Lifting strength of a bouy depending on variables

[troyd1]

I am wondering what would happen in the following scenarios? I am not looking for exact numbers, but generalized results.

Say I have a rigid buoy that has a volumn of 2 gallons. I have a swimming pool or other large body of water. I have the buoy at the bottom of a ten foot deep pool connected to a line on a pulley system with no friction loss. One pulley is at the bottom of the pool, the other is on a stand outside of the pool connected to some lift measuring device.

What happens in the following scenarios?
Pool is filled with fresh water.

1. Buoy is filled with unpressurized air.
2. Buoy is filled with unpressurized hydrogen.
3. Buoy is filled with compressed air.
4. Buoy is under high vacumn.

Also, how does a heavier liquid affect the above scenarios like say salt water?

Thanks in advance for any responses, Troy

 

[Doc Al]

What do you think? What determines the buoyant force on the buoy? What other forces act on the buoy?

 

[sophiecentaur]

Thinks . . . must remember to have a bath tonight ... ah Eureka.

 

[troyd1]

What do you think? What determines the buoyant force on the buoy? What other forces act on the buoy?

I am sorry, I am really not sure. Possibly, that difference between the weight of the water that the buoy is displacing and the weight of the buoy. I am sure that the pressure at the depth of the buoy would also have a factor in this.

 

[troyd1]

Can anyone help?

 

[Doc Al]

Possibly, that difference between the weight of the water that the buoy is displacing and the weight of the buoy.

Yes, that's how you determine the 'lifting strength' of the buoy. The buoyant force is the upward force of the surrounding water, which equals the weight of the displaced water. That buoyant force must lift the buoy itself (its weight) plus anything else you want it to lift. The extra weight it can lift will equal the buoyant force minus the weight of buoy.

I am sure that the pressure at the depth of the buoy would also have a factor in this.

Not really. Unless the pressure is so high that the buoy is crushed (and thus displaces less water) or the depth is so great that the density of water is a bit more.

 

[troyd1]

Doc, thanks for the reply. A couple followups:
1. So what is in the bouy, if it is air is pretty irrelevant as the weight of air vs hydrogen of that volume is pretty small.

2. So, with my pulley setup, the weight it could lift is the same regardless of the depth of the buoy? This is not intuitive to me as it would seem that 1 unit of water by volume at the top would weight less than one unit at say 10 feet below the water because it would compress or does this not happen?

Also, does the temperature of the water affect the lifting strength or is weight to volume fairly steady for water?

 

[russ_watters]

Well first off, there's no such thing as an unpressurized gas (#1 and #2). Did you mean a gas at atmospheric pressure? For #3, what pressure? You can't say the weight of the gas is irrelevant unless you know the weight of the gas!

The density of water changes with pressure and temperature, but not much. Is it enough to matter? Depends on how accurate you want to be with your calculation... plus or minus 10%? Doesn't matter... plus or minus 1%? Might matter...so you might want to calculate these things.