Truth or Myth: If you put a giant box around the Eiffel Tower, the air contained...

[her209]

within the box will weigh more than the Tower itself.

BTW, saw this on a rerun of MythBusters.

 

[blinblue]

According to http://www.tour-eiffel.fr/teiffel/uk/documentation/structure/page/chiffres.html
The tower weighs about 10000 tons
The height is 324m, the base is 125m x 125m. So a total volume of 324*125*125= 5062500 m^3
The density of air is 1.275 kg/m^3
So the weight is 1.275 kg/m^3 *5062500 m^3 =6.4547×10^6 kg

10000 tons is equal to 1×10^7 kg, which is greater than 6.45×10^6 kg

So the tower itself has a greater mass according to the numbers I have

 

[joesmoke]

how is heavy formed?

 

[yankeesfan]

Density of air: 1.2 kg/m3
Height of tower: 324m
Base side length: 100m
Weight of air: 100*100*324*1.2= (3,888,000 kg)(9.8)= 38,102,400 N
Weight of Eiffel tower: (10,000,000 kg)(9.8) = 98,000,000 N

Tower, if it is a box.

 

[freejumps]

false bc air weighs nothing you dummy

 

[silverpig]

According to http://www.tour-eiffel.fr/teiffel/uk/documentation/structure/page/chiffres.html
The tower weighs about 10000 tons
The height is 324m, the base is 125m x 125m. So a total volume of 324*125*125= 5062500 m^3
The density of air is 1.275 kg/m^3
So the weight is 1.275 kg/m^3 *5062500 m^3 =6.4547×10^6 kg

10000 tons is equal to 1×10^7 kg, which is greater than 6.45×10^6 kg

So the tower itself has a greater mass according to the numbers I have

Minus the air displaced because of the tower

 

[Murloc]

false bc air weighs nothing you dummy

there would be no pressure then
*head explodes*

guys your calculations have a flaw: in the box there is the actual tower too, and it occupies a volume. This just helps the "tower has bigger mass" side anyway.

 

[her209]

Someone should tell MythBusters.

 

[Evadman]

BTW, saw this on a rerun of MythBusters.

Then the mythbusters are wrong. It happens sometimes, but they get folks thinking using the scientific method, so kudos to them.

 

[DrPizza]

According to http://www.tour-eiffel.fr/teiffel/uk/documentation/structure/page/chiffres.html
The tower weighs about 10000 tons
The height is 324m, the base is 125m x 125m. So a total volume of 324*125*125= 5062500 m^3
The density of air is 1.275 kg/m^3
So the weight is 1.275 kg/m^3 *5062500 m^3 =6.4547×10^6 kg

10000 tons is equal to 1×10^7 kg, which is greater than 6.45×10^6 kg

So the tower itself has a greater mass according to the numbers I have

I think the volume of air is supposed to be the volume of the cylinder that would hold it, not the volume of a box. The area of a circle is pi/2 times bigger than the square it circumscribes. (easy to figure this out.) So, without going through all of the calculations, the mass of the air would be pi/2 times larger.
This gives a mass of 1.014 x 10^7 kg. Which, alas, is more.

But wait! I'm not looking it up, but if I recall correctly, your density of air is at STP. i.e. the pressure at sea level. Paris is NOT at sea level. And, with a mean annual temperature of about 53 degrees, not at standard temperature either. Furthermore, there's no way that the density of air is the same at the bottom of the tower as it is at the top of the tower. In fact, an altimeter (other than a GPS altimeter) doesn't really measure altitude. It really measures air pressure. At 300 meters (towards the top of the Eiffel tower), the density of air is considerably lower. Well, not considerably, but enough that the 1.014 x 10^7 kg figure is actually going to be BELOW 1.000 x 10^7 kg after doing a fun integration.

A quick calculation shows that even if the base of the tower were at sea level (guesstimate that it's around 200 feet above sea level), the top of the tower is around 1050 feet. At 0 degrees C (standard temperature), at the top of the tower, the density of air would be 96.26% of the density it is at the base. If we found the average density, by averaging the density at the bottom with the top (I'm in a hurry at the moment), then the average density of the air would be 98.1% that at STP. 98.1% of that 1.014 x 10^7kg works out to:

.994 x 10^7 kilograms. CLOSE, but no cigar.

