Physics Question

[mugs]

Originally posted by: letdown427

Originally posted by: mugs
The real question is though, does .999... = 1?

yes.

I was joking. A while back there was a thread debating that fact that went on for ages until some idiot got pissed and started spamming it until the mods locked it.

 

[letdown427]

shame none of you can do maths then isn't it? hehe, it's a dead simple proof.

i would''ve loved to see that. how could they deny something so obvious and clear as that? i mean, that proof is watertight, i don't see where there argument can be founded really? lol

 

[pray4mojo]

Originally posted by: letdown427
pray4mojo, no it's not. the assumption made is that the conveyer can match the speed of the plane in the opposite direction. force is not meniotned. in fact, the very wording of the question implies the plane can move in the first place.

i dont even think force applies to this problem. only speed. and that is 0. and bernoulli says you cant have lift.

 

[letdown427]

well i think you're wrong then. you think speed just happens then? without force? force applies to this problem.

mugs: forgot to say, nice car analogy, with the driven wheels and stuff. How can people not just see, the planes speed forwards is independent of the conveyer belt. surely if they read the thread, they'd realise? don't think they'd b decent enough to say, oh yeah, i was wrong, but still, maybe they'd quieten down a bit?

 

[KillerCharlie]

Basically what ends up happening is the rolling resistance is roughly constant and proportional to the aircraft weight but does not depend on the wheel/ground velocity. It is then quite easy for the airplane/conveyor to reach a trim state where the aircraft is not moving with respect to the fixed reference frame.

 

[mugs]

Originally posted by: letdown427
shame none of you can do maths then isn't it? hehe, it's a dead simple proof.

i would''ve loved to see that. how could they deny something so obvious and clear as that? i mean, that proof is watertight, i don't see where there argument can be founded really? lol

Well, there were people who had advanced degrees in mathematics that argued the opposite. To you and me it's clear that .999... = 1, but other people wonder why people like you and me have such a hard time seeing the difference between the two.

 

[letdown427]

Originally posted by: mugs

Originally posted by: letdown427
shame none of you can do maths then isn't it? hehe, it's a dead simple proof.

i would''ve loved to see that. how could they deny something so obvious and clear as that? i mean, that proof is watertight, i don't see where there argument can be founded really? lol

Well, there were people who had advanced degrees in mathematics that argued the opposite. To you and me it's clear that .999... = 1, but other people wonder why people like you and me have such a hard time seeing the difference between the two.

i hope i meet someone face to face who denies that 0.9999... = 1 (i get the impression you're trying to get one of these n00bs started on this by constantly mentioning it? hehe).

because then you could lead them through the proof, one step at a time, and they'd agree with every step, as it's all true, and then, they'd get to the end, and oh, sh!t, i just proved myself wrong. ahh the look on their faces.




killercharlie, although yes, it is possible for the engines to provide a small enough amount of thrust to equal the resistance of the conveyer belt, the question is could it take off, and the answer is yes, because the engines can provide more thrust than the conveyer can provide resistance, thus the planes will move forward. also, the fact is, the question says, "the plane moves forward" , the conveyer moves in the opposite direction. for the conveyer to provide any resistance, the engines must, by the fact the plane is moving forward, be providing more thrust than the resistance. conveyer speed is opposite of plane speed, not wheel speed.

and stop saying reference frame.

 

[mugs]

Originally posted by: pray4mojo

Originally posted by: letdown427
pray4mojo, no it's not. the assumption made is that the conveyer can match the speed of the plane in the opposite direction. force is not meniotned. in fact, the very wording of the question implies the plane can move in the first place.

i dont even think force applies to this problem. only speed. and that is 0. and bernoulli says you cant have lift.

The conveyor belt can only minimally affect the speed of the plane (due to friction in the wheels). The only way it could work against the trust of the engines is if the wheels were locked.

 

[mugs]

Originally posted by: letdown427
i hope i meet someone face to face who denies that 0.9999... = 1 (i get the impression you're trying to get one of these n00bs started on this by constantly mentioning it? hehe).

No, I'd hate to threadjack.

