That plane/conveyor problem - filmed solution
Discussion
ATG said:
The crux of this is that the question isn't sufficeintly clearly written that there can only be one "correct" way of understanding it. If you assume that "matches the speed" means that the conveyor belt moves at -v if the place is travelling at +v, then the plane takes off so long as its wheels can rotate at twice their normal takeoff speed. If you read the question so that it means that the conveyor belt can spin arbitrarily fast in order to overcome the thrust of the engines, then by definiton the plane remains stationary relative to the ground. If this was an exam question, I'd expect the student to state what assumptions they were making about the meaning of the question, and so long as their answer was consistent with their stated assumptions, they'd get the marks.
So what happens to all the extra energy provided by the thrust of the engines?
GingerNinja said:
For those who still can't see that the plane will take off, someone's made a film to prove the point that it would......
http://videos.streetfire.net/player.a
Apologies if this was shown before.
Oh I don't know, I'm sure the skate board slowed down each time he pulled the rug out!
mackie1 said:
Quite. Although the speed it'd have to run at to generate enough force in the other direction is pretty big! Would it be physically possible to accelerate the wheels so much that they'd counteract 200,000lbs of thrust?
I like it theoretical, so let's not get too bothered about that.
I'm curious that in a model of the plane remaining stationary because the conveyor belt can spin arbitrarily fast, how is the energy from the thrust of the engine expended?
I have been adopting this theoretical approach this whole time but still arrive at the conslusion that the plane would move forward.
the plane will, at first, be stationary......so will the belt.
The thrust builds up and the plane begins to move forward and the belt speeds up in reverse to counter this.
The expansion of hot gases from the engines will push against the plane causing it to move forward in relation to the air.
The belt will speed up at a directly proportional but inverse speed.
Plane takes off because it has reached the optimum speed to gain airflow over it's wings
The belt is at exactly the same speed in reverse
The wheels are rotating ay double the normal take off speed
The thrust builds up and the plane begins to move forward and the belt speeds up in reverse to counter this.
The expansion of hot gases from the engines will push against the plane causing it to move forward in relation to the air.
The belt will speed up at a directly proportional but inverse speed.
Plane takes off because it has reached the optimum speed to gain airflow over it's wings
The belt is at exactly the same speed in reverse
The wheels are rotating ay double the normal take off speed
mackie1 said:
Quite. Although the speed it'd have to run at to generate enough force in the other direction is pretty big! Would it be physically possible to accelerate the wheels so much that they'd counteract 200,000lbs of thrust?
Have you factored in that plane wheels free wheel. Imagine holding a skateboard on a running machine with your hand. THe wheels are turning. Now take your hand off, does the scateboard shoot off the machine at the same speed as the running machine is turning. nope because the wheels are spining freely.
Now do it again and jam something into the wheels when you remove your hand. launch one skateboard
ThePassenger said:
Cotty said:
Now do it again and jam something into the wheels when you remove your hand. launch one skateboard
This could be where the rollerskated aircraft carrier could prove useful.
Yes but the 1000's of guys on board probably wouldnt appreciate being slammed into the walls everytime you wanted to launch a plane.
You would also need the carrier to be able to match the fighters landing sped to do away with the arresting wires.
Im sure its possiple
Edited by Cotty on Monday 11th December 20:16
apache said:
the plane will, at first, be stationary......so will the belt.
The thrust builds up and the plane begins to move forward and the belt speeds up in reverse to counter this.
The expansion of hot gases from the engines will push against the plane causing it to move forward in relation to the air.
The belt will speed up at a directly proportional but inverse speed.
Plane takes off because it has reached the optimum speed to gain airflow over it's wings
The belt is at exactly the same speed in reverse
The wheels are rotating ay double the normal take off speed
The thrust builds up and the plane begins to move forward and the belt speeds up in reverse to counter this.
The expansion of hot gases from the engines will push against the plane causing it to move forward in relation to the air.
The belt will speed up at a directly proportional but inverse speed.
Plane takes off because it has reached the optimum speed to gain airflow over it's wings
The belt is at exactly the same speed in reverse
The wheels are rotating ay double the normal take off speed
but until take off, has the plane actualy gone anywhere? if not, no take off as not air is moving over/under teh wings.
bobthemonkey said:
apache said:
the plane will, at first, be stationary......so will the belt.
The thrust builds up and the plane begins to move forward and the belt speeds up in reverse to counter this.
The expansion of hot gases from the engines will push against the plane causing it to move forward in relation to the air.
The belt will speed up at a directly proportional but inverse speed.
Plane takes off because it has reached the optimum speed to gain airflow over it's wings
The belt is at exactly the same speed in reverse
The wheels are rotating ay double the normal take off speed
The thrust builds up and the plane begins to move forward and the belt speeds up in reverse to counter this.
The expansion of hot gases from the engines will push against the plane causing it to move forward in relation to the air.
The belt will speed up at a directly proportional but inverse speed.
Plane takes off because it has reached the optimum speed to gain airflow over it's wings
The belt is at exactly the same speed in reverse
The wheels are rotating ay double the normal take off speed
but until take off, has the plane actualy gone anywhere? if not, no take off as not air is moving over/under teh wings.
Yes the engine has pushed the plane forwards as there is no resistednce on the wheels to push it back (freewheeling)
My take on this as I never posted on the original thread.
Stationry plane on the conveyor. Switch the conveyor on and the plane will move in reverse. This is down to friction in the wheel bearing and the weight of the plane resting on those bearings. Start the engines and and probably just above idle you would be able to overcome the friction in the wheels.
The plane is now stationry as it has matches the friction in the wheels. Now you can crank the conveyor to whatever you like and the plane will remain stationry as its only fighting friction not the conveyor as its freewheeling. now open the throttles fully the plane moves forward to a point where its speed generates lift and it takes off.
Stationry plane on the conveyor. Switch the conveyor on and the plane will move in reverse. This is down to friction in the wheel bearing and the weight of the plane resting on those bearings. Start the engines and and probably just above idle you would be able to overcome the friction in the wheels.
The plane is now stationry as it has matches the friction in the wheels. Now you can crank the conveyor to whatever you like and the plane will remain stationry as its only fighting friction not the conveyor as its freewheeling. now open the throttles fully the plane moves forward to a point where its speed generates lift and it takes off.
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