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Glass Sphere

Science brain teasers require understanding of the physical or biological world and the laws that govern it.


Puzzle ID:#7611
Fun:*** (2.7)
Difficulty:*** (2.52)
Submitted By:im_para_noid*****
Corrected By:boodler




You are in a glass sphere suspended by a steel chain from the Empire State Building. With you in the sphere are a sugar cube and a small stone, and you are holding a pigeon. You will gain your freedom if you can make the sphere lighter using the pigeon. What is your best strategy for escape? (Note: the pigeon must remain inside the sphere at all times.)

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Oct 01, 2002

what about the sugar?
(user deleted)
Oct 02, 2002

If I'm not mistaken, any air escaping the sphere would be replaced at the same time with incoming air, unless the sphere can contract. If it were a rubber balloon, OK. Once the hole is made, I'd throw out a feather through it. Anyways, would you risk shattering the sphere and tumbling to your death?
Oct 18, 2002

You could just drop the stone and suger cube. For a brief amount of time, as they were in freefall, the sphere would weigh less. You can prove this by weighing an hour glass on a sensitive balance as the sand is falling and compare it to when the sand stops. Of course you may not want to drop the stone if it is heavy enough to break the glass.
Oct 18, 2002

Oh, I see now that you must use the pigean. Ok fine. Knock the pigean out with the stone and drop it.
Oct 27, 2002

If its cold outside, just burn the pigeon and EAT it! ...w/ the sugar of course.
Nov 04, 2003

Are you sure? pressure is transmitted evenly through gases. Wouldn't the air molecules strike the inside of the sphere equally all over if the pigeon was released inside?
Jan 28, 2004

So, looking at fluid dynamics, I understand and accept the supposition that the bird flying would not decrease the weight of a sealed bubble (no more than a fish tank would be lighter because the fish is swimming and not on the bottom of the tank). It is a closed environment with a set amount of mass (and therefore weight, since the amount of gravity acting on that mass we can assume to be constant). So in order to decrease the weight of the sphere, you have to change the fact that it’s a closed environment (i.e. put a hole in the sphere). But what will that do for you? In order for the hole to help you displace gas outside of the bubble, the pressure inside must increase as a result of the bird flying. So...
Jan 28, 2004

Now, I’m not as familiar with bird flight dynamics as I am with airplanes, but let’s look at a few things: Assuming the pigeon was in equilibrium flight (not accelerating in any direction) the lift generated by the wings must be equal to the pigeon’s weight...
Jan 28, 2004

hmm... I'm trying to post the rest of my reasoning and explanation on here, but it doesn't seem to be letting me post anything of length anymore. Any help?
Jan 28, 2004

Okay. That nonsense over. Now, let’s reverse the way we look at how a bird (or airplane) flies – its primary lifting force is the low pressure above the wing ‘pulling’ up, not the wind ‘pushing’ down. By forcing the wing down through the air, the bird is creating a partial ‘vacuum’ (low pressure) from displaced air above the wing, which creates its ‘suction’ force. Obviously, in turn, the pressure below the wing becomes greater, creating the pressure differential enough to sustain flight. (phew!)

I do not believe, however, the net pressure inside the bubble would increase, because the displaced air used to create the higher pressure below the wing also came from within the bubble. In other words, you are moving the air already in the bubble, not adding more. Also, gases of unequal pressure always seek to neutralize the difference—so because of the pressure differential (pressure gradient) created by that partial ‘vacuum’ above the wing, air will move from the higher pressure to that lower pressure in order to neutralize the difference. Putting a hole in the bubble would only let pressure escape if the pressure inside the bubble was greater than the outside pressure to begin with (think a rubber balloon, as Mario suggested). Ultimately, though, a bird flapping its wings inside would create *imbalances* in the pressure within the bubble—not a net change in pressure. (Aside from which, if you were able to expel air from the bubble, it would create a lower pressure inside, which means air from outside would flow right back in to neutralize the pressure gradient.)

So, we have a hole, and we want to be lighter, and we have to use the bird. I like the feather suggestion, but why don’t we go one further: feed the pigeon the sugar cube, and just make sure it excretes the remains through the hole!

I hope all of that made sense - if anyone disagrees or would like clarification, I'd be more than happy to here about it.
Jul 13, 2005

If you can make a small hole with the stone (to release pressure), can't you make the hole bigger and push the stone, sugar and bird out of the sphere.
Apr 16, 2007

Or you could make the bird eat the sugar cube, which would decrease the weight by a teeny weeny fraction, but it would decrease nonetheless.
Aug 03, 2008

If one is allowed to make a hole, then the rock, sugar, or a loogie (non of which is a pigeon) can be displaced from the interior.

Without a hole?


First, do NOT eat the sugar cube. This is a cruel trick, designed to throw you off.

Next, take the rock and kill the pigeon. This will halt its metabolic processes. It will also provide something soft to lay your head on so you can take a nap. Think relaxing thoughts.

Because you and the pigeon are now giving off less body heat, the air inside the sphere will cool slightly. So will the glass sphere, making it shrink. Because the sphere is hanging from a chain, the shrinkage will displace its center of mass upwards. Being further from the center of the Earth, the sphere will now be lighter.

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