# Can a submerged object in a free falling fluid sink faster than falling?

I've been wondering about how sunken objects would behave if you could instantaneously flip their container with water. Like if you had a bucket filled with normal tap water and you dropped a ball in it. Then SOMEHOW you instantly flip the bucket over such that for just a moment, the water is suspended in midair and the ball is still touching the base of the bucket.

What I want to know is, first of all what would happen? I know that if you drop a bowling ball and a bouncy ball from the same height they'd just about reach the ground at the same time, but what about this scenario? If you "drop" water and an object inside the water at the same height, do they reach the ground simultaneously? Or does the object "float" down the falling water?

Second of all, under what conditions could the object fall first? That's what I'm looking for- what kind of object could fall out of the water and reach the ground before the water does? What difference would there be between the object being a sunken wooden ship and a rock?

Third of all, say we take this experiment to the ocean, where the water pressure gets higher as you go down. If there's an object at the bottom of the ocean and we flip the ocean, how does the pressure affect things?

• I think this is interesting, but your third question seems to be redundant. All fluids increase pressure with depth, and that's actually how buoyancy works in the first place. Although the pressure at the bottom of the ocean is way different than the pressure near the surface, the pressure difference due to height only changes a bit due to density. – JMac Jan 24 at 18:15
• Does the base of the bucket also instantly disappear the moment the bucket is flipped? – Caius Jard Jan 27 at 14:15
• Othe, the simple way to understand this is just that each "atom" acts on it's own normally as it would fe nothing else was there. It would all just "fall down". In your third image everything would just look like that forever, until it all hit the ground. Your experiment is literally identical to the hammer-feather thing. (Of course, air resistance etc. affects things, but that's normal, and not what you're asking about.) – Fattie Jan 27 at 17:08

I want to supplement Emilio's intuitive answer discussing what would happen with some thoughts as to why what you propose in your second part cannot happen.

What kind of object could fall out of the water and reach the ground before the water does?

Let's assume the water is a single entity. In order for the object to accelerate faster than the water, the object needs to have a larger downward acceleration than the water does. This would need to come from a downward net force that is larger than the weight of the object, as in free fall both objects will have the same downward acceleration. Where would this force come from? There is no buoyant force in a free-falling fluid, but even if there were the buoyant force would act upwards on the object, not downwards. Therefore, the best your could even hope for is that the object and the water move together, and this is indeed what happens.

Perhaps the confusion comes from why certain objects normally sink. They aren't pulled down by the water, they are pulled down by gravity. In your everyday scenarios it is just that the fluid impedes this "falling". You could even think of us as all sinking in the Earth's atmosphere. Therefore, in your scenario, it is not the case that because the object is in water suddenly means it wants to move down through the water. The water itself is not the mechanism for why objects sink.

• @thegreatemu Thanks for the heads up – Aaron Stevens Jan 27 at 22:41

The Equivalence Principle tells you that physics in free-fall is identical to physics in an inertial frame in the absence of gravity, in which case there is no buoyancy and any changes to the boundary of the liquid come from surface tension and related effects. The same is true for your falling mass of water.

• Hi, I don't understand much of what you said, could you dumb it down please? – OtheJared Jan 24 at 18:23
• @OtheJared - with no gravity there's no buoyancy. If there's no buoyancy, then nothing can "sink"; there's no direction for things to sink to. - E.g., a bottle of water in outer space with a tennis ball in it: it will bounce around in there every which way. But if you bring the bottle back into a gravity field, buoyancy {due to the large volume (the size) of the ball, relative to it's mass (its weight) compared to that of water} ... then it floats. - A lead ball would sink on earth, but it'd also bounce around up there. – Mazura Jan 25 at 3:01
• If the water is falling through air, it won't be in free fall - it will reach terminal velocity. Then the ball would fall through the water, right? I'm not sure if it would fall entirely out of the water, though - could its own terminal velocity be lower than that of the blob of water? – Tom Anderson Jan 27 at 10:09
• Terminal velocity implies that the upward force (due to air resistance) matches that of gravity similar to how the upward (normal) force of the ground matches that of gravity -- either way, net acceleration is zero. Thus sinking and floating would behave as they normally would. What happens when the object falls out of the blob is another matter entirely. – Brendon Boldt Jan 27 at 21:33

The question is well answered by Aaron and Emilio. To make the effects interesting, let us visualise the scenario for a particular case - when the object is hydrophilic (water attracting) and air resistance is negligible, in a qualitative manner.

The following image shows the system at different times:

The "Initial State" as the name suggests is how the system looks immediately after flipping. The second diagram (from left to right) shows the system after some time. You could see, near the bottom, the liquid near the beaker's inner surface has moved lesser distance compared to the liquid near the axis of the beaker. This can be attributed to the viscous forces of water which acts in between different layers. Think it of as a frictional force between different layer of the fluid. At this time, near the top, a somewhat "nothing" vacuum gets created much like when "mercury barometers" are tilted. Let us assume that this suction force due to the vacuum (more precisely the atmospheric pressure at the bottom pushing the liquid upwards into the beaker) is not enough to hold the liquid inside the beaker itself.

The third image shows the situation at a later time. Till now both the object and the centre of mass of the fluid has fallen down at the same rate. The object could have moved downward slightly more than the liquid due to attraction forces provided by the molecules of the liquid. This is best observed in the fourth image. By this time, the entire both water and object have come out of the beaker.

