You have a jet plane sitting on a runway which happens to be a conveyor belt, the wheels of the jet plane has encoders that relay wheel speed to the conveyor runway which instantaneously matches the speed but in the reverse direction to the way the jet plane is facing,
The description is misleading, but I suppose that was the intent. The most obvious interpretation is that the runway works like a treadmill where it moves as fast as the wheels do, but in the opposite direction, which would keep the jet stationary. That seems to be what it says. I guess the key is the interpretation of the word "matches". However, a stationary runway doesn't seem to "match" the description.
Once the jet takes off from the conveyor belt fairly normally, a pound of feathers comes down the conveyor belt, followed by a pound of feathers. Which weighs more?
The description is misleading, but I suppose that was the intent. The most obvious interpretation is that the runway works like a treadmill where it moves as fast as the wheels do, but in the opposite direction, which would keep the jet stationary. That seems to be what it says. I guess the key is the interpretation of the word "matches". However, a stationary runway doesn't seem to "match" the description.
That was the intent so if that is the case are you saying the jet would stay stationary even with the thrusters at full?
Once the jet takes off from the conveyor belt fairly normally, a pound of feathers comes down the conveyor belt, followed by a pound of feathers. Which weighs more?
skylight, I think the problem here is that you stated the problem wrong. In searching the internet, the problem is usually stated as follows:
There is an airplane at rest on a treadmill the size of a runway so that it is big enough for the airplane to take off. However, this is a special treadmill that is designed to move as fast as the airplane's wheels turn but in the opposite direction. So, as the airplane gets up to speed the wheels begin to turn as the airplane moves forward but the treadmill also begins to move just as fast as the wheels. Does the plane take off?
This implies that the treadmill moves as fast as the wheels turn. The only solution that works here is for the airplane to not move, and therefore it can't take off.
skylight, I think the problem here is that you stated the problem wrong. In searching the internet, the problem is usually stated as follows:
This implies that the treadmill moves as fast as the wheels turn. The only solution that works here is for the airplane to not move, and therefore it can't take off.
Yeah perhaps but the inference was that the thrusters would kickstart everything into motion and then the question would be would it take off?
I think the problem here is that you stated the problem wrong.
The problem with most of the ways I've seen the problem stated is that they say the conveyor belt matches the wheels' speed. This is impossible since the wheel speed is the conveyor belt speed plus the air speed (assuming no wind). Once the wheel starts to move, it's impossible for the conveyor belt to catch up (unless you had a really weak airplane motor and a lot of friction in the wheels).
Edit: As I've mentioned in my previous edits, I don't think what I've said here is correct. I don't think conveyor belt would need infinite speed.
Now Now erco you know this is being feverioushly debated in another thread. Unless this is part of the campaign to get Parallax to change their video dress code?
Now Now erco you know this is being feverioushly debated in another thread. Unless this is part of the campaign to get Parallax to change their video dress code?
Hmmm. With my luck, it would be Matt Gilliland in a Speedo, so let's forget I ever mentioned it.
anyway the explanantion that convinced me was that the wheel axle which is fixed to the plane bears no relationship to the ground as the bearings are frictionless and the wheels are not driven like in a car or automobile but freewheeling therefore no matter how fast the wheels would turn and the runway would compensate the plane would be referenced to the air only and the thrusters would indeed push the plane through the air causing flow over the wings and lift.
The only flaw I see is, if the airplane moves forward at all then the runway IS NOT keeping up to the wheel rotation.
Look, this question brings up a lot of ideas and people never see eye to eye on it. It was obviously crafted by some genius to further divide humanity.
All I have to say is this, there is no instrument on the aircraft panel for wheel speed. Why? Because it doesn't matter for takeoff!
You have a jet plane sitting on a runway which happens to be a conveyor belt, the wheels of the jet plane has encoders that relay wheel speed to the conveyor runway which instantaneously matches the speed but in the reverse direction to the way the jet plane is facing, Ignoring any friction in the wheel bearings would the jet be able to take off?
It doesn't matter what the conveyor belt is doing - forwards, backwards, any speed you like. And it doesn't matter whether the wheels have no friction or a bit of friction. The wheels could be replaced with skis. Or it is a seaplane on a flowing river. It still takes off. A plane is a creature of the air, not of the ground!
