Physics question

[cody]

Originally Posted by sperry

There's a nice long thread on NASIOC right now over this simple physics question:

"Imagine a plane is sat on the beginning of a massive conveyor belt/travelator type arrangement, as wide and as long as a runway, and intends to take off. The conveyer belt is designed to exactly match the speed of the wheels at any given time, moving in the opposite direction of rotation.
There is no wind.
Can the plane take off?"

I know the answer, but won't post it right away. Let's see if there are as many idiots here as there are over there!

(Here's the NASIOC thread if you can stand the bickering... I had to leave, I couldn't take anymore. http://forums.nasioc.com/forums/show...0&page=1&pp=50)

I just watched the Mythbusters episode and was really disapointed. Apparently Mythbuster's didn't get the same version as everyone else or, more likely, just didn't want to hassle with a conveyor belt that senses wheel speed. I can't believe how many people, and even the pilot himself!, who think it wouldn't take off, just because the wheels are being driven backward. :roll:

[sperry]

Originally Posted by 100_Percent_Juice

IF there was a MAGICAL conveyor that could speed up to infinite MPH and match the wheel mph keeping the airplane in the same place, then the airplane would not take off. That is why the question online is flawed and could never be proven in a real life application because the airplane would match the conveyor speed and add the takeoff speed causing the conveyor to speed up eventually causing the airplane to look like JC's evo.

Nope. It would still take off. The treadmill and wheels would be going infinity mph + takeoff speed.

Granted, the question as it was posed on NASIOC was poorly worded, but the intent was indeed to show the difference between thrust via air vs. thrust via wheel. But even if you want tackle the stupid messed up version, then you're still dealing with a treadmill/wheel combo that accelerates to infinity that cannot create a force that prevents the plane from taking off.

Because the wheels can't exert a force on the plane, no matter what the treadmill does it can't stop the plane from taking off. You can take every semantic argument you want about how the plane "isn't allowed" to move by the wording, or "treadmills can't spin that fast", or "the wheel bearings would melt", etc and blow them out your ass because without a way for the wheels to impart a force opposite the engine thrust, the plane will accelerate down the treadmill and take off.

[cody]

Did you really just say infinity mph + takeoff speed? And the wheels can't exert force on a plane? Do we also live in a vacuum for this experiment?

If you use the version of the question linked from Corner Carvers, it's a slam-dunk, the plane flies. The version you posted is not "poorly posed". It's a paradox like Dean said.

Originally Posted by Dean

Wish I had seen this earlier...

The question is a paradox and has no solution. Theere are two physical systems that are both mutually dependent, and dicontinious at the same timee that generate conditions that mutual exclusive.

The first system is the wings, and airspeed. This combination is the only thing that can lift the plane.

The second system is a belt and planes wheels. "The conveyer belt is designed to exactly match the speed of the wheels at any given time, moving in the opposite direction of rotation."


Since the plane is at rest to begin with "is sat on the beginning of a massive conveyor belt" Wheel speed is zero, and since there is no force directly applied to the wheels, they can never spin since "The conveyer belt is designed to exactly match the speed of the wheels at any given time, moving in the opposite direction of rotation" -0 +0 = 0 . The wheels can never turn. There are no provisions in the premis for the conveyor belt to move for any other reason, other than the wheels rotating, so it can never turn. This is the limiting factor in the wheel/conveyor belt system.

The plane of course though can thrust all it wants, and that force should cause motoin, airspeed, and eventually lift. But the tires/conveyor belt cannot turn/move, so neither can the plane.

Paradox...

Go hop in your time machine and kill your grandfather before your father was born if you don't beleive me.

[100_Percent_Juice]

This is what would happen if you started talking about this question at work...

how to get rid of annoying co-workers.
http://break.com/index/how-to-get-ri...o-workers.html

[MPREZIV]

I begged you Austin. I BEGGED YOU!!!

[knucklesplitter]

Let's put an F15 on the magical conveyor, shall we? And draw a free-body diagram of it for us engineering types:



Thrust Force Ft = 50,000 lbs
Aerodynamic resistance Fa=? but it is negligable compared to 50k lbs for our purposes = 0
Mass M = 32,000lbm

F = MA

I would like somebody to tell me how a conveyor, no matter how magical, can hold back that jet by touching those little tiny freewheeling wheels.