 

[flashbacck]

OP should put whether or not we're in physics-magic-land where the conveyor belt and airplane wheel barings are frictionless and industructible. If we are, then I'm gonna say no, the plane cannot take off.

 

[KillerCharlie]

Originally posted by: letdown427
well i think you're wrong then. you think speed just happens then? without force? force applies to this problem.

mugs: forgot to say, nice car analogy, with the driven wheels and stuff. How can people not just see, the planes speed forwards is independent of the conveyer belt. surely if they read the thread, they'd realise? don't think they'd b decent enough to say, oh yeah, i was wrong, but still, maybe they'd quieten down a bit?

The answer lies in the wording of the problem, and they did a craptastic job at wording it. If an engineer did it they would include a coordinate system and clearly state what velocities are relative to which coordinate systems.

But either way, the friction force from the wheels is constant and does not depend on the conveyor velocity. It is then possible to get the plane to move the opposite direction of the conveyor so that to an observer, the airplane doesn't move.

 

[TuxDave]

Originally posted by: dawks

Originally posted by: TuxDave

Originally posted by: mugs
Yes, I believe it can. A plane is not like a car, it does not move by exerting force against the ground. The wheels are freespinning, so the plane will move. It's wheels will be spinning as though it's moving twice as fast as it is.

And if you don't believe that, even if the plane had a ground speed of 0 it could still take off - it would just need a gust of several hundred mile per hour wind.

Yeah so.. the question is, are the wheels freespinning?

Nearly. Pick up a bike and spin the wheel.. does it spin? Can you do the same with an airplane? Yes, might take some more force to spin the wheel, but a jet engine can provide more then enough thrust for that no doubt.

By freespinning I mean if you spin the wheel it'll spin forever.

 

[letdown427]

even if they were indestructible (physics thought experiments are often in physics magic land, as it makes things easier/more complicated) the conveyers speed is governed by the planes movement, as defined in the original question.

there is no way that the friction the conveyor can provide at any speed below 200mph could compete with the thrust of the plane. you must be able to see that? and since at that 200mph the plane would be gone anyway, it can take off, off into the physics magic land sky, immune from viscous drag.

 

[Bartolo]

The plane will not fly as there will be no lift generated. The speed of the plane relative to the conveyor belt would certainly be high enough, but the speed relative to air will be zero.

 

[yhelothar]

Yup it would fly. And yeah the reasonings have already been stated in this thread, but here's my explanation.
The plane isn't a car. The thurst isn't generated by the wheels, but by the air turbines. Thus the plane will move forward regardless of conveyer belt moving the wheels backwards.

 

[letdown427]

they actually did a pretty good job of wording it in my opinion, as even after 6 pages, we're still reading things into it.

"It is then possible to get the plane to move the opposite direction of the conveyor so that to an observer, the airplane doesn't move." yes, and then, you can increase the thrust from the engines, and get the plane to move a bit more.

the state you referred to is when the constant frictional force provided by the conveyor is equal to the thrust of the engines. you said yourself the fricional force is constant, and that is what provides the --> force, thrust provdiing the <-- force. so pilot can then increase thrust, to saaay, <----- force, and friction is still only ->> force, as it is constant, as you said. plane moves faster. plane continues to move faster, at a rate governed by the resultant force, which will equal force due to thrust minus resistance from the conveyor. this reultant force is of course = to the mass of the plane multiplied by the acceleration, and as this resultant force is now >0 (as thrust is bigger than resistance) the acceleration is equal to this resultant force divided by the planes mass. even if this is very small, it is acceleration. and as such, the plane will eventually reach the speed necessary for it to take off.


"virtualgames0" 1
"Bartolo" 0

 

[imported_LoKe]

Originally posted by: letdown427

Originally posted by: mugs
The real question is though, does .999... = 1?

yes.

The way I, and many oter people probably see it

Let:

0.99999999.... = x

Multiply both sides by one hundred.

99.999999999..... = 100x


Subtract x from both sides (remember x = 0.9999.....)


=> 99 = 99x

Diveide both sides by 99.

1 = x = 0.999999999......


So yes it does.


jon855, you're wrong too. go back to school.

That logic is flawed.

