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

AI Thread Summary
To determine how much gravel to add to a plastic cup so it sinks to the rim but floats without taking in water, Archimedes' principle is key, stating that the buoyant force equals the weight of the displaced fluid. The discussion highlights the importance of measuring the cup's volume and the density of the gravel, as these factors will influence the calculations. Participants emphasize the need to clarify whether the gravel can be measured by weight or volume, as this affects the approach to the problem. It is suggested that if the gravel is weighed, the bulk density does not need to be considered. Understanding these principles will aid in successfully completing the lab assignment.
Terrified Virus
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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!
 
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Can you formulate Archimedes' principle ?
 
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.
 
Are you allowed to weigh the gravel, or do you have to determine what level to pour it to in the cup?
 
Terrified Virus said:
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?
 
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
 
Terrified Virus said:
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.)
Terrified Virus said:
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.
 
Okay, I think I get it. Thanks everyone!
 
haruspex said:
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).
 
  • #10
Chestermiller said:
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.
 
  • #11
haruspex said:
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.
 
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