[Kevin M]

Originally Posted by knucklesplitter

I would like somebody to tell me how a conveyor, no matter how magical, can hold back that jet by touching those little tiny freewheeling wheels.

Never underestimate the power of semantic arguments on the intarwebs. ALL. POWERFUL.

[Nick Koan]

Originally Posted by knucklesplitter

I would like somebody to tell me how a conveyor, no matter how magical, can hold back that jet by touching those little tiny freewheeling wheels.

Friction from the wheel bearings?

[knucklesplitter]

BTW in engineering/science when somebody talks about the speed of something, especially something that spins or rotates as well as displaces, they generally are talking about the speed of the centroid of the object. The speed of the wheels' centroid is the same as the speed of the plane, because they are attached to the plane at their centroid (approximately - but very close). They didn't say "surface speed" or rotatiomal speed" in the question. So the conveyor is moving at the speed of the plane in the opposite direction, so the wheels would be spinning twice as fast with this magical conveyor as they would normally.

[100_Percent_Juice]

STOP SAYING MAGICAL CONVEYOR!!!




im over it. This thread sucks

[knucklesplitter]

magical conveyor... magical conveyor... magical conveyor... magical conveyor...



"In the world of magic... everything is an illusion!
Thank youuuu."

RIP Doug Henning... sniff... sniff...

[cody]

Originally Posted by knucklesplitter

I would like somebody to tell me how a conveyor, no matter how magical, can hold back that jet by touching those little tiny freewheeling wheels.

Maybe it remotely engages the brakes. Maybe it has a large "claw" that holds the plane in place. WTF knows? We only know that we're told in the problem that the conveyor belt matches the speed of the wheels. What do we know about a vehicle who's wheels are matched by a conveyor belt in the opposite direction? It stays stationary. This plane aint movin' cuz as soon as it moves fwd relative to the position of conveyor, it has violated a condition of the problem.

I'll put it in terms that I've seen used recently.

I would like somebody to tell me how a plane can take off when it's wheels are not allowed to spin any faster than the conveyor belt it's sitting on which always matches it's wheel speed in the reverse direction? And I don't want to hear any BS about the wheels slipping on the surface of the conveyor or the plane being a harrier.

Solve the problem we're given, not the one in your head that's based on a realistic conveyor.

[100_Percent_Juice]

lock it now...

[100_Percent_Juice]

Originally Posted by knucklesplitter

magical conveyor... magical conveyor... magical conveyor... magical conveyor...



"In the world of magic... everything is an illusion!
Thank youuuu."

RIP Doug Henning... sniff... sniff...

You are officially old.

[knucklesplitter]

Originally Posted by cody

We only know that we're told in the problem that the conveyor belt matches the speed of the wheels. What do we know about a vehicle who's wheels are matched by a conveyor belt in the opposite direction? It stays stationary.

See my post about the wheels moving meaning the centroid of the wheels moving. If your vehicle is going 50mph your wheels are going 50mph, *even is the wheels are locked up*. If the line lock is engaged on a stationary drag car and it is spinning the wheels during a burnout at 1000rpm, the wheels are moving at 0 mph depite spinning furiously. If you back your 74 Cutlass up at 30mph in reverse and slam it into drive and light the tires up to do a "rolling J" the wheels are still moving backwards at about 30mph despite spinning in the forward direction. This really isn't semantics it is scientific convention.

I miss my 74 Cutlass.

[knucklesplitter]

Originally Posted by 100_Percent_Juice

You are officially old.

Thank youuuu!

[cody]

Originally Posted by knucklesplitter

See my post about the wheels moving meaning the centroid of the wheels moving. If your vehicle is going 50mph your wheels are going 50mph, *even is the wheels are locked up*. If the line lock is engaged on a stationary drag car and it is spinning the wheels during a burnout at 1000rpm, the wheels are moving at 0 mph depite spinning furiously. If you back your 74 Cutlass up at 30mph in reverse and slam it into drive and light the tires up to do a "rolling J" the wheels are still moving backwards at about 30mph despite spinning in the forward direction. This really isn't semantics it is scientific convention.

