Author |
Topic: Weighing Air (Read 1033 times) |
|
william wu
wu::riddles Administrator
Gender: 
Posts: 1291
|
 |
Weighing Air
« on: Apr 18th, 2003, 6:15pm » |
 Quote  Modify
|
Here is an experiment that determines whether air has mass.
1. Weigh an empty balloon on a triple beam balance. Record that number.
2. Fill up the balloon with air.
3. Weigh the filled balloon. If the new weight is larger than the old one, air has mass. Else, air has no mass.
Explain why this experiment works, or does not work.
|
|
 IP Logged |
[ wu ] : http://wuriddles.com / http://forums.wuriddles.com
|
|
|
LZJ
Junior Member
Gender:
Posts: 82
|
|
Re: Weighing Air
« Reply #2 on: Apr 18th, 2003, 7:22pm » |
Quote Modify
|
It should work, but not for the reason stipulated: the air in the balloon should be more pressurized than the air in the atmosphere due to the elasticity of the balloon, and therefore, the upthrust on the balloon cannot fully negate the weight of the pressurized air inside the balloon.
|
|
IP Logged |
|
|
|
aero_guy
Senior Riddler
Gender:
Posts: 513
|
|
Re: Weighing Air
« Reply #3 on: Apr 21st, 2003, 4:13pm » |
Quote Modify
|
But you would get a MUCH smaller weight for the air than it is in actuality. In fact, the pressure is not the concern, but rather the compressibility of air. As all of us aero people know, the differences in compressibility you would see for the pressures inside a balloon would fall below the level of error of any scale. So, no weight change.
|
|
IP Logged |
|
|
|
Icarus
wu::riddles Moderator
Uberpuzzler
Boldly going where even angels fear to tread.
Gender:
Posts: 4863
|
|
Re: Weighing Air
« Reply #4 on: Apr 21st, 2003, 4:47pm » |
Quote Modify
|
I get a density increase of about 10-5 kg/Liter times the change in pressure, in Pascals, between the interior and exterior of the balloon. I'm not sure how much the pressure difference would be, but Pascals are pretty wimpy, so I suspect that the weight difference for a large balloon would be measurable on a really sensitive balance (I have no idea anymore how sensitive a triple beam balance is). You would definitely need one shielded from air currents.
|
|
IP Logged |
"Pi goes on and on and on ...
And e is just as cursed.
I wonder: Which is larger
When their digits are reversed? " - Anonymous
|
|
|
Icarus
wu::riddles Moderator
Uberpuzzler
Boldly going where even angels fear to tread.
Gender:
Posts: 4863
|
|
Re: Weighing Air
« Reply #5 on: Apr 21st, 2003, 4:50pm » |
Quote Modify
|
But putting that aside, here is a much easier proof that air has mass: Put your hand in front of your mouth. Blow. Feel it? If air had no mass, you wouldn't, because air would have no momentum to transfer to your hand (since it is travelling much less than the speed of light, which is the only speed anything can go at and have momentum without mass).
|
|
IP Logged |
"Pi goes on and on and on ...
And e is just as cursed.
I wonder: Which is larger
When their digits are reversed? " - Anonymous
|
|
|
Chronos
Full Member
Gender:
Posts: 288
|
|
Re: Weighing Air
« Reply #6 on: Apr 22nd, 2003, 9:42pm » |
Quote Modify
|
I'm not sure that that's all that much easier, Icarus. When you do that, you just shift the burden of proof. Now, you need to prove that A, air travels at less than the speed of light, and B, that the speed of light is the only speed such that a massless object can have momentum. Of course, we already knew both of those things, but then again, we also already knew that air has mass.
Of course, you could also use a non-elastic container, instead of the balloon, so as to be able to pressurize the air much more.
|
|
IP Logged |
|
|
|
Kozo Morimoto
Junior Member
Posts: 114
|
|
Re: Weighing Air
« Reply #7 on: Apr 22nd, 2003, 11:58pm » |
Quote Modify
|
Would the experiment make a difference if the balloon was one of those Swiss Balls you find in the gym? Thick rubber and 1m in diameter?
|
|
IP Logged |
|
|
|
Eigenray
wu::riddles Moderator
Uberpuzzler
Gender:
Posts: 1948
|
|
Re: Weighing Air
« Reply #8 on: Apr 26th, 2003, 2:07pm » |
Quote Modify
|
Well, if that's too easy, what would happen if you took an empty (perfectly reflective) balloon and "filled" it with photons?