I wonder if the plane would take off if the brakes were on? (a fun calculation involving the mass of the plane, thrust, and the coefficient of friction of rubber on tarmac *grin*).
The only flaw I see is, if the airplane moves forward at all then the runway IS NOT keeping up to the wheel rotation.
Could you explain why the wheel is not keeping up with the runway? I mentioned the dots would stay in sync so in theory the wheeel and the runway are matched for speed.
It doesn't matter what the conveyor belt is doing - forwards, backwards, any speed you like. And it doesn't matter whether the wheels have no friction or a bit of friction. The wheels could be replaced with skis. Or it is a seaplane on a flowing river. It still takes off. A plane is a creature of the air, not of the ground!
I wonder if the plane would take off if the brakes were on? (a fun calculation involving the mass of the plane, thrust, and the coefficient of friction of rubber on tarmac *grin*).
If the brakes were applied wouldn't the plane go backwards? Also if there was any friction in the wheel bearings then the wheels would influence the motion of the axle
Could you explain why the wheel is not keeping up with the runway? I mentioned the dots would stay in sync so in theory the wheeel and the runway are matched for speed.
This is what went wrong in the Mythbuster's episode. They start out with a static model on a conveyor belt and end up with an airplane being dragged by a truck. Two totally different experiments with two entirely different results.
Relative airspeed is the only thing that can give a wing lift. A normal aircraft may produce enough thrust but it is not pointed the right way. Takeoff allows the aircraft to rest its weight on the wings not the ground because of relative airspeed, not ground speed.
An airplane can have a negative ground speed too. If it can fly 54kts and it has a 60kts headwind you could be moving backwards 6kts on the ground while the airplane thinks you're moving 54kts.
So... if you can produce enough wind at the right angle of attack you will have lift, if not you won't take off.
This is what went wrong in the Mythbuster's episode. They start out with a static model on a conveyor belt and end up with an airplane being dragged by a truck. Two totally different experiments with two entirely different results.
Relative airspeed is the only thing that can give a wing lift. A normal aircraft may produce enough thrust but it is not pointed the right way. Takeoff allows the aircraft to rest its weight on the wings not the ground because of relative airspeed, not ground speed.
An airplane can have a negative ground speed too. If it can fly 54kts and it has a 60kts headwind you could be moving backwards 6kts on the ground while the airplane thinks you're moving 64kts.
So... if you can produce enough wind at the right angle of attack you will have lift, if not you won't take off.
Agreed if you take wind as a cause of engine thrust as it's a calm day.
What xanadu (and other said). All that matters is the speed of the wind relative to the wing.
If the brakes were applied wouldn't the plane go backwards? Also if there was any friction in the wheel bearings then the wheels would influence the motion of the axle
That was a tongue in cheek suggestion but to answer it, if the brakes were on, the wheel encoder would say the wheel is not going round, so the treadmill would also stop. (that was the setup, right?). Ah - but would the plane still be able to take off? It would be skidding along the treadmill, and presumably the treadmill is made of rubber and so is the wheel so you can work out the coefficient of friction there. But in simplistic terms, say the plane had a thrust to weight ratio of 1:1 (which some planes do, though realistically most are less than this). But say it is 1:1, then there is a force downwards of the weight of the plane, and there is a force forwards of the same weight (technically, a force in newtons rather than weight), and so those are two vectors that add head to tail and I think that ends up being the same as the plane sitting on a 45 degree slope. Are the tyres sticky enough to keep it there? Rubber on rubber, or rubber on tarmac. Gut feeling here, but on a dry day they probably are, and on a wet day or with any snow or ice around, then no.
I don't think wheel friction matters though - that is very tiny compared with the thrust of a plane.
My physics teacher at school used to ask these curly questions. And you only had 5 mins in a test to think it through and give the correct answer!
what I meant was with frictionless bearings the wheel would just spin and not push the axle but with friction the bearings would cause a force to act on the axle.
My physics teacher at school used to ask these curly questions.
Good for your physics teacher! These are the kinds of chestnuts that sharpen one's intuition about how things work. No formulas needed!
I had a physics prof that enjoyed torturing us with questions like that. Here's one of my favorites:
You're standing on earth shining a flashlight into space, sweeping the beam back and forth. Beyond some very distant point, the beam will be sweeping through space faster than the speed of light. How is this possible, given the limits of relativity?
what I meant was with frictionless bearings the wheel would just spin and not push the axle but with friction the bearings would cause a force to act on the axle.
