocW]

7. Here

Silver has a density of 10.5 X 10^3 kg/m^3 and a resistivity of 1.60 X 10^-8 Ohm*m at room temperature. On the basis of the classical free electron gas model and assuming that each silver atom contributes one electron to the electron gas, calculate the average time between collisions of the electrons.

Answer: 3.80 X 10^-14 s

[Shiver]

9. That's the kind of thing I'm looking for!

One question, though... how would you speak that answer?

[krispos42]

10. 38 femtoseconds

:-)

[Shiver]

11. I have no idea what that means

Perfect! :D

[krispos42]

14. The prefix "femto-" means...

one-quadrillianth of something.

.000000000000001 of something

1/1,000,000,000,000,000th of something

:-)

http://en.wikipedia.org/wiki/Femto-

[Shiver]

15. Yeah, I looked it up

It's a mind-boggling concept that time can be reduced to a fraction so small it becomes difficult to even fathom it...

[krispos42]

16. We can measure things down to the attosecond range now..

...which is 1/1,000th of a femtosecond.


Neat, huh? :-)

[hunter]

12. Double pendulums, chaotic waterwheels, any of those things...

http://www.math.hmc.edu/~jacobsen/demolab/waterwheel.html

There are many problems where the behavior of an idealized model is wildly divergent from the reality. I'd pick something like that, where the model equations might be solved, but are irrelevant in the real world of chaotic systems.

There are many models that look good on paper, with equations that can be solved, that nevertheless fail spectacularly as descriptions of reality. (Most equations written by economists and market players seem to fall into that catagory, btw.)

The correct "solution" to these questions is to recognize the gross inadequacies of the models. If you look at the chaotic water wheel for example the "solution" is that the wheel will turn one way or the other, at some velocity or another, limited by the amount of energy available to the system -- in this case the energy of the falling water.

In a good "trick" question the chaotic nature of the problem would be hidden in some subtle way, and could even be woven into the fabric of your story.

[Shiver]

13. Interesting...

These options do open that possibility up quite a bit... I hadn't intended for the question/anmswer to have any real impact on the story - it was just a scene showing how abnormally intelligent one of the characters has become in so short a time - but it would be a lot stronger if I could connect the actual problem to the story...

Thanks :D

[TechBear_Seattle]

18. "The behavior of an idealized model is wildly divergent from the reality"

My grandfather (an engineer who specialized in pumps) used to call these kinds of problems "the culling of true engineers from mathematical theorists." One story I remember him telling....

Take a rubber ball with a diameter of 1 meter. Drop it from a height of 10 meters, as measured from the center of the ball. It bounces, and ascends to a height of 9 meters. It bounces again and ascends to a height of 8.1 meters. From this we conclude that, with each bounce, the ball will ascend to 90% of its previous height. How many times will the ball bounce before it is at rest?

A mathematician will say that the ball never comes to rest; like the limit of 1/x -> 0, it will approach a state of rest but never reach it.

An engineer will say that once the "bounce" is less than the radius of the ball (again, we are measuring from the center), the ball will exhibit no perceptible bounce and be at rest for all intents and purposes. If you wanted to turn this into a trick question, maybe...

The following function defines the height of each bounce of a rubber ball, as measured from the ball's center. Find the minimum x such that the ball is at rest.

f(x) = f(x - 1)
f(0) = 10
The domain of x is positive integers

The first instinct of a mathematician will be to take the limit of an infinite sum :evilgrin:

The answer, by the way, is 22, as f(22) is the first case where the result is less than 1.

Added

Or if you really want to be nasty...

A is the ordered set of all integers.
B is the ordered set of all even integers.

Which answer is true?

1) A > B because A contains every element in B and A contains elements that are not in B.

2) A < B because every element B(x) = 2A(x).

3) A = B because both are infinite sets.

4) All of the above.

5) None of the above.

I believe the correct answer is (5): there is no definition of equality between infinite sets.

[BadgerKid]

23. Check out countably infinite sets.

Two sets whose elements can be put into 1-1 correspondence have the same number of members.

Also check out "levels of infinity" like Aleph_0, Aleph_1, ....

[TechBear_Seattle]

17. I remember one about the minimum volume of a hole drilled through a sphere

Given a sphere of diameter x, what is the minimum volume for a hole drilled through the center of the sphere?

It turns out that, if you give the hole a diameter of zero, the hole has a volume of zero. PROVING, however, requires setting up a rather complex integral.

[pokerfan]

19. Equivalent resistance of a cube of identical resistors

It's my personal favorite. No two resistors are directly in series or parallel so you can either do it the hard way (simultaneous equations) or use a trick...

http://www.physics.ucsb.edu/~lecturedemonstrations/Composer/Pages/64.42.html

[hunter]

20. It reminds me of the old analog models of aquifers...

http://www.sws.uiuc.edu/hilites/achieve/gwmodpic.asp?p=06

[pokerfan]

22. Analog computing is so cool

http://dcoward.best.vwh.net/analog/">The Analog Computer Museum

The http://en.wikipedia.org/wiki/Antikythera_mechanism">first analog computer? It's sad to realize that the Greeks and Romans had advanced science to a point that we wouldn't see again for about twelve centuries.