Are We Heavier Than the Scale Says Due to Buoyant Force?

[adsf]

NOTE: This is not a homework question. Rather, this is a conceptual question I developed as I was reading the book.

1) Aren't we a little heavier than what the scale says (a very miniscule amount) because the buoyant force is equal to p sub fluid times g time volume that is submerged?

2) I don't understand how there is a (at the molecular level) buoyant force pressing us upwards (in a gas like air pressure). Is it because the atoms elastically bounce off each other, therefore the atoms that bounce upwards hit us and pushes us upwards?

3) Then (related to part 2) shouldn't the buoyant force be a little less then because gravity constantly pulls the atoms downwards?

If possible, please include website links.
I thank you in advance :)

 

[mgb_phys]

1) Aren't we a little heavier than what the scale says (a very miniscule amount) because the buoyant force is equal to p sub fluid times g time volume that is submerged?

Yes,
Suppose a person weights 75kg, people are approximately water so have a density of 1000kg/m^3 so an average person has a volume of 0.075m^3
Air has a density of 1.2kg/m^3 so you have a buoyant force of 0.075*1.2 = 0.1kg

2) I don't understand how there is a (at the molecular level) buoyant force pressing us upwards (in a gas like air pressure). Is it because the atoms elastically bounce off each other, therefore the atoms that bounce upwards hit us and pushes us upwards?

They don't have to bounce upwards, molecules hitting you sideways also push you up - it's a bit easier to picture with a ball pool and someone being squeezed.

3) Then (related to part 2) shouldn't the buoyant force be a little less then because gravity constantly pulls the atoms downwards?

There is a small effect, there are in theory a bigger density of molecules at your feet which gives more air pressure than at your head, but the effect is tiny compared to the air moving around

If possible, please include website links.
I thank you in advance :)[/QUOTE]

 

[adsf]

thanks for the quick response!
Can anyone confirm mgb phys' answers?

And can anyone explain mgb phys' answer to #3?

 

[FoxCommander]

NOTE: This is not a homework question. Rather, this is a conceptual question I developed as I was reading the book.

1) Aren't we a little heavier than what the scale says (a very miniscule amount) because the buoyant force is equal to p sub fluid times g time volume that is submerged?

2) I don't understand how there is a (at the molecular level) buoyant force pressing us upwards (in a gas like air pressure). Is it because the atoms elastically bounce off each other, therefore the atoms that bounce upwards hit us and pushes us upwards?

3) Then (related to part 2) shouldn't the buoyant force be a little less then because gravity constantly pulls the atoms downwards?

If possible, please include website links.
I thank you in advance :)

1) yes we do because any object submerged in a liquid or gas has a boyant force, although since the density of air is so tiny compared to water the effect is not very noticable. And yes that formula is correct
2) The way that boyant forces occur is that let's say that you have a cylinder pointing straight up completely submerged in a liquid. If you don't already know, the pressure is the density of the liquid times gravity times the height under the liquid. So if you think about it, the bottom of the cylinder will have a higher pressure than the top. And so you take that pressure on the bottom times the area of the base of the cylinder and subtract the pressure on top of the cylinder times the area, and you will get that the force on the bottom will be greater than the top. Which will you the boyant force.
It has to do with the fact that the atoms are constantly hitting us from all sides its just the the ones at the bottom are hitting us harder than the ones on top if that makes sense.
3) as for the force being weaker? the fact is that no matter how deep you go or how heavy you are, as long as you keep the same volume you will always have the same force. and also its pulling the atoms of the liquid and the body in the liquid at the same rate so its not like the liquid or the body is being pulled harder or something.
Hope this helps. Let me know if i have gotten something wrong or you don't understand something

 

[adsf]

Thanks for the response, again!

I just have a question related to #3. I guess I didn't make my question too clear... :(
My question is: we know that we have air pressure pushing us upwards (result of number 2). But shouldn't the air pressure pushing us upwards be a little less than if you were to consider an object whose top is at the level where the bottom of this object is... Essentially, my question is: shouldn't the air pressure at the same point or line or plane (note all these have to be horizontal) from above be a little more than the air pressure from underneath since gravity tugs at the particles hitting the plane from underneath while gravity pulls and accelerates the particles hitting the plane from above?

I thank you in advance.

 

[sophiecentaur]

Point 3: an alternative way of looking at it.
The pressure lower down in the air will be higher than it is at the top because of extra the weight of air above (i.e. Atmospheric pressure at the top plus a bit). If you work out the actual resulting upthrust it comes to "the weight of fluid displaced" which is what good old Archimedes said all those years ago. It applies to water and, to a much lesser extent, to air.

 

[adsf]

Thanks for the response...

