Air I would need in order to be able to safely float 1000kg

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In summary, the conversation discusses the concept of buoyancy and how it relates to floating objects, specifically in water and air. The key equation used is PV=nRT and the importance of density in determining buoyancy is emphasized. It is also mentioned that the weight of the object being floated must be less than the weight of the displaced medium. The conversation also touches on the stability of floating objects and how the center of mass and center of buoyancy play a role.
  • #1
Clasi
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1. The problem statement, all variables and given/known
I have absolutely minimal concepts of this subject so if somebody could help me with the most simple language I'd really appreciate it.
I'd like to know how to calculate the volume of air I would need in order to be able to safely float 1000kg spread out on top.

Homework Equations

The Attempt at a Solution


I found many explanations about water displacement and how things float but it doesn't seem to be helping me getting any closer to understanding what I need to do.
 
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  • #2
The same physics (Archimedes Principle) applies to floating a hot air balloon that applies to floating something in water. In the case of the hot air balloon, (or a helium blimp), it needs to be quite large to displace the weight of air that is equal to the weight of the payload plus the weight of the balloon. ## \\ ## The buoyant force is equal to the weight of the displaced air: This air needs to be converted to a vacuum or to a lower density in order to supply any buoyant force. i.e. that's why the term "displaced" is used. A hot air balloon converts the air to a lower density inside the balloon: thereby the air inside of the hot air balloon weighs less once it is heated=upon heating, some air gets removed=this air that is removed is the "displaced air". ## \\ ## Editing: Starting with ## PV=nRT ##, and using pressure ## P=1 \, atm ##, you can compute density ## \delta= n/V ## in moles/liter. This needs to be converted to mass density ## \delta_{mass} ## in grams/liter. If you can estimate the Molecular Weight of an average air molecule, the conversion is straightforward.
 
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  • #3
Clasi said:
I'd like to know how to calculate the volume of air I would need in order to be able to safely float 1000kg spread out on top.
Is this supposed to be an air mattress or a hot air balloon?
 
  • #4
To float 1000kg on water you need a "boat" that can displace 1000kg of water without sinking. Water has a density of 1000kg per cubic meter so the "boat" will sink in until it has displaced 1 cubic meter of water.

So in theory you could fill a balloon with 1 cubic meter of air and put 1000kg on top. It would just about float on water.

In practice the balloon itself weighs something so it needs to be slightly bigger than 1 cubic meter. The centre of boyancy would be below the centre of mass making it unstable, and likely to turn upside down. For stability the centre of mass should be below the centre of boyancy at all times.
 
  • #5
CWatters said:
To float 1000kg on water you need a "boat" that can displace 1000kg of water without sinking. Water has a density of 1000kg per cubic meter so the "boat" will sink in until it has displaced 1 cubic meter of water.

So in theory you could fill a balloon with 1 cubic meter of air and put 1000kg on top. It would just about float on water.

In practice the balloon itself weighs something so it needs to be slightly bigger than 1 cubic meter. The centre of boyancy would be below the centre of mass making it unstable, and likely to turn upside down. For stability the centre of mass should be below the centre of boyancy at all times.
It would not be the cubic meter of air that is causing the 1000 kg load to float unless the air were also at very high pressure. If the air is inside a solid container of volume 1m^3, the buoyancy would be coming from the water and not from the air.
 
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  • #6
jbriggs444 said:
Is this supposed to be an air mattress or a hot air balloon?
Thanks
Actually something floating on water. Like a raft floating on a lake.
 
  • #7
Charles Link said:
It would not be the cubic meter of air that is causing the 1000 kg load to float unless the air were also at very high pressure. If the air is inside a solid container of volume 1m^3, the buoyancy would be coming from the water and not from the air.
Charles Link said:
It would not be the cubic meter of air that is causing the 1000 kg load to float unless the air were also at very high pressure. If the air is inside a solid container of volume 1m^3, the buoyancy would be coming from the water and not from the air.
From the water:sorry: o_O Does it mean that the water is trying to push the object back out?
 
  • #8
Clasi said:
From the water:sorry: o_O Does it mean that the water is trying to push the object back out?
Then the density of the medium that it is floating in is ## \delta_{mass}= ## 1 gram/cm^3. This is not the question that you posted in the OP though. You wanted to calculate the "volume of air..." If the mass is more dense than the water, it will sink. To make it float, you might need a boat.
 
  • #9
o0)Thanks I'm more or less still confused but with what you posted so far I'll see if I can figure something out.
Thanks for you help!
 
  • #10
Can I suggest you make a drawing of what you want. An air bed with a volume of just over 1 cubic meter will just about support 1000kg but will be unstable as I mentioned above.
 
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  • #11
story.php

CWatters said:
Can I suggest you make a drawing of what you want. An air bed with a volume of just over 1 cubic meter will just about support 1000kg but will be unstable as I mentioned above.
story.php
story.php

CWatters said:
Can I suggest you make a drawing of what you want. An air bed with a volume of just over 1 cubic meter will just about support 1000kg but will be unstable as I mentioned above.
CWatters said:
Can I suggest you make a drawing of what you want. An air bed with a volume of just over 1 cubic meter will just about support 1000kg but will be unstable as I mentioned above.
I'm afraid the image isn't visible!
I'll try again.
My apologies.
I'll try again.
 
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  • #12
Clasi said:
story.php


story.php
story.php
Your posting of images is not working. Try using the Upload button in the lower right to upload JPEG or PDF images from your PC to the forums.
 
  • #13
Clasi said:
From the water:sorry: o_O Does it mean that the water is trying to push the object back out?
Water pressure at a depth of (for instance) 10 cm is greater than water pressure at the surface. So yes, if the raft sits 10 cm deep in the water then that pressure is "trying to push" the raft upwards.

That is exactly what buoyancy is all about.
 

1. How does air density affect an object's ability to float?

The density of air plays a crucial role in an object's ability to float. The denser the air, the more buoyant force it can provide to an object, making it easier for the object to float. On the other hand, if the air is less dense, the object will experience less buoyant force and may have difficulty floating.

2. What is the relationship between the mass of an object and the amount of air it displaces?

According to Archimedes' principle, the buoyant force experienced by an object is equal to the weight of the fluid it displaces. Therefore, the more mass an object has, the more air it needs to displace in order to float. In order for a 1000kg object to safely float, it would need to displace 1000kg worth of air.

3. Can the shape of an object affect its ability to float?

Yes, the shape of an object can greatly impact its ability to float. Objects with a larger surface area will displace more air and experience more buoyant force, making it easier for them to float. In contrast, objects with a smaller surface area may not displace enough air and may have difficulty staying afloat.

4. How does air pressure affect an object's ability to float?

Air pressure also plays a role in an object's ability to float. The higher the air pressure, the greater the buoyant force it can provide to an object. This is why objects tend to float more easily at sea level where the air pressure is higher than at higher altitudes where the air pressure is lower.

5. Is there a limit to the amount of weight an object can float with the help of air?

Yes, there is a limit to the amount of weight an object can float with the help of air. This is because the amount of buoyant force provided by air is limited by the density and volume of the air. Additionally, the size and shape of the object can also affect the maximum weight it can float with the help of air.

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