NB: photons have no mass, though they are affected by gravity.
|
|
IP Logged |
|
|
|
Chronos
Full Member
Gender:
Posts: 288
|
|
Re: Weighing Air
« Reply #9 on: Apr 27th, 2003, 2:34pm » |
Quote Modify
|
Correction to Eigenray's hint: A single photon does not have mass, but a collection of photons can (and usually does). But that probably confuses more than it helps. Instead, consider this hint: First, fill the box with equal numbers of electrons and positrons. Then, let them all annihilate so there's nothing but photons left. Is it possible for the weight on the scale to change?
|
|
IP Logged |
|
|
|
Kozo Morimoto
Junior Member
Posts: 114
|
|
Re: Weighing Air
« Reply #10 on: May 2nd, 2003, 2:10am » |
Quote Modify
|
I am very curious to the answers for the photon question posed above. I've always believed that photons had no mass, but after reading the above, I googled and found that current understanding has changed since I did my physics at uni. Something about differentiating between rest mass and gravitational mass and relativistic mass.
|
|
IP Logged |
|
|
|
LZJ
Junior Member
Gender:
Posts: 82
|
|
Re: Weighing Air
« Reply #11 on: May 2nd, 2003, 6:29am » |
Quote Modify
|
In short, the weight will still remain the same because gravity acts on photons due to their relativistic 'mass'. 
|
|
IP Logged |
|
|
|
Chronos
Full Member
Gender:
Posts: 288
|
|
Re: Weighing Air
« Reply #12 on: May 2nd, 2003, 9:44am » |
Quote Modify
|
It's not the "relativistic mass", and that's not necessary anyway for gravity to affect the photons. The key is that even though a single photon cannot have rest mass, any set of photons, so long as they're not exactly parallel, does have a rest mass.
To elaborate on my electron-positron hint: We can turn electrons and positrons into photons, and then turn the photons back into electrons and positrons, as many times as we wish, at no energy cost. Suppose that the weight changed when we did that. Then, you just hang the box from a pulley, and put a counterweight on the other side with a weight in between the electron box and the photon box. Then, when we turn them into photons, the box rises, and when we turn them back into electrons, the box falls. This is perpetual motion, which we know is impossible. Therefore our supposition is wrong, and the weight of the box cannot change.
|
|
IP Logged |
|
|
|
Icarus
wu::riddles Moderator
Uberpuzzler
Boldly going where even angels fear to tread.
Gender:
Posts: 4863
|
|
Re: Weighing Air
« Reply #13 on: May 2nd, 2003, 3:58pm » |
Quote Modify
|
on May 2nd, 2003, 2:10am, Kozo Morimoto wrote:| I googled and found that current understanding has changed since I did my physics at uni. Something about differentiating between rest mass and gravitational mass and relativistic mass. |
|
I'm pretty sure this dates back to at least the 1950s. Anyway, I think I am older than you are, and I learned it in HS or college (I'm not sure which now).
So it is not new understanding, just something that was never made clear to you. Hardly surprising - I doubt anyone graduates understanding physics half as well as they think they do.
|
|
IP Logged |
"Pi goes on and on and on ...
And e is just as cursed.
I wonder: Which is larger
When their digits are reversed? " - Anonymous
|
|
|
LZJ
Junior Member
Gender:
Posts: 82
|
|
Re: Weighing Air
« Reply #14 on: May 2nd, 2003, 6:05pm » |
Quote Modify
|
Umm...please clarify what's wrong with my thought, Chronos:
The weight of an object is the gravitational pull on it. However, photons also experience the pull of gravity, and for this balloon case, the radiation pressure (in the balloon) downwards will be greater than that upwards, giving the balloon a certain extra weight. That doesn't necessarily indicate that the photons have any rest mass, just that they are affected by gravity.
|
|
IP Logged |
|
|
|
Icarus
wu::riddles Moderator
Uberpuzzler
Boldly going where even angels fear to tread.