Now, the situation will be similar to having no gravity. As we've neglected air resistance, water takes nearly a spherical shape. Further, as the object is hydrophilic, attraction forces balance out only near the centre of the water sphere and so, the system will look like the last image denoted by "Final State".

In reality, if we include air resistance, we may have to account for the distortions in the spherical shape of the liquid. Also this might alter the position of the object inside the liquid.

Edit 1:

It seems some do not understand why the object moves towards the centre of the liquid sphere. To eliminate this confusion, let us consider the following diagram, which shows the adhesive interactions between molecules of water and the object in red coloured arrows:

The object placed off centred, has a non uniform distribution of water molecules around it. So, the distribution of forces is also not uniform and hence net force is towards the centre. You can imagine this like different people pulling the object using a rope with equal forces but the number of people on different directions is different and hence causing a difference to the state of rest of the object.

Edit 2:

It was asked in the comments how can something not in contact with the ball exert force? How can the force be unbalanced?
The reason is adhesive interactions are electrostatic forces. These reduce with increase in the separation between the interacting objects. Further, these forces can act even if there is no physical contact between them.

Note:

I'm not saying the object at an off-centred position goes towards the centre of the water sphere due to "hydrophilic" interactions. It's because of the "adhesive forces" which act between the molecules of water and the object. Adhesive forces can act even if there is no physical contact as they are electrostatic in nature as described previously.

The main source of confusion in the comments below was misunderstanding of adhesive forces as hydrophilic interactions. The main reason why I considered hydrophilic objects over hydrophobic is: in the case of hydrophobic objects due to the initial state of the system, the object would remain out of the liquid and the liquid would not swallow the object due to adhesive interactions as repulsive forces are stronger than attractive forces.

If the hydrophobic object were swallowed the energy of the system increases or in other words it'll be less stable and so the object and the liquid fall down as separate entities.

Image Courtesy: My own work :)

• I don't see how the object being hydrophilic means it here pulled to the center of the water sphere. If that were the case, then hydrophilic objects would sink faster into deeper pools of water, which doesn't really make sense. – Aaron Stevens Jan 25 at 5:27
• Basically you assume that the interactive forces ball/water don't go off far from the interface? Or they do so? It is not clear to me why a different (far from interface) distribution of water molecules should generate that "centripetal" force. This requires cumulative effect which are not straightforward to me. Not to say it is wrong. Just I don't see it, at least clearly. – Alchimista Jan 25 at 8:59
• The confusion is that hydrophilic interactions only occur at the surface of the object. They don't act at a distance. If you had this object in space next to a water droplet, you seem to suggest that the object would be pulled towards the water due to its hydrophilic nature. – Aaron Stevens Jan 25 at 13:00
• I don't believe having more water to one side causes the ball to move to the center. The ball is completely submerged so it feels equal forces on all sides. Electrostatic interactions are short range so they only act on the surface (for neutral objects). If the sphere of liquid is rotating though it is a whole different story. Bubbles will now move to the center because centrifugal forces make the densest fluid move to the outside of the sphere. Could you provide a link of this ISS video to make sure the liquid is not rotating? – AccidentalTaylorExpansion Jan 25 at 16:45
• @GuruVishnu Adhesive interactions are based on electrostatic forces, but these forces are understood to diminish quite rapidly (a couple of molecular layers, less than 1 nm) - because the molecules rearrange to balance the charges. It takes special conditions to create anything more than a bilayer of molecules at the interface. This is a phenomenon of importance in battery science, and is well documented as the electric double layer. There is no net force on the particle from surface interactions once it is fully wetted. – Riet Jan 27 at 19:15

under what conditions could the object fall first?

Air resistance.

If there is enough air resistance to slow down the water, then the denser than water object will fall faster than the water.

Except OP said the liquid was free falling, so air resistance doesn't apply here

flip the ocean, how does the pressure affect things

This is quite different.

For one thing, it's not free-falling.

The high pressure water that is now at the top will expand - some of the water at the top will initialy be pushed up, possibly with enough force to lift the heavier-than-water object. It will then fall. Water not at the top will fall from the instant the sea is 'flipped', though perhaps sink is a better word because this isn't free-fall, it's compression (at the bottom) and it's decompression (at the top).

There would be more than a bit of bouncing and turbulence, but before too long, the original pressure distribution will be restored.

Meanwhile, possibly after having initially been thrown upwards, the heavier than water object will again sink to the bottom. Depending on friction, the object might drag down some water with it, but most of the water at the top will stay more or less the top, and most of the water at the bottom will stay somewhere near the bottom - until temperature convection and other causes of turbulence come into play. But I think that's going beyond the scope of the original question.

once you tip the bucket over the water,ball system is in free-fall.

in free-fall gravitational forces have no effect on the arrangement (except for tidal effects which a very weak at this scale) so everything falls at the same speed. you have a blob of water with a ball near the top.

what could cause the ball to move faster.

• Springiness, if the ball was slightly squashed at the bottom of the bucket it springs off the bottom of the bucket moving slightly faster than the water

• Magnets, if the ball was made of some magnetic substance (like steel) it could be attracted to a nearby magnet. water is also slightly repelled by magnets.

• Currents. Atmospheric drag will push the outer layers of water backwards creating a current in the water that moved it backwards behind the ball.

Third of all, say we take this experiment to the ocean, [...] and we flip the ocean, how does the pressure affect things?

The pressure goes away as soon as you flip. pressurised things at the bottom of the ocean expand suddenly. otherwise same.