Ah, yes, that is correct. In general terms you can think about such forces in terms of energy loss. Does the bearing get hot? If so, lots of energy is being lost. A roller bearing does not rub as much as a friction bearing. I suspect a bearing might get warm but not hot. (it can't get too hot otherwise the hardened steel in the rollers would soften). So then heat in the bearings might be a few tens of watts, compared with the megawatts of a jet turbine. So the forces due to the bearing would be very small.
Thinking of planes on treadmills, I have this strange image of a plane that works like Fred Flintstone's car, and all the passengers have their legs poking out the bottom and they have to run as fast as they can in order to help get the plane in the air...
You're standing on earth shining a flashlight into space, sweeping the beam back and forth. Beyond some very distant point, the beam will be sweeping through space faster than the speed of light. How is this possible, given the limits of relativity?
-Phil
The law applies to physical items. Information like seeing something does not have this law.
And would start having empty slots as you are drawing in the sky faster than the ink can arrive.
If someone in the plane ran forward and hit the bulkhead the plane would move forward a small amount causing the wheel to rotate a small amount and the runway would compensate. This would cause the wheel to move more and the runway to compensate more. this would continue to build until the tires were rotating at a speed where they would explode and the plane would be stuck on the runway and as such would not fly.
If someone in the plane ran forward and hit the bulkhead the plane would move forward a small amount causing the wheel to rotate a small amount and the runway would compensate. This would cause the wheel to move more and the runway to compensate more. this would continue to build until the tires were rotating at a speed where they would explode and the plane would be stuck on the runway and as such would not fly.
Unfortunately for your theory the force the man applies to the plane floor to accelerate him forward would cause the plane to move backwards. The force of him hitting the bulkhead would only cancel that backward motion.
Is physics a required course in high school or college?
Being a Brit we will have to clarify some terms, I never did get my head around the American educational system.
What I was taking about was that kind of school in England that you attended from age 11 up to 17. Though in fact I am old enough that when I was there one could leave education altogether after 14.
Those schools were "secondary schools". Except there were better quality schools were called "grammar schools". Later these streams got merged in to "comprehensive schools"
Back to the question. Even in my crappy secondary school we ended up doing CSE examinations in Pysics, Maths, Biology, English, History, Geography and a few others at age 15.
For the first few years there was no "physics" as such but physics, chemistry, some electronics was all bundled up into "science" class. Biology was separate. They were all mandatory until age 15 I think then a bit of specialization happened.
The mathematics here was not so heavy, Newtons laws of motion and such.
So yes we would have known enough physics by age 14 to wonder why anyone is asking such a simple question.
The most obvious interpretation is that the runway works like a treadmill where it moves as fast as the wheels do, but in the opposite direction, which
would keep the jet stationary
Why? It matters not what the wheels do, provided they have a mostly frictionless connection to the plane as intended of wheels. The jet is being pushed forwards but the thrust of it's jet motor. It will accelerate.
It matters not what the wheels do, provided they have a mostly frictionless connection to the plane as intended of wheels.
Yep, the non-powered wheels are an indicator of relative, not absolute motion. Just like the old tablecloth & plates trick, picture the jet sitting on a runway with a giant tablecloth underneath it. Yank it out quickly forward or backward. Wheels are free to spin as needed, so they go along for the ride, forward or backward, but the jet remains stationary and there's no airflow over the wing.
Comments
Don't look until you're certain and committed to your answer! http://wiki.answers.com/Q/Which_weighs_more_a_pound_of_gold_or_a_pound_of_feathers
The problem with most of the ways I've seen the problem stated is that they say the conveyor belt matches the wheels' speed. This is impossible since the wheel speed is the conveyor belt speed plus the air speed (assuming no wind). Once the wheel starts to move, it's impossible for the conveyor belt to catch up (unless you had a really weak airplane motor and a lot of friction in the wheels).
Edit: As I've mentioned in my previous edits, I don't think what I've said here is correct. I don't think conveyor belt would need infinite speed.
Hmmm. With my luck, it would be Matt Gilliland in a Speedo, so let's forget I ever mentioned it.
All I have to say is this, there is no instrument on the aircraft panel for wheel speed. Why? Because it doesn't matter for takeoff!