But again, my question is the mechanism of the upward buoyant force - isn't it affected by gravity?

Thanks for the response, again!

I just have a question related to #3. I guess I didn't make my question too clear... :(
My question is: we know that we have air pressure pushing us upwards (result of number 2). But shouldn't the air pressure pushing us upwards be a little less than if you were to consider an object whose top is at the level where the bottom of this object is... Essentially, my question is: shouldn't the air pressure at the same point or line or plane (note all these have to be horizontal) from above be a little more than the air pressure from underneath since gravity tugs at the particles hitting the plane from underneath while gravity pulls and accelerates the particles hitting the plane from above?

I thank you in advance.

 

[sophiecentaur]

Weight = Mass times g.
But you needn't take into account the miniscule difference in g over the height of any object you are likely to have!

 

[adsf]

Okay - this is getting quite annoying. Quite frankly, it seems that people don't understand my question. But it is a simple, yes or no, conceptual question. So please reply with a simple yes or no (and then give an explanation). Thank you.

Thanks for the response...

But again, my question is the mechanism of the upward buoyant force - isn't it affected by gravity?

I just have a question related to #3. I guess I didn't make my question too clear... :(
My question is: we know that we have air pressure pushing us upwards (result of number 2). But shouldn't the air pressure pushing us upwards be a little less than if you were to consider an object whose top is at the level where the bottom of this object is... Essentially, my question is: shouldn't the air pressure at the same point or line or plane (note all these have to be horizontal) from above be a little more than the air pressure from underneath since gravity tugs at the particles hitting the plane from underneath while gravity pulls and accelerates the particles hitting the plane from above?

I thank you in advance.

AT this point you might be wondering, WHO CARES? I mean, realistically it wouldn't matter much, but this is just a conceptual question to let me understand physics (and chemistry) a little better.
Thank you.

 

[sophiecentaur]

The upward force is only there because of gravity. Without it there would be no weight so no pressure, because the gases would all drift away.
BUT there is no significant difference in g at the different heights and the molecules must be, on average, not moving up or down because the air is not moving.
The particles are all moving at the same average speed (gravity doesn't count significantly in the kinetic behaviour of gas molecules - their KE is much higher than any possible changes in GPE) at the same temperature.
Because the density is slightly higher underneath, there are MORE collisions per second underneath than on top. That gives you the upthrust in air.

I think you need to re-examine the model that you have in your head to include the dominant effect of the kinetic energy of the air molecules. Then what I say may make more sense.

 

[mgb_phys]

Still slightly confused about #3

The upward force depends on the mass of air (or other fluid) you displace
The mass of the fluid depends on the density - which is why you float in water but not air -
The density will be slightly higher at your feet because of the weight of the air above pressing down on the air at your feet - so you would weight slightly less if you lie down!

But the difference is unimaginably tiny - you would have to go the top of everest to have half the air pressure

 

[adsf]

Thanks for the quick replies! but...

@ sophiecentaur: I have in fact looked a little over kinetic theory of gases and I do understand there is something called the Maxwell distribution of speeds, but...

My question still stands: shouldn't the air pressure at the same point or line or plane (note all these have to be horizontal) from above be a little more than the air pressure from underneath since gravity tugs at the particles hitting the plane from underneath while gravity pulls and accelerates the particles hitting the plane from above?

Like without getting too "physics - y", conceptually, please answer the question above. Imagine it like a true or false. The question is, which would you pick and why.

Can people just answer a yes or no (followed by an explanation)? I truly appreciated the responses I have received and hope many more will follow.

 

[Jackadsa]

The pressure in air is isotropic - which means it is equally strong in all directions at a point. I think you are suggesting that the force of gravity will make the average downwards particle velocity at a particular horizontal plane greater than the average upward velocity, and so the downwards force will be greater than the upwards. This clealy can't be true in equilbrium, because then the air density will shift downwards until equilibrium is reached. Now, there is a downwards force on each atom because of the graviatational force on it as you suggest, as well as the weight of all the air above it (speaking from a statistical averaging point of view) - but in equilibrium this is exactly canceled by the upwards force due to the pressure gradient - the bouyancy affects not only objects in the air but the air itself. So the average vertical velocity of a gas particle in equilibrium is zero.

I hope this helps with your 3.

EDIT: Just to clarify, when I say "the average vertical velocity of a gas particle in equilibrium is zero" I mean the average of the velocities as a vector quantity. So the mean square speed is non zero, but there is no net upwards or downwards velocity, and hence no excess upwards or downwards force.

 

[Gerenuk]

1) Aren't we a little heavier than what the scale says (a very miniscule amount) because the buoyant force is equal to p sub fluid times g time volume that is submerged?

