The plane takes off, 0.999... = 1, but what about...

[NuclearNed]

The OP has described a classic chemistry lab experiment.

Take exactly 1 liter of water and combine it with exactly 1 liter of alcohol. The resulting solution will take up less than 2 liters.

Here is another one that helps people visualize what is going on:

Take one liter of very large marbles and combine them with one liter of very small marbles. You will get less than 2 liters of marbles because the small marbles will fit in the gaps present among the large marbles.

 

[newmachineoverlord]

Regarding the plane: The incarnation that was on this forum last year explicitly stated that there was no lift-generating airflow. This was the clause that prevented the plane from taking off, because in light of it, all else is irrelevant. Without lift, the only force pushing up on the plane is the ground, all other forces besides gravity are horizontal. This is why the plane does NOT take off, and it is also why that plane is different from the hypothetical plane on snopes (which does take off).

 

[JohnCU]

if i'm on a treadmill with rollerblades, but i'm able to pull myself forward with a rope attached to a wall infront of me, am i not going to move?

this is exactly what the plane is doing, pulling itself through the air.

 

[L00ker]

As a simple concept of airfoil design illustrates (see link below) the plane will not takeoff, regardless of what method it uses to provide thrust, the plane has to move forward in order to create the imbalance of pressure between the top of the wing (airfoil) and bottom, without sufficient forward motion (which your riddle indicates that the treadmill will travel at such a speed to equal the planes forward thrust) there will be no lift without lift planes don't fly...

http://www.av8n.com/how/htm/airfoils.html

 

[akshatp]

Originally posted by: JohnCU
if i'm on a treadmill with rollerblades, but i'm able to pull myself forward with a rope attached to a wall infront of me, am i not going to move?

this is exactly what the plane is doing, pulling itself through the air.

Huh? I have never seen a plane attached to a wall with a rope?!?

 

[JohnCU]

Originally posted by: akshatp

Originally posted by: JohnCU
if i'm on a treadmill with rollerblades, but i'm able to pull myself forward with a rope attached to a wall infront of me, am i not going to move?

this is exactly what the plane is doing, pulling itself through the air.

Huh? I have never seen a plane attached to a wall with a rope?!?

i meant the ability to pull yourself forward.

 

[akshatp]

Originally posted by: JohnCU

Originally posted by: akshatp

Originally posted by: JohnCU
if i'm on a treadmill with rollerblades, but i'm able to pull myself forward with a rope attached to a wall infront of me, am i not going to move?

this is exactly what the plane is doing, pulling itself through the air.

Huh? I have never seen a plane attached to a wall with a rope?!?

i meant the ability to pull yourself forward.

Ummmm I know... That was my feeble attempt at being funny...

 

[JohnCU]

Originally posted by: akshatp

Originally posted by: JohnCU

Originally posted by: akshatp

Originally posted by: JohnCU
if i'm on a treadmill with rollerblades, but i'm able to pull myself forward with a rope attached to a wall infront of me, am i not going to move?

this is exactly what the plane is doing, pulling itself through the air.

Huh? I have never seen a plane attached to a wall with a rope?!?

i meant the ability to pull yourself forward.

Ummmm I know... That was my feeble attempt at being funny...

sorry too early haha

 

[akshatp]

Originally posted by: JohnCU

Originally posted by: akshatp

Originally posted by: JohnCU

Originally posted by: akshatp

Originally posted by: JohnCU
if i'm on a treadmill with rollerblades, but i'm able to pull myself forward with a rope attached to a wall infront of me, am i not going to move?

this is exactly what the plane is doing, pulling itself through the air.

Huh? I have never seen a plane attached to a wall with a rope?!?

i meant the ability to pull yourself forward.

Ummmm I know... That was my feeble attempt at being funny...

sorry too early haha

Too early for you.. too late for me... i am in the 10th hour of a 12 hour overnight shift!

 

[Calin]

Originally posted by: JohnCU
If you have 2 liquids (you don't know what they are), 1 mL of each and you add them together, can you be 100% sure that the resulting solution is 2 mL?

No, you can not
However, if you add 1ml of very cold water (above freezing, a bit more than a gram of water) with 1ml of hot water (close to boiling), you end up with 2 ml of warm water
If you have reactions between the two liquids, you could end up with less than or more than 2ml of solution. Less when some gasses are produced, more could be possible when the reaction break a product with a high density into products of lower density (and I have no idea of an example right now)

 

[Calin]

Originally posted by: akshatp

Originally posted by: JohnCU
if i'm on a treadmill with rollerblades, but i'm able to pull myself forward with a rope attached to a wall infront of me, am i not going to move?

this is exactly what the plane is doing, pulling itself through the air.

Huh? I have never seen a plane attached to a wall with a rope?!?

Carrier launched planes? They are not using a rope, but a kind of hook that engage into the catapult (the catapult being just another hook that runs just above deck level).

 

[L00ker]

I actually retract my statement the Plane does takeoff, the explanation in brief is that the plan does not need to exert force against the treadmill in any way, only against the surrounding air which is not changed in any way byt the rotation of the treadmill... therefor the opposing force is the air which the engines use to push against to provide forward movement and move the airfoils (wings) through the air to generate lift, the conveyor is inconsequential and merely a distractor of the actual issue.

 

[jagec]

Originally posted by: Calin
However, if you add 1ml of very cold water (above freezing, a bit more than a gram of water) with 1ml of hot water (close to boiling), you end up with 2 ml of warm water

That's not entirely true...you'd have to calculate the changes in density due to temperature. It depends on how close to freezing and boiling your water was.

And, of course, we're always assuming that everything takes place under atmospheric pressure. The term "incompressible fluid" is a bit of a misnomer, I've seen water at densities of about 1.5 g/cm^3 at the lab where I work