In summary: nonsense. At STP, the calculation says yes for a cylinder. But, that completely ignores that the density of air varies with altitude, that the average annual temperature in Paris is in the low 50's (F), the elevation of Paris is above sea level, and that the density of air at the top of the cylinder is less than the density of air at the bottom of the cylinder.

That was fun.

 

[freejumps]

I think the volume of air is supposed to be the volume of the cylinder that would hold it, not the volume of a box. The area of a circle is pi/2 times bigger than the square it circumscribes. (easy to figure this out.) So, without going through all of the calculations, the mass of the air would be pi/2 times larger.
This gives a mass of 1.014 x 10^7 kg. Which, alas, is more.

But wait! I'm not looking it up, but if I recall correctly, your density of air is at STP. i.e. the pressure at sea level. Paris is NOT at sea level. And, with a mean annual temperature of about 53 degrees, not at standard temperature either. Furthermore, there's no way that the density of air is the same at the bottom of the tower as it is at the top of the tower. In fact, an altimeter (other than a GPS altimeter) doesn't really measure altitude. It really measures air pressure. At 300 meters (towards the top of the Eiffel tower), the density of air is considerably lower. Well, not considerably, but enough that the 1.014 x 10^7 kg figure is actually going to be BELOW 1.000 x 10^7 kg after doing a fun integration.

A quick calculation shows that even if the base of the tower were at sea level (guesstimate that it's around 200 feet above sea level), the top of the tower is around 1050 feet. At 0 degrees C (standard temperature), at the top of the tower, the density of air would be 96.26% of the density it is at the base. If we found the average density, by averaging the density at the bottom with the top (I'm in a hurry at the moment), then the average density of the air would be 98.1% that at STP. 98.1% of that 1.014 x 10^7kg works out to:

.994 x 10^7 kilograms. CLOSE, but no cigar.

In summary: nonsense. At STP, the calculation says yes for a cylinder. But, that completely ignores that the density of air varies with altitude, that the average annual temperature in Paris is in the low 50's (F), the elevation of Paris is above sea level, and that the density of air at the top of the cylinder is less than the density of air at the bottom of the cylinder.

That was fun.

you sound like my physics teacher /confused

 

[BurnItDwn]

Air has neutral buoyancy, so as long as it's not pressurized any different than the atmosphere, it's weight will be zero, no?

Note: weight = mass times force. if neutral buoyancy then force = 0, thus, no weight.

 

[MikeMike]

you sound like my physics teacher /confused

that's because he is a physics teacher

 

[PieIsAwesome]

Air has neutral buoyancy, so as long as it's not pressurized any different than the atmosphere, it's weight will be zero, no?

Note: weight = mass times force. if neutral buoyancy then force = 0, thus, no weight.

The weight is still there, just that there is an equal and opposite force opposing the weight (the "buoyancy" I guess) if the body with weight (in this case a volume of air) is not accelerating up or down.

Maybe to get the exact mass of the air in the invisible box, someone can find the density of the air as a function of height, make a nice little integration, and somehow take into account the space taken up by the tower. D:

 

[D1gger]

Is this before or after the bomb threat empties the Eiffel Tower?

Bomb Threat Story

 

[BrunoPuntzJones]

I think the volume of air is supposed to be the volume of the cylinder that would hold it, not the volume of a box. The area of a circle is pi/2 times bigger than the square it circumscribes. (easy to figure this out.) So, without going through all of the calculations, the mass of the air would be pi/2 times larger.
This gives a mass of 1.014 x 10^7 kg. Which, alas, is more.