Gender:
Posts: 4863
|
|
Re: Weighing Air
« Reply #15 on: May 4th, 2003, 6:57pm » |
Quote Modify
|
My understanding (I've never checked the numbers myself) is that if you assume that the effect of gravity on light is due to mass (using Newton's Law) then you get either half or double (I don't remember which) the deflection of light than that predicted by Einstein's theory of relativity. Observations of deflection around the sun support Einstein's predictions. Apparently gravity affects light only through the bending of spacetime, and not by attraction of mass. In other words - the relativistic mass of a photon is not a gravitational charge.
|
|
IP Logged |
"Pi goes on and on and on ...
And e is just as cursed.
I wonder: Which is larger
When their digits are reversed? " - Anonymous
|
|
|
towr
wu::riddles Moderator
Uberpuzzler
Some people are average, some are just mean.
Gender:
Posts: 13730
|
|
Re: Weighing Air
« Reply #16 on: May 5th, 2003, 12:39am » |
Quote Modify
|
I guess the deflection would be double if photons had mass, since they would 'attract', and 'be attracted', rather than just the latter.
|
|
IP Logged |
Wikipedia, Google, Mathworld, Integer sequence DB
|
|
|
Chronos
Full Member
Gender:
Posts: 288
|
|
Re: Weighing Air
« Reply #17 on: May 6th, 2003, 1:50pm » |
Quote Modify
|
If you assume that photons have small, but nonzero, mass, and that they follow Newtonian physics, you get a deflection half as large as what Einstein says. I'm pretty sure (but not certain) that this factor of 1/2 is the same factor of 1/2 which doesn't show up in E = mc2 (as compared to the Newtonian kinetic energy equation E = (1/2)mv2).
Yes, the radiation pressure on the bottom of the box will be greater than on the top, and yes, this is because of a gravitational effect on the light (specifically, gravitational red/blue shift), but it's not because of the "relativistic mass" of the photons.
|
|
IP Logged |
|
|
|
Lightboxes
Full Member
Gender:
Posts: 203
|
|
Re: Weighing Air
« Reply #18 on: May 18th, 2003, 10:29pm » |
Quote Modify
|
I think you CAN weigh the air in the balloon because:
Image a flattened cardboard box, you weigh it...then you unfold the box to make a 3D cube...is it going to weigh more because it has air in it? Of course not.
The only diff. is that the balloon can create pressure on the air and compress more air in a smaller space that would normally be. Thus the weight would increase (like water pressure...more water directly above will create more pressure/weight).
This would suggest that air has mass and the mass is being compressed to create greater "atmospheric" pressure.
|
|
IP Logged |
A job is not worth doing unless it's worth doing well.
|
|
|
Speaker
Uberpuzzler
Gender:
Posts: 1118
|
|
Re: Weighing Air
« Reply #19 on: May 22nd, 2003, 2:00am » |
Quote Modify
|
Hi Lightboxes
Great name for this thread. I think your conclusion was made in a prior post, but it was determined that the increase in weight would be so small as to be undetectable on a triple-beam scale. As the triple beam scale was a condition of the original question, it seems to fail as a proof that air has mass. But, then again, no conditions were made for the balloon. So, if, as was mentioned above, you could fill the balloon with lots of air, maybe appropriate amounts of liquid oxygen and liquid nitrogen and other trace elements... Then the scales would move.
|
| « Last Edit: May 22nd, 2003, 2:01am by Speaker » |
IP Logged |
They that can give up essential liberty to obtain a little temporary safety deserve neither liberty nor safety. <Ben Franklin>
|
|
|
Icarus
wu::riddles Moderator
Uberpuzzler
Boldly going where even angels fear to tread.
Gender:
Posts: 4863
|
|
Re: Weighing Air
« Reply #20 on: May 22nd, 2003, 4:48pm » |
Quote Modify
|
Actually my calculation of ~10-5 Kg/Liter/Pascal would indicate a measurable amount of weight. An ordinary balloon contains 1-4 liters when inflated. I still have no idea how many Pascals difference there is between the inside and outside pressures, but Pascals are a VERY small unit of measure, so I am sure that the number of Pascals is certainly greater than 1, and very likely greater than 5. That gives a mass on the order 0.1 grams - easily measurable.
|
|
IP Logged |
"Pi goes on and on and on ...
And e is just as cursed.
I wonder: Which is larger
When their digits are reversed? " - Anonymous
|
|
|
|
RIDDLES SITE
WRITE MATH!
Home 
Help 
Search 
Members 
Login 
Register
Reply
Notify of replies
Send Topic
Print