# Archimedes force due to air on a person

1. Nov 11, 2009

### ttja

1. The problem statement, all variables and given/known data

Calculate the Archimedes' force due to air on your body.

2. Relevant equations

F = pVg

3. The attempt at a solution

This problem is more so conceptual, I believe, than calculation-based. My first thought was that the buoyant force equals to the weight of the air displaced by my body. If that were the only case, then it would be just finding out the weight of air that my volume displaces. But since I am in a very hard physics class, it would never be this simple. The surface area that buoyant force can act on my body might also be a factor. Can anyone please help me think through this conceptually?

2. Nov 11, 2009

### mgb_phys

It's as simple as you thought, the upthrust is just the weight of the air you displace.

Unless you are going to account for the difference in air pressure between your head and toes (probably negligible unless your initials are K.K.) there isn't much else to it.

3. Nov 11, 2009

### ttja

yeah...Im studying the K.K. intro to mechanics book...

sighs...

But it doesnt have any fluid section. so yeah :T.

4. Nov 11, 2009

### ideasrule

No, he was referring to King Kong, not the K&K book. Even for King Kong, the pressure difference would probably be negligible (unless you want 3 or more significant digits).

5. Nov 11, 2009

### ttja

lol i did not get the joke, how slow am i XD.

I also have another question. Doesnt the surface area available for the air to push up an important factor in calculating the Archimedes force? Because air has to be able topush up forom the bottom. Analogously, if i were to lie flat on the earth, and assumes there's no air underneath, then buoyant force would not exert any stress right?

6. Nov 11, 2009

### mgb_phys

Yes I meant King Kong.
I didn't realise Kleppner&Kolenkow was still the standard.
I used that as an ugrad MANY years ago - I suppose Newtonian mechanics hasn't changed much since Newton.

7. Nov 11, 2009

### ttja

out of curiosity, where did you go for undergrad mgb ?

8. Nov 11, 2009

### ideasrule

As long as air can flow freely around the object, surface area plays no role; only volume matters. Think of it this way. If you were made out of air, the surrounding air would need to push up with a force equal to your weight to prevent you from accelerating. The surrounding air doesn't know that you're flesh and not air, so it pushes up with the same force as it does on an "air person". That's why Archimedes' principle works.

You're right that if there's absolutely no air underneath you, there would be no upwards buoyant force. In fact, the air would press you downwards onto the ground. This is the principle behind suction cups.