Physics Question

[letdown427]

completely irrelevant of x? what are you on. read it again. and again. until you realise, and THEN you will feel as dumb as you are making yourself look.

 

[letdown427]

Originally posted by: Bartolo
i concede defeat, lol

kudos for being a man

 

[TuxDave]

Originally posted by: letdown427
completely irrelevant of x? what are you on. read it again. and again. until you realise, and THEN you will feel as dumb as you are making yourself look.

Math bully?

 

[KillerCharlie]

Originally posted by: 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.

Yeah, so we agree on the physics of the problem and just disagree on the wording of the problem. I took the problem to mean that you are sitting at the gates looking out the window. Outside is a plane sitting on a conveyor. The conveyor increases its speed and the plane increases engine power such that the plane doesn't move from your perspective.

The only reason this is so widely circulated and argued about is because the question is too ambiguous.

(Oh, and I have one minor detail to nitpick--you said the plane, even with very little force, will eventually reach takeoff speed. This isn't true because drag increases with speed and you need a certain amount of thrust to overcome the drag at the required velocity for takeoff.)

 

[letdown427]

loke mate, the bit u put in bold is where you are wrong. hilariously.



0.8888888888... = x

100 . x = 88.8888888888
88.8888888888 - x = 88 <----Right there

yes 88.88888 - x does = 88, but also, from earlier, we defined that 100x = 88.888888 also? you forgot that bit.

so, what we should have is

88.88888888 - x = 100x - x

you see how that works? because 88.88888888 and 100x ARE THE SAME THING, AS YOU DEFINED THAT YOURSELF EARLIER IN THE EQUATION

88.8888888888 / 88 = 1.0101010101 <-- that is also true, but a completely random equation unrelated to this in all but number content.

continuing that equation, 88 = 99x, x = 8/9, which is true.

This formula is how you get a fraction from a recurring decimal. IT'S JUST HOW IT IS. I presume you do art or something?

 

[imported_LoKe]

Originally posted by: letdown427
completely irrelevant of x? what are you on. read it again. and again. until you realise, and THEN you will feel as dumb as you are making yourself look.

I don't feel dumb. I don't pretend to be some king of math. I'm pointing out the flaw in your arguement and am asking where you got the divide by 99 crap. If you're using 99 because it's 0.999, then why not use 88 because it's 0.888

If you can explain this to me, and use real proof, I'll admit you're right.

 

[letdown427]

Originally posted by: KillerCharlie

Originally posted by: 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.

Yeah, so we agree on the physics of the problem and just disagree on the wording of the problem. I took the problem to mean that you are sitting at the gates looking out the window. Outside is a plane sitting on a conveyor. The conveyor increases its speed and the plane increases engine power such that the plane doesn't move from your perspective.

The only reason this is so widely circulated and argued about is because the question is too ambiguous.

(Oh, and I have one minor detail to nitpick--you said the plane, even with very little force, will eventually reach takeoff speed. This isn't true because drag increases with speed and you need a certain amount of thrust to overcome the drag at the required velocity for takeoff.)

true, although, i assumed as we have a huge conveyor belt that can instantaneously match the planes speed, i assumed we were in magic physics land where we ignore things that we don't like, like air resistance. lol. but yep, that's true, if the resultant force was that small, it wouldnt take off. unfortunately though, it would move from your perspective over at the gate.

 

[letdown427]

Originally posted by: LoKe

Originally posted by: letdown427
completely irrelevant of x? what are you on. read it again. and again. until you realise, and THEN you will feel as dumb as you are making yourself look.

I don't feel dumb. I don't pretend to be some king of math. I'm pointing out the flaw in your arguement and am asking where you got the divide by 99 crap. If you're using 99 because it's 0.999, then why not use 88 because it's 0.888

If you can explain this to me, and use real proof, I'll admit you're right.

ok, i'm sorry for using capitals at you.

the 99 comes from when we multiplied both sides by 100.

we started with

x = 0.999999999999999.....

we multiply both sides by 100.

w get:

100x = 99.999999999999.....

say

x = 1

we multiply both sides by 2, we get

2x = 2. it's the same thing, but with different numbers.

Hopefully that'll clear it up.

 

[imported_LoKe]

Originally posted by: letdown427
loke mate, the bit u put in bold is where you are wrong. hilariously.



0.8888888888... = x

100 . x = 88.8888888888
88.8888888888 - x = 88 <----Right there

yes 88.88888 - x does = 88, but also, from earlier, we defined that 100x = 88.888888 also? you forgot that bit.

so, what we should have is

88.88888888 - x = 100x - x

you see how that works? because 88.88888888 and 100x ARE THE SAME THING, AS YOU DEFINED THAT YOURSELF EARLIER IN THE EQUATION

88.8888888888 / 88 = 1.0101010101 <-- that is also true, but a completely random equation unrelated to this in all but number content.

continuing that equation, 88 = 99x, x = 8/9, which is true.

This formula is how you get a fraction from a recurring decimal. IT'S JUST HOW IT IS. I presume you do art or something?

I copied your equasion down and changed all 9's to 8's. If I'm wrong, naturaly, you're wrong. No?

 

[letdown427]

trust me mate, i'm not wrong. I appreciate that that sounds incredibly arrogant, but i did not prove this equation. it is a mathematical fact, that i merely regurgitated (correctly)

i promise, i am not trying to belittle you or prove myself right. that equation is a mathemtical fact. it uses simple definate rules to prove something that admittedly isn't immediately obvious to peple who may not be mathematically minded.

