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

[Clasi]

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.

 

[Charles Link]

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.

 

[jbriggs444]

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?

 

[CWatters]

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.

 

[Charles Link]

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.

 

[Clasi]

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.

 

[Clasi]

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.

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 Does it mean that the water is trying to push the object back out?

 

[Charles Link]

From the water 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.

 

[Clasi]

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!

 

[CWatters]

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.

 

[Clasi]

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.

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.

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.

 

[berkeman]

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.

 

[jbriggs444]

From the water 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.