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

• Terrified Virus
In summary, Archimedes' principle can be used to calculate how much gravel to add to a cup so that it sinks to a certain point but then floats, so that no water is let inside the cup. However, this is only possible if the weight of the gravel is not greater than the weight of the cup with water.
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!

Hello TV,
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).

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.

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.

## 1. What is Archimedes' Principle?

Archimedes' Principle is a scientific law that states that the buoyant force on an object submerged in a fluid is equal to the weight of the fluid that the object displaces. In simpler terms, it explains why objects float or sink in fluids.

## 2. How does Archimedes' Principle relate to making a cup float to a certain height?

According to Archimedes' Principle, the buoyant force acting on a submerged object is equal to the weight of the fluid it displaces. By increasing the volume of the cup (by adding air), the weight of the displaced fluid also increases, causing the cup to float at a higher height in the fluid.

## 3. What factors affect the ability to make a cup float to a certain height using Archimedes' Principle?

The main factors that affect the ability to make a cup float to a certain height using Archimedes' Principle are the density of the fluid, the volume of the cup, and the weight of the cup. The density of the fluid and the volume of the cup determine the amount of displaced fluid, while the weight of the cup affects how much the buoyant force can support.

## 4. Can Archimedes' Principle be applied to other objects besides cups?

Yes, Archimedes' Principle can be applied to any object that is submerged in a fluid, regardless of its shape or size. This principle is commonly used in designing ships, submarines, and other floating objects.

## 5. Are there any limitations to Archimedes' Principle in making a cup float to a certain height?

While Archimedes' Principle is a fundamental law of physics, there are some limitations to its application. For example, the shape and weight distribution of the cup can affect its ability to float at a certain height. Additionally, the surface tension of the fluid and the presence of other objects in the fluid can also impact the accuracy of the results.

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