Archimede's Principle to Make a Cup Float to Certain Height

[Terrified Virus]

Homework Statement

I am given a water tank, a small plastic cup, and some gravel. How could I use Archimede's principle to determine how much gravel to put in the plastic cup such that it sinks to a certain point (namely the rim), but then floats, so that no water is let inside the cup?

Homework Equations

I'd imagine the most relevant equations to this problem would be those of pressure, buoyant force, mg in general, and density.

I am quite unsure of where to start, let alone calculate the exact value. I have limited knowledge of buoyant mechanics, so any help would be greatly appreciated. Thank you!

 

[BvU]

Hello TV,
Can you formulate Archimedes' principle ?

 

[Terrified Virus]

Hello, thank you. Archimedes principle states that the weight of fluid displaced is equal to the buoyant force on an object submerged in a fluid. I am unsure of how to apply it to solve this problem.

 

[Chestermiller]

Are you allowed to weigh the gravel, or do you have to determine what level to pour it to in the cup?

 

[haruspex]

Hello, thank you. Archimedes principle states that the weight of fluid displaced is equal to the buoyant force on an object submerged in a fluid. I am unsure of how to apply it to solve this problem.

Right.
Clearly you will need to know or measure some facts about the cup, gravel and water. Are you given any, or tools with which to measure? What facts do you think would help?
Is "how much" gravel in terms of mass or volume?

 

[Terrified Virus]

Now these I am unaware of, for it is a future lab. I just know this will be the subject. I'm more interested in learning how I could do this with just volume, as with mass if I'm not mistaken I would just measure the mass of the cup and gravel and assure it doesn't exceed the weight of the cup with water, if I'm not mistaken

 

[haruspex]

just measure the mass of the cup and gravel and assure it doesn't exceed the weight of the cup with water

Yes, if you assume the weight of the cup (or the difference between its density and that of water) can be ignored.
(Pedantic point: compare masses or compare weights, not mass compared to weight.)

how I could do this with just volume

If volume of cup, you can calculate the mass of water it would hold. If volume of gravel, you would need to know the mean density of the loose gravel, including the air spaces; I doubt you would be expected to go that route.

 

[Terrified Virus]

Okay, I think I get it. Thanks everyone!

 

[Chestermiller]

Yes, if you assume the weight of the cup (or the difference between its density and that of water) can be ignored.
(Pedantic point: compare masses or compare weights, not mass compared to weight.)

If volume of cup, you can calculate the mass of water it would hold. If volume of gravel, you would need to know the mean density of the loose gravel, including the air spaces; I doubt you would be expected to go that route.

If you could add the gravel by weight, you wouldn't need to get its bulk density (including voids).

 

[haruspex]

If you could add the gravel by weight, you wouldn't need to get its bulk density (including voids).

Right, but it was not clear whether the gravel could be measured by weight or had to be measured by volume.

 

[Chestermiller]

Right, but it was not clear whether the gravel could be measured by weight or had to be measured by volume.

Yes. In case of weight, I just wanted to emphasize that this was OK.