I recently went on an Institute of Physics funded trip to visit CERN in France/Switzerland, and they handed out some free beer mats. These beer mats have some interesting physics condundrums I'd like to share. They're fairly simple, but make for some interesting thought experiments (or indeed real experiments, if you're that way inclined).

- Two filled beer cars, one frozen and one liquid, roll down a short smooth slope. Which one gets to the bottom first?

- What happens if you try to light a candle inside an oribiting space station?

- What is the maximum distance from the sun's centre to the centre of mass of our solar system?

Answers on a postcard please.

I'm actually stumped on these:

- I'd suspect same time, but I'm curious how the intertia of the liquid affects things
- You don't get any, because presumably you left your partner back on earth
- Hm, I'm going to go with the sun's radius

#2 =

I don't know what a beer mat is but I want one from CERN!

I thought everyone knew what a beer mat is. It's the piece of carton that beer is usually served on.

I'm going to just take a guess:

1. I would say they'd get there at the same time. If the can is completely full, the liquid shouldn't have any effect on the can. I think?
2. This I'm pretty sure on. It would light of course, but the resulting flame would bubble out around the wick (probably mostly spherical), as the heat no longer "rises".
3. I assume this question is asking where the true center of mass is for the solar system in relation to the sun? If so I have no idea, but I'll just go with "very close", since the sun is much more massive than the other planets combined.

#1 - I think the frozen one will roll more smoothly - I suspect the sloshing may slow the other one down. The other thought I had was "how cold do you have to go to freeze beer? And does that have any effect..?"

#2 - Not sure what to think of this one. I'll ponder.

#3 - I reckon it's well within the solar radius, maybe about 30 or 40% of the distance from the centre to the edge.

The only one I had any good idea on was #3, and I guess you could work that out by approximating everything as point masses on a line and... taking moments? That's the first thing I'd do when faced with a dozen masses on a suspiciously thin bar. And, I guess, finding the distance from the center of the sun (well, the distance from the point mass that represents the sun) by equating the moments at zero at x, or something.

Then again, the difficulty would be in how far you define the solar system (I'd guess just out to Pluto) and what to do about the asteroids, since there's no real way they'd conveniently bunch up in a nice line like the rest of the planets. Although in that respect you could do it as a distributed load...

Gah, I'm thinking way too much about this.

As for number #2? I wouldn't know where to start.

#2 - RING OF FIRE.

#1 seems simple to me, or am I missing something?

The only changing variable is temperature. You're not adding or reducing any mass. It's all still there, it's all still in the shape of a can. The cans are filled, therefore no "sloshing" about of liquids as there is no air supposedly.

If we're getting practical: The only things I can think of that might affect it (but only on an absolutely tiny scale) would be the temperature reducing the size of the beer slightly, making it a slightly tighter cylinder. But I can't remember off the top of my head the inertia principles so maybe even that is irrelavent.

Another practical experimental issue would obviously be the condensation on the side of the can acting as lubricant. Unless the can is magical.

Also, filling a can fully without air would be difficult, and similarly freezing one without slight deformation would be problematic. Magical cans can fix that too.

But maybe I'm reading into it a little too much for a beer mat...

2# The wick would guide the flame to an extent, but surely once the candle starts to melt, the wax might not be received as effectively since there's nothing to really keep it against the wick. Maybe the laws of thermodynamics might play a role here too? Though I guess in a space station there is no obvious "cold" area it would be drawn towards.

3# Would be surprised if it was past the radius.

1) Get home late
2) Find you have no cold beers, stock the fridge up but feel this is unnecessarily time consuming
3) Put one in freezer so you can drink it sooner
4) Forget about it

It was such a tragic waste of beer...

I thought everyone had seen this picture.

Wait, what?

1: is not possible, as the beer can would explode due to the expansion of the water in the beer as it freezes (and it will have water in it, because beer is not pure alcohol)

2: see kyle90's picture

3: the sun has a very erraticaly shaped orbit around the center of mass of the solar system, which means that the maximum distance would take weeks of computing orbital dynamics and how the planets (esp. jupiter) pull on the sun (this pull is also one method that we use to find planets around other stars) and simulating a very long period of time.

tl;dr the question has no real meangful answer

I haven't wondered about #2 for quite a while. Thanks kyle!

Oh, regional word. Just a coaster here.

For the beer cans rolling down a hill, I thought about it in terms of conversion of energy. At the top of the hill, the cans will have the same initial gravitational potential energy (mgh, where m is mass, g is acceleration due to gravity and h is the height difference). This is converted into rotational kinetic energy as they roll down the hill (½Iω^2, where I is the moment of inertia and ω the angular velocity.

For the can of frozen beer, the beer is attached to the inside of the can and rotates with it. In the unfrozen one, the liquid does not rotate very much (depending on the viscosity). The moment of inertia for the liquid can is lower as the contents is not rotating (or at least rotating much less than the frozen can), and the liquid can will have less rotational kinetic energy than the frozen one.

Because the liquid in the can obviously can't move any faster than the can surrounding it, the frozen can should always reach the bottom of the slope first. Also, a can filled with a high viscosity liquid (like honey) should reach the bottom before a can filled with lower viscosity (like olive oil) because more of the liquid will rotate with the can.