I need a physics buff

I've been thinking about how fluid suspension works, and I'd like to know if a fish inside a fishbowl adds to the net weight of the object.

Say you've got a fishbowl full of water, weighing approximately 2 kilograms, suspended from a tension scale. Would the weight increase or remain the same if you added a fish to the system?

My hypothesis is no. I'll give my amateur proof after some of you supply answers and reasonings.

 

This is a really good question. There's two ways I'm looking at it.

Obviously the mass of the water is acting on the bowl which gravity acts on in its entirety therefore 9.81m/s x Mass = Force or Weight in this case. The addition of the fish would add not add to the mass because its technically floating in the space therefore the force of gravity acting on the fish would not be considered when calculating the total weight of the object.

The other way I'm looking at is the mass of the fish would be taken into consideration as the fish is technically still part of the total mass of the fluid as it still exerts a downward force on the fish which must be counteracted by the pressure of the water thus creating a force in the opposite direction, i.e downwards force. If we take into account the force downward caused by gravity + the force downward created by the fish acting on the fluid the total force downward must be counteracted by the force of the spring in the scale therefore it would read a larger mass.

 

It's seriously been driving me nuts, I keep contradicting and disproving myself, or else resorting to ridiculous analogies to rationalize it. Such as, imagine you're neutrally buoyant in a closed container of atmosphere. It's easy to then realize that you're "floating", and it's easy to associate "floating" with "weightless".

But then I think, no. Astronauts are technically floating by that logic, but they're still being acted upon by 90% of earth's gravity. The only thing that KEEPS them floating in that they're rocketing through the air at thousands of miles per hour...

So then counter act gravity. But the downward force would apply a force on the enclosure that you're in, wouldn't it? Adding weight, stretching the tension scale more

 

I edited my post probably 25 times changing my opinion. I want to go with my second option because the fish must have a force holding it from sinking from the bottom which in my opinion is the density of water but in that case it would act as a solid or the normal force acting against the force of gravity of the fish therefore increasing the total downward force acting on the bowl.

 

I'm glad you say so, because then I'd argue: isn't buoyancy a force in and of itself? If gravity is a force that acts through fluid (air, water, etc), does that mean buoyancy is an equal and opposite force if the object is perfectly buoyant? If you look at it that way, the fish isn't applying a downward force on the water (it's not "resting" on the water, compressing it, adding weight). In fact, the force is coming from the fish itself, an upward force from a less dense object in a more dense fluid, perfectly matched to gravity.

And infact, wouldn't that mean that it would eliminate some of the weight of the system, since the buoyancy could be also pushing up water molecules that are in direct contact with the top of the fish? Support them? It'd be a VERY slight change in weight, granted

 

It depends entirely on the work performed by the fish. If it puts out the "perfect" amount of work to remain suspended, then no, weight will not increase. If it falters and begins to sink, weight will increase. If it moves up, weight will increase. It must be perfectly suspended.

Also to address this:

Buoyancy acts as a type of normal force, yes. You're also right that there is mass pressing down above the fish, but it is more than likely negligible depending again on work done and the orientation of the fish. The weight of the system will not however decrease from its normal "rest" weight.

 

I'm pretty sure the work done by the fish has no impact on this.

The weight of the tension scale will increase. Look at it this way: If you have a bowl of water, but put an ice cube in it, will the weight of the bowl of water increase? (Even though the ice cube is suspended in it?).

The only force that can keep the fish from falling to the floor is the Normal Force from the bottom of the bowl (if the fish is resting on the floor) or the buoyancy force from the water.

You guys are accounting for the buoyancy force, but you have to take into account that the buoyancy force is just the weight of the water displaced. If you have displaced water, in a fish tank, the water has to go up. Hence, there is more pressure on the bottom of the fish tank, and hence, there is a greater total force on the bottom of the tank, so the tension of the scale is greater to counterbalance it.

I'm typing this as a stream-of-consciousness thing, let me know if any of it is unclear -- I draw a diagram later if you need it.

 

Very interesting topic indeed, thanks for this Mohtasa

I'd say that the waterbowl would be heavier with the fish.
Let me explain my reasoning with this.

If you lie on a bed, would the bed be heavier with you on it if you put the bed on a scale?
Yes obviously because you are sitting on the surface of the bed.

If you lie under the covers, but on a bed, would the bed be heavier with you on it if you put the bed on a scale?
Yes obviously because you are on the surface of the bed. Being under the covers doesn't matter.

If you lie on a waterbed, would the waterbed be heavier with you on it if you put the waterbed on a scale?
Yes obviously, because you are sitting on the surface of the bed. The bed containing water doesn't matter.

If you would rip the top off a waterbed, and lie in that waterbed (let's say it's held together even with the top off) would the waterbed be heavier with you in it?
Yes it would. You being on the surface of the object or in the surfacetension doesn't matter. Imo surface tension only affects the state, position and speed of the object. Not the mass as the mass is distibuted over the liquid, rather than the solid space of a bed.

Feel free to prove me wrong

 

Interesting question, but the net weight of the bowl would be heavier.

The density of a 1 pound fish is the same density as the water.

What you guys are also lost on is...

Fish using their internal organs, air bladders, they control their buoyancy to be neutral. There is no downward force.

The only way the mass of said bowl is to remain equal is if water managed to splash out equal to what the fish weighed.

You can't just add mass to something and act like it disappears. Where does it go?