I googled up an explanation of bouyancy, and quote it here in part:

"If a cubic centimeter of aluminum was suspended in a fluid such as water with a very thin and negligible thread, the metal cube would have the fluid exerting pressure on the cube. Try to imagine that if the cube were to disappear, and the fluid would magically replace the cube, then the surrounding water would support this cube that is now containing water, so that the cube of water would be motionless. That is, the forces would be balanced. The cube of water would push out on the surrounding water and the surrounding water would push back on the cube. The fluid would be static, or stationary. Now replace this same cube of water with the original cube of aluminum. The surrounding water would not 'know' that the cube has been replaced with another substance. It would still push inward and upward and downward with the same force that it pushed on the cube of water. The sideways forces would be balanced and oppose each other equally, but the upward and downward forces would not be the same. The pressure at the bottom of the cube is greater than the pressure at the top of the cube, because pressure increases with increased depth. The difference between the upward and downward forces acting on the bottom and the top of the cube, respectively,is called buoyancy."

This difference between the upward and downward forces referred to in the above explanation is known as a pressure differential. The amount of bouyant force is equal to the weight of the water displaced.

 

Yep! you are indeed warped, but this answer certainly gets the prize...

 

Either way you slice it, you still need gravity for the downward force. In free-fall there is no downward force, so the cork is not bouyant.

Like someone else just said, let's agree to disagree, and call it a day

 

Hate to burst all you guys bubbles - Bubba isn't weightless ...... physically impossible. Look at the formulae for gravitational attraction- there is no where in the Universe, or known space where Bubba is weightless. All mass exerts gravitational pull on Bubba, and yourself.

Ok, when you all get to the point where you can believe this, I'll tell you about Bubba in a box........

 

Put a cork in it.

 

And this statement is where your version of physics falls short. In free-fall (an object falling to the earth), there IS a downward force (gravity), that's why it is ACCELERATING at -9.8m/s^2. The reason to not include air resistance is that it takes out the effect of the frictional FORCES (which are upward when an object is moving downward), which would cause the object to reach terminal velocity if dropped from a sufficient height. The reason astronauts float within (and outside) their ship is that they are at orbital velocity--the ship and the astronauts are still being pulled to earth by the force of gravity (even a couple hundred miles out), but they are moving fast enough in a direction tangential to the curvature of the earth to stay at altitude, but not fast enough to break away. The lower the orbit, the higher the orbital speed needs to be to remain in orbit.

Before the bucket is released, there are two forces acting on it, which cancel each other out: the force of gravity (bucket's mass times gravitational acceleration of -9.8m/s^2), and a tensional force in the arm of whoever is holding the bucket (5 gallons of water would be about 42 pounds of tensional force). Since the forces are equal in magnitude and opposite in direction, the bucket does not move relative to the earth. Once the bucket is dropped, the tensional force in the arm is taken away, leaving only the force of gravity to act on the bucket, so the bucket begins to accelerate toward the earth: F=ma. 5 gallons of water has a certain, fixed mass, and now it has acceleration, too. Weight would be a bit of a fuzzy term, as it is only measurable when acceleration is zero relative to the earth, but the units of weight (kg m/s^2) are the same as force. So, in a sense, weight is a measure of ONE of the forces acting on a body at rest relative to the earth.

Back to the question now. I think pchristman has the best answer so far. There is a pressure differential in the water--roughly 1 additional atmosphere per 10 meters of depth, if I recall correctly. In other words, the water at the bottom of the bucket is denser than the water at the top of the bucket. This is what makes it possible to suspend objects in water, such as fish and submarines--the quantity of air and water contained within them as well as their component materials give them an overall density. If their density is less than the bottom "layer" of water, they will stay off the bottom. And, as long as the density of the object is more than the top layer of water, it will remain below the surface. In general, gasses are about 1000 times less dense than liquids, which is why air bubbles are "vehemently" buoyant. Cork contains a fair amount of trapped air, which greatly reduces its overall density. That buoyancy can be expressed as a force, since in the case of a cork floating on top of water, the cork is at rest relative to the earth (its pushing on the water with the force of its weight, and the water is pushing back with a buoyancy force equal to that weight). Since the water is not a rigid material, it is displaced by the cork (the amount of water displaced would weigh the same as the cork).

Now, at the instant the bucket is dropped (and the cork released), we have removed the tension force supporting the bucket, and removed the frictional force that counteracts the buoyancy force. Some new forces come into play. The pressure differential between the top and bottom of the water will now tend to normalize--that is the water will expand, in effect, it will push the bucket downward until the water is of uniform density. The effect of this is that the buoyancy force will go to zero, but this effect will take a small amount of time. During that short time, the cork will be accelerating under gravitational force, but will be pushed upwards by the buoyancy force until that force becomes zero. So the cork will likely be suspended somewhere near the bottom of the bucket, until the bucket hits the ground. At that time, depending on the relative depths of the water and the bucket, some of the water, and probably the cork, will shoot out the top of the bucket. Why does the water shoot out the top of the bucket? Because under the rapid deceleration when the bucket hits the ground, the water is going from its uniform density during the fall to a state where the top of the water is less dense than the bottom, plus the bottom "layer" of water stops first and is then displaced by water above it which is coming to an abrupt halt. The sides of the bucket redirect this displacement upwards.

Darn my fingers are tired, but my physics prof would be proud. If we were to start defining some quantities (bucket dimensions, amount of water, size and density of the cork, height of the starting point), the distance of separation between the bottom of the bucket and the cork could be calculated without too much trouble.

Jason

P.S. Maybe in the next couple days I'll type out an explanation of the 200-lb. Bubba falling with a scale underneath him.