I miss my 74 Cutlass.

So you're saying that the wheels/tires can slip? I agree with you then. I mean, if the plane can take off without unlocking the brakes (RE: wheels don't spin), then sure, it can take off. Maybe lube up the magical conveyor first?

While we're at it, let's go ahead and put the first conveyor belt on another conveyor belt that moves the plane and first conveyor belt at the right speed for the plane to take off.

Originally Posted by knucklesplitter

So the conveyor is moving at the speed of the plane in the opposite direction, so the wheels would be spinning twice as fast with this magical conveyor as they would normally.

So let's say the centroid of the wheels are traveling across the surface of the conveyor at 100 mph (relative to the conveyor of course). If the conveyor is also going at 100 mph (as per the constraints of the problem), how fast is the plane traveling (again, relative to this stationary conveyor) assuming a no slip condition?

[knucklesplitter]

The conveyer belt is designed to exactly match the speed of the wheels at any given time, moving in the opposite direction of rotation.

Note that it does not say the "surface speed of the wheels' outer diameter", it says the "speed of the wheels".

If the plane is at rest, the wheels are too - going 0mph, and the conveyor belt is not moving either.

If the plane is going 5mph, the wheels are also going 5mph (right along with the plane they are attached to no matter how fast they are spinning). The conveyor belt is going -5mph (the "-" meaning the opposite direction). If the plane had a speedo connected to the wheels it would falsely read 10mph. You would use 10mph to calculate the RPM of the wheels given the diameter.

If the take-off speed of the plane is 150mph, the wheels are also going 150mph (moving right along with the plane). The conveyor belt is going -150mph. If the plane had a speedo connected to the wheels it would falsely read 300mph. You would use 300mph to calculate the RPM of the wheels given the diameter.

Whenever you talk about the speed of one thing versus another, like say a wheel versus a conveyor belt (note it says "belt" not roller nor the whole conveyor), you have to use the same units of measure. I have designed and spec'd 100's of conveyors. When you talk about conveyor belt speed the unit of measure is m/sec, or feet/sec - in other words linear speed which of course mph is. Rotational speed is not the same thing - an object can be spinning at 1000 rpm and still be going 0m/sec (like a house fan for example). So if you are going to say that a conveyor belt is going "to exactly match the speed" as a wheel it has to be in linear speed units.

[Nick Koan]

Originally Posted by AtomicLabMonkey

I'm tempted to lock this thread preemptively before the arguments start again.

shouldawouldacoulda

[Paul@dbtuned]

Holy fucking stupid shit.

The wheels are free spinning, ans as such, cannot transmit any torque to the aircraft!!!

The wheels play no part of this problem.

[sperry]

Originally Posted by Paul@dbtuned

Holy fucking stupid shit.

The wheels are free spinning, ans as such, cannot transmit any torque to the aircraft!!!

The wheels play no part of this problem.

Hurray for basic intelligence!

Ya'll can argue all day long about the wording of the question, but at the end of the day, you still can't explain how any wheel/treadmill interaction can create an appreciable force that could overcome the thrust of the plane's engine and prevent it from taking off.

And that's really the answer. A treadmill cannot affect a plane's takeoff, because the plane's thrust is from the prop/jet pushing against the air, not through the wheels to the ground/treadmill/ice/water/giant block of jello/etc. Sure in the real world, there's friction in the bearings, and rolling resistance of the tire, etc, but nothing that's at all significant in proportion to the engine thrust.

How this argument ever got so big is beyond me... I think people just decided to argue about it 'cause it's the internet and that's what people do, but somewhere along the line the people playing devil's advocate started believing their own bullshit and ended up convincing a bunch of stubborn retards with popsicles that the plane couldn't take off.

[cody]

Originally Posted by knucklesplitter

Note that it does not say the "surface speed of the wheels' outer diameter", it says the "speed of the wheels".

If the plane is at rest, the wheels are too - going 0mph, and the conveyor belt is not moving either.

