Cork in a water bucket, knowing our day-to-day world

[lalbatros]

Hello,

I have found a nice http://www.upscale.utoronto.ca/Gene...Rel/GenRel.pdf#search=" puzzle filetype:pdf"".
It ends with a puzzle that I like very much.
Juggling with Christoffel symbols and curvature tensors is not needed!
Writing the equations of motion is a technical answer, could you try?
however, would be a short answer. How short could you do it? (explanation included!)

Cork in a water bucket
A bucket of water has a spring soldered to the bottom, as shown on the picture.
A cork is attached to the the spring, and is therefore suspended under the surface of the water.
You are on top of the CN tower, holding the bucket, and step off.

While falling towards the ground:

* do you see the cork move towards the top of the water,
* towards the bottom of the bucket,
* or stay where it is relative to the bucket and the water?

Michel

 

[Danger]

I would see nothing because I would have my eyes shut and be screaming in terror.

 

[J77]

Everything would move together - it's not like the cartoons where Wiley Coyotes head follows his body and neck off the ravine after a short, thinking about it, moment.

 

[Galileo]

Yeah, jumping off of a tower sounds like a fun experiment. Be sure to write down whether the corks goes up or down before you hit the ground though.


By the way, I think it will go down.

 

[WhyIsItSo]

The cork moves towards the bottom of the bucket.

Why?

Gravity accelerates cork and water at the same rate. Water has more mass per volume, so the force is greater per volume. At rest, the bucket is preventing everything from falling, it provides an opposing force. Because the water has a greater force acting downward than the cork, it is under greater pressure, so the water tries to displace the cork upwards, thus stretching the spring.

When you jump, the opposing force dissappears therefore so does the pressure on the water. The water no longer applies upward force on the cork, so the spring pulls it down to the spring's own equilibrium.

 

[WhyIsItSo]

I would see nothing because I would have my eyes shut and be screaming in terror.

Think I'd dump the water, keep the cork and spring, and put my feet in the bucket hoping the spring and cork might break my fall a little

 

[Danger]

Think I'd dump the water, keep the cork and spring, and put my feet in the bucket hoping the spring and cork might break my fall a little

I suppose this is essentially the same phenomenon as a balloon moving against the acceleration of a car.

 

[caybo]

Simple answer:it would go up!

Because the cork is floating there, all forces are equal, and is simulating a zero gravity chamber. the cork goes with the motion of its environment, or any other force acting upon it, which in this case is only water. Assuming bucket is perfectly symmetrical, and lands perfectly on perfectly level ground, then if the cork is perfectly in the center, then due to the shape of the illustrated bucket, the water forces on the perimeter of the bucket is greater than that of the center due to more water pushing in on the bucket from the outside, and so the water would would be forced upwards in the middle, and the cork would go slightly up! Take that you silly cork and general(simple) relativity!

This is directly analogous to the fly in the car situation, a fly is flying in the car and the car hits the wall, does the fly continue into and smack the wall?

If there was absolutely no environment, pure space, there would be no particles to force anything anywhere, then it would stay perfectly still. If the car just dissappeared, the fly would continue.

Diagram of the movement of the water in the bucket bucket: ^,v,<,>=up,down,left,right

\vv>>>^^^^<<<vv/
.\vv>>>^^^<<<vv/
..\vv>>>^^<<<vv/
...\v>>>>^<<<<v/
...\>>>>><<<<</
...\__________/

See the water pushes against the walls,and goes inwards, forcing more force in the middle pushing the water in the middle up

 

[BillClarkson]

At rest in a 1g field, the buoyancy of the water on the cork is offsetting the pull of the spring.
Buoyancy has to do with the mass of the water displaced -- that's why steel ships float! When you drop the apparatus, all the external forces disappear (in free fall). But the force of the spring on the cork is an internal force, unaffected by acceleration. So it continues to pull on the cork, but with no forces to oppose it, it pulls the cork down.