Lift a hemispherical dome filled with water by rotating it

In summary, the problem involves a hemispherical dome filled with water and weighing 30 tons, which can be lifted by giving it a constant angular velocity around its vertical line of symmetry. The dome has a hole on the top and the task is to determine the minimum angular velocity needed for the dome to be lifted. The solution can be found using the given equations and the correct answer is 1.95 rad/s, while the initial answer was 2.91 rad/s. There is a question about how rotating the dome can cause it to be lifted, as it may seem to violate the conservation of momentum. However, it is clarified that only the hemisphere is being lifted, not the water inside.
  • #1
Bohr1227
13
0

Homework Statement


A hemispherical dome filled with water, radius 2 m and weight 30 tons, can be lifted by giving it a constant angular velocity around its vertical line of symmetry. The dome has a hole on the top. Decide the minimum angular velocity.

My answer is 2.91 rad/s .
The correct answer is 1.95 rad/s.

Homework Equations


Shown in the attached picture.

The Attempt at a Solution


Shown in the attached picture.
phys.png
 
Last edited:
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  • #2
I don't understand this problem . Angular velocity of what ? How does whatever it is act on the hemisphere to lift it ??
 
  • #3
Nidum said:
I don't understand this problem . Angular velocity of what ? How does whatever it is act on the hemisphere to lift it ??
I'm sorry, I have tried to make the problem clearer now :)
 
  • #4
How does rotating something cause translation? Sounds like a breach of conservation of momentum?

Edit: So the water isn't lifted, just the hemisphere?
 

1. How does rotating a hemispherical dome filled with water lift it?

Rotating the dome creates centripetal force, which pushes the water towards the outer edge of the dome, creating a higher water level and lifting the dome.

2. What factors affect the amount of lift created by rotating the dome?

The amount of lift is affected by the speed of rotation, the size and shape of the dome, and the amount of water inside.

3. Is it possible to lift a hemispherical dome filled with any type of liquid?

Yes, the principle of centripetal force applies to any liquid, so it is possible to lift a dome filled with any type of liquid as long as the other factors are taken into consideration.

4. Can the lifting effect be increased by using a larger dome or more water?

Yes, a larger dome and more water will create a greater centrifugal force and thus, a higher lift. However, there is a limit to how much lift can be achieved based on the strength of the materials used for the dome.

5. Are there any practical applications for this concept of lifting a dome with rotating water?

Yes, this concept has been used in the design of water towers and reservoirs to increase the amount of water that can be stored in a smaller space. It has also been studied for potential use in space habitats for creating artificial gravity.

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