If the plane is going 5mph, the wheels are also going 5mph (right along with the plane they are attached to no matter how fast they are spinning). The conveyor belt is going -5mph (the "-" meaning the opposite direction). If the plane had a speedo connected to the wheels it would falsely read 10mph. You would use 10mph to calculate the RPM of the wheels given the diameter.

If the take-off speed of the plane is 150mph, the wheels are also going 150mph (moving right along with the plane). The conveyor belt is going -150mph. If the plane had a speedo connected to the wheels it would falsely read 300mph. You would use 300mph to calculate the RPM of the wheels given the diameter.

Whenever you talk about the speed of one thing versus another, like say a wheel versus a conveyor belt (note it says "belt" not roller nor the whole conveyor), you have to use the same units of measure. I have designed and spec'd 100's of conveyors. When you talk about conveyor belt speed the unit of measure is m/sec, or feet/sec - in other words linear speed which of course mph is. Rotational speed is not the same thing - an object can be spinning at 1000 rpm and still be going 0m/sec (like a house fan for example). So if you are going to say that a conveyor belt is going "to exactly match the speed" as a wheel it has to be in linear speed units.

Well, whenever I've run my fat ass on a conveyor belt, it clearly displays the MPH that I'm running, so obviously when you know the size and distance of the rollers (from eachother), you can determine the speed (in MPH) of the belt. Additionally, when the wheels of a vehicle spin, it's possible for a speedometer to use their RPM as a way to display MPH. The speedometer isn't displaying the speed at which the wheels are traveling through the air, it's displaying the speed (albeit theoretical speed) of the outside diameter of the tire.

When I read the question, I believed it was referring to the above type of measurements when it uses the word "speed". I certainly defer to those of you that obviously know more about physics based terminology than I do.

However, I do maintain that if if the word "speed" in the problem refers to rotational speed at the outside of the wheels (RE: what typical speedometers in cars and trucks display), without a harrier or a slipping tire, the plane is prevented from moving forward by the constraints of the problem (RE: wheel speed is matched by conveyor in opposite direction).

Furthermore, as soon as any thrust is exerted on the plane at all (presumably by the props/jets), the wheels would instantly accelerate to infinite MPH and SECCS would implode into a blackhole that sucks my brain out through my nose.

[knucklesplitter]

The question is obviously worded poorly, because reasonable people (and Dean too ) disagree on the basic constraints. I made the case for how I see it, and I... am... done.

[cody]

Originally Posted by sperry

Hurray for basic intelligence!

Ya'll can argue all day long about the wording of the question, but at the end of the day, you still can't explain how any wheel/treadmill interaction can create an appreciable force that could overcome the thrust of the plane's engine and prevent it from taking off.

Nor would anyone need to. If the way I interpreted the question is the "correct" way, the plane will take off, sure, but it will have broken the constraints of the problem while rolling down the runway. So I guess my answer is sure, the plane will take off, but the wheel speed was greater than the belt speed of the conveyor.

The question doesn't define the terms so there are two answers. I really wish the question would have stipulated how the speed is measured so that only one answer would be correct.

[sperry]

Originally Posted by cody

Nor would anyone need to. If the way I interpreted the question is the "correct" way, the plane will take off, sure, but it will have broken the constraints of the problem while rolling down the runway. So I guess my answer is sure, the plane will take off, but the wheel speed was greater than the belt speed of the conveyor.

The question doesn't define the terms so there are two answers. I really wish the question would have stipulated how the speed is measured so that only one answer would be correct.

I'm pretty sure that because the details regarding the operation of the treadmill's speed matching ability are missing due to the imprecise phrasing of the original question, you can make a pretty good guess that the author wasn't exactly being meticulous about how it was phrased. I guarantee the author's goal wasn't to make up a semantic conundrum in an attempt to see how many people would catch the paradox (i.e. it's not a trick question, which is what tons of people seem to imply when they state the plane's not "allowed" to move, therefor it doesn't take off).

So, really it's a straight forwards riddle to see if you understand the difference between the thrust of an airplane engine vs. the thrust of a car via its wheels. If it was meant to be more than that, don't you think it would have been worded very carefully to describe the speed matching feature of the treadmill?