You mean the right thing.
To be precise the scale should show the weight in units of Newton. How to convert this weight into mass (kilogramms), depends on factor like which planet you are on and also other influences like the buoyant force. The scale approximately assumes $m=F/9.81ms^{-2}$ and you are right, that theoretically this should be corrected by a tiny amount due to the buoyant force.

2) I don't understand how there is a (at the molecular level) buoyant force pressing us upwards (in a gas like air pressure). Is it because the atoms elastically bounce off each other, therefore the atoms that bounce upwards hit us and pushes us upwards?

Yes. Molecules bounce off in all directions. The molecules below us, hit us going upwards and the molecules from above hit us when traveling downwards. However below us the density of molecules is larger, so that during a time interval more molecules hit us from below and therefore summing over all tiny bounce forces that we experience, there is a net upward force.

3) Then (related to part 2) shouldn't the buoyant force be a little less then because gravity constantly pulls the atoms downwards?

No, the effect of gravity is already included in the pressure gradient between top and bottom, as explained in #2. There is no additional correction.
In fact, without gravity you wouldn't have a buoyant force.

 

[adsf]

either I'm not getting it or something:


My question still stands: shouldn't the air pressure at the same point or line or plane (note all these have to be horizontal) from above be a little more than the air pressure from underneath since gravity tugs at the particles hitting the plane from underneath while gravity pulls and accelerates the particles hitting the plane from above?

Like without getting too "physics - y", conceptually, please answer the question above. Imagine it like a true or false. The question is, which would you pick and why.

Can people just answer a YES or NO (followed by an explanation)? I truly appreciated the responses I have received and hope many more will follow.

 

[mgb_phys]

ok I understand -
You are saying the force on the top of a sheet of paper should be more than the force underneath because of gravity on the air above.
Not quite - imagine the molecules all push on each other equally, like oiled ball bearings. So the extra force form the ones on top push ones on the side which push up the ones below.

 

[Phrak]

adsf. You might ask yourself why a cube of air doesn't fall to the floor. Or, what are the forces on a ball of air. When these makes sense, add some additional mass to either.

 

[FoxCommander]

Thanks for the quick replies! but...

@ sophiecentaur: I have in fact looked a little over kinetic theory of gases and I do understand there is something called the Maxwell distribution of speeds, but...

My question still stands: shouldn't the air pressure at the same point or line or plane (note all these have to be horizontal) from above be a little more than the air pressure from underneath since gravity tugs at the particles hitting the plane from underneath while gravity pulls and accelerates the particles hitting the plane from above?

Like without getting too "physics - y", conceptually, please answer the question above. Imagine it like a true or false. The question is, which would you pick and why.

Can people just answer a yes or no (followed by an explanation)? I truly appreciated the responses I have received and hope many more will follow.

Ok so no the air pressure on top should not be greater.
Explination: I understand your question now. So what you are saying that esencially the molecules underneath the plane are being pulled down, which is correct since gravity tugs at everything. But what is the surrounding molecules doing, they are also trying to go down. Which means that when you put the plane in there you have moved the molecules away. So the molecules will be pushing back according to the height that they are at. So yes the molecules on top will be pushing back with the weight of the ones above them but the ones on the bottom will be pushing up with more force because they are being pushed up by the weight or the surrounding molecules, and since they are at a lower height then there is more molecules to push back with... I hope this makes sense. If not let me know which part and i will try to explain

 

[sophiecentaur]

ASDF
As I said /implied earlier, the effect of gravity on individual molecules is tiny, compared with the bashing they keep getting due to the thermal (kinetic) motion of their neighbours. Agreed, if you had a single molecule in a vacuum, it would be accelerated down towards the Earth and it would hit a top surface and not a bottom surface. But that's not the situation. A molecule does not fall far enough to 'gain speed' when it is constantly being bombarded by others. The result is, as was said above, an isotropic situation.
You seem reluctant to let go of your original model but you will have to, if you want to get to the bottom of this problem. We are not talking ball bearings bouncing on the top of a tin lid compared with ball bearings bouncing around underneath the tin - under those conditions, you might have a bit of a point but it's not like that.

 

[Gerenuk]

I edit my answer:

This effect you mention is probably smaller than the statistical fluctuations of particle numbers. The molecules in the plane will be subject to gravity itself! So after all I guess there wouldn't be any additional effect due to gravity.

 

[FoxCommander]

ASDF
As I said /implied earlier, the effect of gravity on individual molecules is tiny, compared with the bashing they keep getting due to the thermal (kinetic) motion of their neighbours.

If this were true then the molecules would be bouncing out of the liquid, hence either boiling or evaporating, The reason why its a liquid is because the energy in each molecule isn't strong enough to overcome gravity or their molecular bonds for that matter