The answer is d. The way I thought of it was, if the original angular momentum is to the left, and the new angular momentum is slightly South of West, then the change in angular momentum is mostly South. A South angular momentum corresponds to the briefcase rotating top to the left... but that would be increasing the total angular momentum. Instead, the briefcase goes the other way (top left) in order to counteract the effect. I'm not sure if this explanation is 100% as gyroscopic motion is rather complicated. If you idealize the flywheel as a square pip with water flowing in a 'circle' and think about it using forces... then you can arrive at the same conclusion. This is a like a 3.5/5 difficulty I'd say.
MasterOfChaos was first to provide the correct answer, and I think evanthebouncy! provided a good, alternate explanation.
Question 5 Gravity Imagine two small droplets of water floating in empty space. Our conventional theory of gravity says that they will attract and accelerate towards each other. But what if instead you had water everywhere except for two small bubbles (empty spaces) nearby in the large mass of water?
The bubbles would:
a) Move Apart b) Not Move At All c) Move towards each other (attract)
Once again, please make sure to include explanations (in spoilers) along with your answer. This one is rather tricky in my opinion. This is also a nice lead-in for fluids next time.
Last edit: 2008-10-16 08:56:11
Haste. Exalted. Flying. Deathtouch. Lifelink. Protection from Red.
But the Hamiltonian wasn't Hermitian!
raiame United States. October 16 2008 09:09. Posts 405
I think the answer would be a, because if it were completely filled then nothing would happen at all, so these bubbles have effectively negative mass. Although the force of gravity would attract water together, towards the center, the bubbles would move apart.
Insane Lane United States. October 16 2008 09:22. Posts 397
B. If you have an infinite volume of water, the system has no center of mass.
Edit: If the mass of water is finite, there exists a center of mass that the water will gravitate towards, which will push the bubbles outwards, radially. Unless the bubbles begin on the same radius, they will be moving away from each other.
Last edit: 2008-10-17 06:56:14
doghunter United States. October 16 2008 09:46. Posts 23
first of all my english sucks xD well my answer would be C,,, you are just replacing an empty space by an space full of water, so i think a bubble would deform that space, which is full of water, so due to that deformation the other bubble will be attracted to the first one. So attraction will be the answer ,,,IMO xD.
Underwhelmed United States. October 16 2008 14:13. Posts 207
we aren't talking about the water, i don't believe he also specifies that the bubbles are just the empty space when he says "bubbles (empty spaces)"
edit: oh wait, i think i get what you're saying. that the water around the bubble moves towards an area, effectively moving the entire bubble itself. not sure which one micronesia means, we'll just ask him tomorrow.
Last edit: 2008-10-16 14:35:43
MasterOfChaos Germany. October 16 2008 18:40. Posts 2896
Assume the pressure/density is constant in the whole space except the two bubbles. I assume newtonian gravity, no general relativity/deformation of spacetime. Because else space itself might collapse. Now I assume that the bubbles are shielded against the water, ie by a thin glass wall, else they'd simply fill with water. The gravity field points cleary away from the bubbles, so the water moves outward until the gravity is compensated by a density/pressure gradient with lower pressure in the space between the bubbles. During the beginning this process the water might take the bubbles outward a bit. In this new situation the bubbles try to move to the lower pressure and since no gravity affects them they will move inward. So my answer is c) Move towards each other (attract)
Last edit: 2008-10-16 18:42:23
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Luddite United States. October 17 2008 02:59. Posts 2153
I always though that every object attracts each other, even if you put 2 bottles they still attract each other. Thing that keeps them apart is friction (which is much higher than their force to attract each other.