# Question on how to calculate bouancy force

1. Aug 11, 2009

### mmaker

Does anyone know how to calculate the lifting power of air when trying to lift a car, for example, on the bottom of a lake? For example, if an object, weighing 1,000 lbs, is resting 100 feet below the surface, what volume of air would it take to lift the object to the surface? Also, can the volume of air needed be converted into a unit of force? Thanks so much.

2. Aug 11, 2009

### kuruman

I would assume that the air you are talking about is contained in a balloon placed underneath the car. This appears to be a straightforward application of Archimedes's Principle. The buoyant force (weight of displaced water) must be at least equal to the weight of the car for the car to float.

You cannot convert volume into force; they have different dimensions. However, 1000 kg of water occupy a volume of 1.0 m3 so if you displace that much water you get a 9800 N of upward force; if you displace that much liquid mercury, you get a much bigger force.

I don't know how complicated you want to make this, but you may have to take into account the additional buoyant force as the car displaces water and additional weights of the balloon skin and air inside.

Can you take it from here?

3. Aug 11, 2009

### mmaker

Hi Kuruman.......Thanks so much for your reply. Please forgive me if I seem a little dumb (my mother used to bring home lead slugs for me to play with when she worked as a reporter.. but who knew back then) so if I understand correctly, it would take 1 cubic meter of air to lift 1000kg and so the 9800 N produced would equal about 13,300 ft lb (or torque)?

4. Aug 11, 2009

### kuruman

Yes, you can say that a cubic meter of water will support 9800 N of weight. This corresponds to about 2200 lbs of force, not torque. The conversion that I found in wikipedia is 1 N = 0.22481 lb-force. I don't know where you got the 13,300 ft lb.

5. Aug 11, 2009

### mmaker

Please forgive me as explained before, does the equation mean that if I had a container that was one cubic meter filled with air, would that lift the 1000 kg object to the surface? Ultimately, that is what I am looking for. A way to calculate how big of a container of air would I need to lift different weights.
Also, I got the 13300 ft lbs by using the equation below from convertunits.com
I divided 9800 by .737

from convertunits.com:

The SI derived unit for energy is the joule.
1 joule is equal to 1 newton-meter, or 0.737562149277 foot pounds.

6. Aug 11, 2009

### kuruman

I see. Forget energy. Force is the issue here.

Yes, a one cubic meter container filled with air will lift a 1000 kg object against gravity. However, to be exact, in the 1000 kg you must include the mass of the container in kg and (for purists) about 1.5 kg which is the mass of the air in the container. So the "payload" will be less than 1000 kg.

7. Aug 11, 2009

### mmaker

Thanks so much. With my limited knowledge of physics, I thought energy and force were sort of the same thing. I'm assuming in this case, that the one cubic meter container would just about lift the object from the surface and would kind of float there. I guess my next question would be, if I had a two (or three, four, five, etc.) cubic meter container, how fast or how much force would that create by lifting the same weight? Is there a way to calculate that?

8. Aug 11, 2009

### Staff: Mentor

You may also want to include the buoyancy of the car in the calculations, as the apparent weight of the car is lower in water than in air.

A much bigger factor is that air expands if not confined, when it rises through water. There are airbags designed specifically for lifting objects in water and they are open underneath so that the excess air can just spill out as the bag rises.

And one more thing: filling an airbag deep under water requires pressurizing the air to the pressure of the water at that depth.

9. Aug 11, 2009

### mmaker

Thanks Russ for responding. As you may see from the previous posts, I wanted to find out if there is a way to calculate the volume of air needed to lift various weights, say at a 100ft depth, for example, and also to know if there is a way to calculate the speed or force of different volumes of air when lifting an object to the surface. I realize the water pressure would change but I don't need to be that exact. thanks