But wait! I'm not looking it up, but if I recall correctly, your density of air is at STP. i.e. the pressure at sea level. Paris is NOT at sea level. And, with a mean annual temperature of about 53 degrees, not at standard temperature either. Furthermore, there's no way that the density of air is the same at the bottom of the tower as it is at the top of the tower. In fact, an altimeter (other than a GPS altimeter) doesn't really measure altitude. It really measures air pressure. At 300 meters (towards the top of the Eiffel tower), the density of air is considerably lower. Well, not considerably, but enough that the 1.014 x 10^7 kg figure is actually going to be BELOW 1.000 x 10^7 kg after doing a fun integration.

A quick calculation shows that even if the base of the tower were at sea level (guesstimate that it's around 200 feet above sea level), the top of the tower is around 1050 feet. At 0 degrees C (standard temperature), at the top of the tower, the density of air would be 96.26% of the density it is at the base. If we found the average density, by averaging the density at the bottom with the top (I'm in a hurry at the moment), then the average density of the air would be 98.1% that at STP. 98.1% of that 1.014 x 10^7kg works out to:

.994 x 10^7 kilograms. CLOSE, but no cigar.

In summary: nonsense. At STP, the calculation says yes for a cylinder. But, that completely ignores that the density of air varies with altitude, that the average annual temperature in Paris is in the low 50's (F), the elevation of Paris is above sea level, and that the density of air at the top of the cylinder is less than the density of air at the bottom of the cylinder.

That was fun.

Do those figures take into account that the tower displaces less air the further up you go?

 

[DrPizza]

Air has neutral buoyancy, so as long as it's not pressurized any different than the atmosphere, it's weight will be zero, no?

Note: weight = mass times force. if neutral buoyancy then force = 0, thus, no weight.

Ahhh! And let's get even more technical, shall we. If we were to stick the Eiffel Tower into the ocean and put a giant bathroom scale under it, we would see that the weight was less. That's because of the buoyant force exerted on the tower. Well, the air actually exerts a buoyant force on the Eiffel tower. So, do they mean a mass of 10^7 kg, or an equivalent weight. And, if they mean an equivalent weight, is that weight measured in a vacuum? Or at STP?

And, in case you doubt that gases exert a buoyant force,
http://www.youtube.com/watch?v=XjCmwuGKR6g
Note the aluminum foil boat floating in sulfur hexafluoride.

 

[OutHouse]

According to http://www.tour-eiffel.fr/teiffel/uk/documentation/structure/page/chiffres.html
The tower weighs about 10000 tons
The height is 324m, the base is 125m x 125m. So a total volume of 324*125*125= 5062500 m^3
The density of air is 1.275 kg/m^3
So the weight is 1.275 kg/m^3 *5062500 m^3 =6.4547×10^6 kg

10000 tons is equal to 1×10^7 kg, which is greater than 6.45×10^6 kg

So the tower itself has a greater mass according to the numbers I have

<<<Twitching

 

[MikeMike]

Do those figures take into account that the tower displaces less air the further up you go?

does it also take into account that the tower is not completely solid, air exists within the columns that are hollow, is there an official "displacement" for the tower?

 

[theflyingpig]

You can't put a giant box around the Eiffel Tower, so none of this matters. Everyone knows this.

 

[silverpig]

Ahhh! And let's get even more technical, shall we. If we were to stick the Eiffel Tower into the ocean and put a giant bathroom scale under it, we would see that the weight was less. That's because of the buoyant force exerted on the tower. Well, the air actually exerts a buoyant force on the Eiffel tower. So, do they mean a mass of 10^7 kg, or an equivalent weight. And, if they mean an equivalent weight, is that weight measured in a vacuum? Or at STP?

And, in case you doubt that gases exert a buoyant force,
http://www.youtube.com/watch?v=XjCmwuGKR6g
Note the aluminum foil boat floating in sulfur hexafluoride.

Then there's the archimedes forces...

I distilled it down to mass, and a rectangular box. The only other options that are valid in physics are a spherical box and a cylinder, both being a stretch in this case.

 

[911paramedic]

Shrink wrap it.

/thread

 

[OutHouse]

The plane DOES NOT take off!

/thread

 

[ussfletcher]

The plane DOES NOT take off!

/thread

Oh but it does.

 

[zerocool84]

So have we concluded yes or no? All I see is a bunch of numbers, no definite answer yet.