P.P.S. The Vomit Comet works by imparting an upward velocity to the subjects (plane flies up at about 45 degrees), then the pilot pushes the nose of the plane down gradually. Since the subjects don't experience the air resistance the plane does, they keep going upward in an arc until the force of gravity takes away all their upward motion. The object of the pilot then is to keep the floor of the plane a couple feet below the subjects, making them appear to float in the plane. Once the pilot has to pull up, the subjects are pressed into the floor of the plane with a force greater than their weight--they're "pulling G's".

 

And this statement is where your version of physics falls short. In free-fall (an object falling to the earth), there IS a downward force (gravity), that's why it is ACCELERATING at -9.8m/s^2.

In free-fall, the bucket, the water, AND THE CORK are all accelerating at the same time.

No bouyancy.

 

I'll be curious to see how this comes out.

Hmm...

1) Force of gravity= constant
2) Wind resistance= Irrellevant/Zero (disallowed)
3) Object 'A' (bucket) presumed Metal, therefore higher density than the other objects.
4) Object 'B' (water) medium density if 3) is true.
5) Object 'C' (cork) is the least dense.

One theory has it that in the absense of wind resistance, a feather will fall as rapidly as a brick - therefore everything hits the pavement at once, and in the same relative positions. After that, they will all go everywhere...

Because of stipulation 2), it is not reasonable to expect anything but apparent local weightlessness, since without wind resistance acting in opposition to the force of gravity, no resultant portion of gravitic force will act on the three objects as to bring bouyancy into play. The cork might drift around within the volume of water if there is any perceptable eddy current, but since the only force acting on the objects is for our purposes gravity alone, the objects will each fall at the same rate of accelleration.

Until they stop.

In practical usage, if stipulation 2) did not apply - air resistance would cause some opposition to the force of gravity, and some bouyancy would exist, thus causing the cork to rise to the top of the water.

If the bucket were perfectly balanced and did not tumble, the cork might be drawn up out of the bucket, and some of the water. The cork would be left behind due to air resistance if this happens. It is entirely reasonable that a partial vaccuum will have formed above the bucket, which would tend to retain the cork in the bucket.

Not all of the water would depart, since a bucket filled with air in cross section must reach a point where the air resistance will not allow it to travel faster than some portion of the following water, my guess is that in this case ( #2 not applied) most of the water will remain with the bucket.

 

Greywolf, you seem to have gotten a grasp on the problem

Air resistance introduces "weight" to the equation because you're resisting the acceleration.

Let's do this: The bucket is dropped on the MOON.

 

In that instance the water will boil away in the vacuum, carrying the cork with it, the cork due to internal air pockets will explode (explosively decompress) and the bucket will fall at one sixth the rate it might have in the first instance.


"I am not irrelevant! I am a human being..."
*snikkerrezz*

 

Krewat, what you're neglecting is that before the bucket is dropped, the cork is being held to the bottom in opposition to the buoyancy force. The buoyancy is caused by the variation in density of the water from top to bottom and the density of the cork. Once the bucket is dropped, it takes a small amount of time for that force to go to zero (it will take time for the water to expand). During that small amount of time, the cork will rise in the water (even if only slightly).

This is similar to the Bubba problem. If Bubba is standing on a scale that reads 200 lbs (in a vacuum) at a given height, and the bottom is dropped out from underneath him, the scale will go zero as its springs push upwards on Bubba, which means his acceleration will be briefly less than gravitational acceleration. Once the action of the springs in the scale bring the weight to zero, both Bubba and the scale will be accelerating downward together, in contact.

The cork may only rise off the bottom of the bucket a tenth of a millimeter, but it will rise.

Greywolf, at least you got the bucket on the moon problem correct, provided the bucket is open on top.

If the bucket is closed to prevent the boil-away, the same thing I described above will happen, just the magnitude of the forces are one-sixth of what they are on earth.

Jason

 

Buoyancy does not exist in freefall. Follow link for references. The cork, bucket, water all fall at the same rate and the cork does not float to the top of the bucket until the situation changes.

http://www.google.com/search?hl=en&q...=Google+Search

Edit: The link does not work go the Google and type in "Buoyancy under weightlessness conditions" as the search term.

 

The original question asks whether the cork will float to the top of the bucket normally, slower than normal, faster than normal, or not at all. It is immaterial whether the cork moves a tenth of a millimeter then stops or never moves at all.

 

Having read a lot of this thread but not enough time to go back and look at a book about this, wouldn't the cork still be bouyant in the falling bucket? It is in a fall but not in a weightless environment like space. I think the bucket will fall and most of the water will stay in it (with no air friction allowed, and the bucket magically has no tumble, due to perfect release and conditions) and eventually the cork will rise to the top. Let's assume it has a long way to fall. Once the cork, water, and bucket are at the falling velocity I would think the force of gravity, which still is working in this case, and the density difference between cork and water will make the cork rise to the top. Yes,no?

By the way, I think a simpler explanation for what happens in the vomit comet is simple free fall, you are a parachutist with no chute, and no air resistance, you're just falling but you're in a closed environment so it feels like you are in the space shuttle. Yes, you and all the stuff you are playing with are weightless because you are not sitting or standing on anything to apply your weight.

 

Variation in density? There is none. And, that's NOT what causes bouyancy.

Look at the bucket at rest with water in it. Insert cork. Water level goes up. The amount of water displaced by the cork is what gives the cork bouyancy. Any object that weighs less than the amount of water it displaces will float. Any object that weighs more than the amount of water it displaces sinks.

Since gravity is what is working on the water to produce the bouyancy, as soon as the gravity is gone (or at least, it's effect in free-fall), there is no bouyancy.

Never mind, I give up.