It doesn't matter what the conveyor belt is doing - forwards, backwards, any speed you like. And it doesn't matter whether the wheels have no friction or a bit of friction. The wheels could be replaced with skis. Or it is a seaplane on a flowing river. It still takes off. A plane is a creature of the air, not of the ground!
I wonder if the plane would take off if the brakes were on? (a fun calculation involving the mass of the plane, thrust, and the coefficient of friction of rubber on tarmac *grin*).
This is what went wrong in the Mythbuster's episode. They start out with a static model on a conveyor belt and end up with an airplane being dragged by a truck. Two totally different experiments with two entirely different results.
Relative airspeed is the only thing that can give a wing lift. A normal aircraft may produce enough thrust but it is not pointed the right way. Takeoff allows the aircraft to rest its weight on the wings not the ground because of relative airspeed, not ground speed.
An airplane can have a negative ground speed too. If it can fly 54kts and it has a 60kts headwind you could be moving backwards 6kts on the ground while the airplane thinks you're moving 54kts.
So... if you can produce enough wind at the right angle of attack you will have lift, if not you won't take off.
That was a tongue in cheek suggestion but to answer it, if the brakes were on, the wheel encoder would say the wheel is not going round, so the treadmill would also stop. (that was the setup, right?). Ah - but would the plane still be able to take off? It would be skidding along the treadmill, and presumably the treadmill is made of rubber and so is the wheel so you can work out the coefficient of friction there. But in simplistic terms, say the plane had a thrust to weight ratio of 1:1 (which some planes do, though realistically most are less than this). But say it is 1:1, then there is a force downwards of the weight of the plane, and there is a force forwards of the same weight (technically, a force in newtons rather than weight), and so those are two vectors that add head to tail and I think that ends up being the same as the plane sitting on a 45 degree slope. Are the tyres sticky enough to keep it there? Rubber on rubber, or rubber on tarmac. Gut feeling here, but on a dry day they probably are, and on a wet day or with any snow or ice around, then no.
I don't think wheel friction matters though - that is very tiny compared with the thrust of a plane.
My physics teacher at school used to ask these curly questions. And you only had 5 mins in a test to think it through and give the correct answer!
I had a physics prof that enjoyed torturing us with questions like that. Here's one of my favorites:
-Phil
Ah, yes, that is correct. In general terms you can think about such forces in terms of energy loss. Does the bearing get hot? If so, lots of energy is being lost. A roller bearing does not rub as much as a friction bearing. I suspect a bearing might get warm but not hot. (it can't get too hot otherwise the hardened steel in the rollers would soften). So then heat in the bearings might be a few tens of watts, compared with the megawatts of a jet turbine. So the forces due to the bearing would be very small.
Thinking of planes on treadmills, I have this strange image of a plane that works like Fred Flintstone's car, and all the passengers have their legs poking out the bottom and they have to run as fast as they can in order to help get the plane in the air...
And would start having empty slots as you are drawing in the sky faster than the ink can arrive.
-Phil
Unfortunately for your theory the force the man applies to the plane floor to accelerate him forward would cause the plane to move backwards. The force of him hitting the bulkhead would only cancel that backward motion.
What I was taking about was that kind of school in England that you attended from age 11 up to 17. Though in fact I am old enough that when I was there one could leave education altogether after 14.
Those schools were "secondary schools". Except there were better quality schools were called "grammar schools". Later these streams got merged in to "comprehensive schools"
Back to the question. Even in my crappy secondary school we ended up doing CSE examinations in Pysics, Maths, Biology, English, History, Geography and a few others at age 15.
For the first few years there was no "physics" as such but physics, chemistry, some electronics was all bundled up into "science" class. Biology was separate. They were all mandatory until age 15 I think then a bit of specialization happened.
The mathematics here was not so heavy, Newtons laws of motion and such.
So yes we would have known enough physics by age 14 to wonder why anyone is asking such a simple question.
Why? It matters not what the wheels do, provided they have a mostly frictionless connection to the plane as intended of wheels. The jet is being pushed forwards but the thrust of it's jet motor. It will accelerate.
Yep, the non-powered wheels are an indicator of relative, not absolute motion. Just like the old tablecloth & plates trick, picture the jet sitting on a runway with a giant tablecloth underneath it. Yank it out quickly forward or backward. Wheels are free to spin as needed, so they go along for the ride, forward or backward, but the jet remains stationary and there's no airflow over the wing.