0.9999999999... = x

100 . x = 99.9999999999
99.9999999999 - x = 99
99.9999999999 / 99 = 1.0101010101


0.8888888888... = x

100 . x = 88.8888888888
88.8888888888 - x = 88
88.8888888888 / 88 = 1.0101010101

The result is the same no matter how you apply that math. With that logic, 0.8888... = 1, 0.7777... = 1

 

[drinkmorejava]

Easy, NO, in order for the plane to take off, it must have a fast enough airspeed; as in how fast the air is going over the wings. If the conveyor belt is keeping the plane in the same place by going the opposite direction, there will be no displacement and thus, no air moving over the wings.

 

[KillerCharlie]

The question is worded very poorly. Given proper wording (such as giving the velocities in terms of a coordinate system), I am sure I will be right on the answer.

I am an aerospace engineer getting my MS in aerodynamics.

 

[TankGuys]

Yes, the plane takes off, with no trouble at all.

Text

 

[TuxDave]

Originally posted by: LoKe

That logic is flawed.

0.9999999999... = x

100 . x = 99.9999999999
99.9999999999 - x = 99
99.9999999999 / 99 = 1.0101010101


0.8888888888... = x

100 . x = 88.8888888888
88.8888888888 - x = 88
88.8888888888 / 88 = 1.0101010101

The result is the same no matter how you apply that math. With that logic, 0.8888... = 1, 0.7777... = 1

Exactly what are you trying to prove with that statement?

x = 0.888...
100x = 88.88...
100x - x = 99 x = 88.888... - 0.888... = 88
99x = 88
x = 8/9. Which is true.

 

[letdown427]

Originally posted by: LoKe

Originally posted by: letdown427

Originally posted by: mugs
The real question is though, does .999... = 1?

yes.

The way I, and many oter people probably see it

Let:

0.99999999.... = x

Multiply both sides by one hundred.

99.999999999..... = 100x


Subtract x from both sides (remember x = 0.9999.....)


=> 99 = 99x

Diveide both sides by 99.

1 = x = 0.999999999......


So yes it does.


jon855, you're wrong too. go back to school.

That logic is flawed.

0.9999999999... = x

100 . x = 99.9999999999
99.9999999999 - x = 99
99.9999999999 / 99 = 1.0101010101


0.8888888888... = x

100 . x = 88.8888888888
88.8888888888 - x = 88
88.8888888888 / 88 = 1.0101010101

The result is the same no matter how you apply that math. With that logic, 0.8888... = 1, 0.7777... = 1

oh god, dont. just don't. man why did you do that? fine.



x = 0.99999..... (we agree this ... means recurring yes? i.e repeated infinitely? good)

multiply by 100

100x = 99.9999999....... (again, the 999.... means repeated infinitely.)

If we subtract x from BOTH SIDES, AS YOU DO IN ACTUAL MATHS THAT GIVES REAL ANSWERS)

we get:

99x (100x - x = 99x yes?)
is equal to

99 (99.9999.... - 0.9999.... = 99 YES? YOU SEE?)

99x = 99. Need i do the rest?

seriously man.i don't know why you had to do that. i call troll on you. phone up stephen hawking ok? he will tell you. i PROMISE.

 

[imported_LoKe]

Originally posted by: TuxDave

Originally posted by: LoKe

That logic is flawed.

0.9999999999... = x

100 . x = 99.9999999999
99.9999999999 - x = 99
99.9999999999 / 99 = 1.0101010101


0.8888888888... = x

100 . x = 88.8888888888
88.8888888888 - x = 88
88.8888888888 / 88 = 1.0101010101

The result is the same no matter how you apply that math. With that logic, 0.8888... = 1, 0.7777... = 1

Exactly what are you trying to prove with that statement?

Using the same numbers, just an equal variation of each, the result is the same.

Or is there a particular reason why 99 is used, completely irrelevant to x?

 

[Bartolo]

i concede defeat, lol

 

[TuxDave]

Originally posted by: LoKe

Using the same numbers, just an equal variation of each, the result is the same.

Or is there a particular reason why 99 is used, completely irrelevant to x?

But the question is so 88.88.../88 = 1.01010.... (I'll take your word on it)

What does that have to do with solving for x? In other words where's the x = ? statement?