 

[letdown427]

Our actions on an equation must be balanced, else it is false.

For example,

If i put

1 = 1

and then opt to subtract one from the left hand one, I must do the same to the right hand side also, otherwise we get

0 = 1 which is false. (you may see a proof proving that to be true, but the proof divides by zero halfway through, and so is just an 'amusing' s) farce)

so, we start, with the equation

x = 0.9999......

The 0.9999...... means 0.99999999999999999999999999999999999 and so on to an infinite number of 9s.

If we multiple x by 100, we must also multiply 0.9999..... by 100 yes? for the resons above.

so we then have

100x = 99.9999.....

I think that might be the bit that is bothering you? because we are multiplying by one hundred, effectively we are just moving the decimal place two places to the right. since 0.9999..... is infinitely long to the right, we still have the same infinite number of 9s after the decimal point.

this is where the magic happens. lol.


as we now have 100x = 99.9999..... as one equation, and we previously defined x as equal to 0.9999.....

we can subtract x from both sides.

this equals

99x on the left, and 99 on the right.

99 on the right because, we have taken the 99.999.... with it's infinite nines to the right of the decimal point, and subtracted x, which = 0.9999....., with it's infinite number of 9s to the right of the decimal point.


99x = 99 is what we get. that is where 99 comes from.

now we divde by 99, and so get

x = 1.

however we defined earlier that x = 0.9999....., therefore we have proven that x = both 1 and 0.9999....., and so the only logical solution is that

1 = 0.9999.....

i honestly cannot break it down any more than that.

 

[letdown427]

i just wasted 10minutes of my life making that as easy to follow as possible. i hope that helps. if not, i'm not sure anything will. good night.

 

[dawks]

Originally posted by: 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.

The wheels are "free spinning". It doesnt matter how fast the belt goes, the wheels will speed up to match that speed.

Now add in an addtional variable, thrust from the engines, 'pulling' the aircraft forward through the air.. the plane will be able to generate lift and take off.

Past a certain threashold, the wheels being in contact with the belt become a non issue. The free spinning wheels makes it just like flying with the gear down. Your biggest issue will be wind resistance on the gear.

 

[imported_LoKe]

There's one way you can prove it to me. Write out the equasion as if you were trying to prove that 0.88888.. = 1

 

[letdown427]

but 0.8888 doesn't equal one, so that would be impossible?

 

[letdown427]

0.999... does equal one. that's why it is proveable. 0.888.... equals 8/9 .

 

[imported_LoKe]

Originally posted by: letdown427
but 0.8888 doesn't equal one, so that would be impossible?

But try it. Apply the same math as you did before and see how far you get.

 

[mugs]

I hate to say I told you so

 

[letdown427]

either way

x = 0.888.....

multiply by 100


100x = 88.888888

subtract x from both sides.

99x = 88

x = 8/9 which is true. it doesn't equal one. you're doing this on purpose, you must be. if you really are that dumb, then hello Mr G W Bush, how's life treating ya?

frankly, i don't care if you think i'm right or not. i am. lol, night.

 

[imported_LoKe]

Originally posted by: letdown427
100x = 88.888888

subtract x from both sides.

99x = 88

That's where I messed up. I completely forgot about 100x - x = 99x like you were trying to point out earlier. That's why I used 88x.

Now, I admit, I am wrong.

 

[letdown427]

sh!t happens i guess!

sorry for 'shouting' at you lol, it's late...

 

[imported_LoKe]

I don't blame you. I hate explaining simple things over and over to people too. For some reason, I just never noticed that. Not sure why, must be tired, or just not paying enough attention.

 

[letdown427]

this is literally the first time on a forum where i've had like, an argument with someone, but as in, a civilized one, whereby it's not just, oh i'm right you're wrong, you're momma is so fat etc etc. in all fairness, i tend to jsut stay out of those arguments, but yeh, it's cool to actually have a proper like, polite argument about stuff, like earlier on in this thread.

i guess the cliffs are:

-no hard feelings
-i'm going to bed. it's now 3:40 'over here'

 

[imported_electron]

haha I like how this turned into the old 0.999...=1 argument. Which is funny cause you only need the simplest of math to understand why 0.999...=1

Ask yourself this: What's the difference between 1 and 0.999...?

When you can answer that, you have your answer to if they are = or not.

Simply put: if two numbers are equal their difference is 0. So what is 1-0.999...? What's the difference? Its not 0.0001 is it? it's not 0.00000001 is it? it's 0.000...01, well if there was such a thing. But there isn't. You can't ever write that last 1 at the end of 0.0000...01 Because ... means it goes on forever. Like 0.999.... the 9s go on forever, the zeros in 0.0000...1 go on forever. So what is that? 0. The difference between 1 and 0.999... is 0.

See? Now even math noobs can understand.

 

[letdown427]

i'd prefer proof over simplistic thought chains any day. As with your way, maths n00bs will think, yeh but infinity plus 1 man, and treat infinity as a number. at least with the proof, you can walk them through it and suddenly it happens, and they can tangibly see it. also, i think it's easier for 'them' to imagine an infinite series of 9s, tha an infnite series of 0s, with a 1 on the end. lol. meh.