Archimedes force due to air on a person

[ttja]

Homework Statement

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

Homework Equations

F = pVg

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?

 

[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.

 

[ttja]

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

sighs...

But it doesn't have any fluid section. so yeah :T.

 

[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).

 

[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?

 

[mgb_phys]

Yes I meant King Kong.
I didn't realize 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.

 

[ttja]

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

 

[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.