Leaving on a jet plane (or, how smart are you again?)
- Thread starter Turok
- Start date
Max:
>the speed of the treadmill is set to the
>ROTATIONAL speed of the wheels?
No. A savy individual will quickly realize that since macal is pushing the wheelchair up the treadmill runway (or in the original problem, the propeller/jet is pulling the plane up the runway), it is ABSOLUTELY IMPOSSIBLE to make the speed of the treadmill match the *rotating* speed if the wheels. I'll explain ...
Runway treadmill is sitting perfectly still as macal is pushing the wheelchair up the runway at 5mph (remember, macal isn't on treadmill - but the wheelchair is). Wheelchair wheels *rotational* speed at this point is also 5mph. Treadmill dude smiles and says to himself "I'll fix macal and his little runway adventure" -- he reaches over and sets the runway dial to 5mph to match the *rotational* speed of the wheels.
He watches, surprised as macal continue pushing up the runway unabated. "Darnit" he says -- "what did I do wrong? I set it to 5mph and that should have stopped him". He now notices that the even though macal is still puttering up the runway at 5mph, the wheels of the wheelchair are now *rotating* at 10mph (macal speed + treadmill speed). "OK", he thinks ... "I can solve this little problem" as he reaches over and sets the treadmill to 10mph to match the *rotational* speed of the wheels.
He watches macal continue pushing up the runway unabated. "Darnit" he says -- "what did I do wrong? I set it to 10mph and that should have stopped him". He now notices that the even though macal is still puttering up the runway at 5mph, the wheels of the wheelchair are now *rotating* at 15mph (macal speed + treadmill speed). "OK", he thinks ... "I can solve this little problem" as he reaches over and sets the treadmill to 15mph to match the *rotational* speed of the wheels.
He watches macal continue pushing up the runway unabated. "DAMMIT" he says -- "what did I do wrong? I set it to 15mph and that should have stopped him". He now notices that the even though macal is still puttering up the runway at 5mph, the wheels of the wheelchair are now *rotating* at 20mph (macal speed + treadmill speed). "OK", he thinks ... "I can solve this little problem" as he reaches over and sets the treadmill to 20mph to match the *rotational* speed of the wheels.
On and on...
See, using the *rotational* speed of the wheels to set the treadmill is IMPOSSIBLE -- as long as the pilot wants to take off (or as long as macal wants to push the wheelchair) it CAN'T BE DONE. Not sure where you got the idea that the problem is asking you to do the impossible, but to each his own.
>how does the speed of the wheels relate to the
>speed of the plane, please clarify?
Well, unless the wheels are mounted on some sort of fore/aft sliding mechanism (they're not), the speed of the wheels will always match the speed of the plane.
JB
>the speed of the treadmill is set to the
>ROTATIONAL speed of the wheels?
No. A savy individual will quickly realize that since macal is pushing the wheelchair up the treadmill runway (or in the original problem, the propeller/jet is pulling the plane up the runway), it is ABSOLUTELY IMPOSSIBLE to make the speed of the treadmill match the *rotating* speed if the wheels. I'll explain ...
Runway treadmill is sitting perfectly still as macal is pushing the wheelchair up the runway at 5mph (remember, macal isn't on treadmill - but the wheelchair is). Wheelchair wheels *rotational* speed at this point is also 5mph. Treadmill dude smiles and says to himself "I'll fix macal and his little runway adventure" -- he reaches over and sets the runway dial to 5mph to match the *rotational* speed of the wheels.
He watches, surprised as macal continue pushing up the runway unabated. "Darnit" he says -- "what did I do wrong? I set it to 5mph and that should have stopped him". He now notices that the even though macal is still puttering up the runway at 5mph, the wheels of the wheelchair are now *rotating* at 10mph (macal speed + treadmill speed). "OK", he thinks ... "I can solve this little problem" as he reaches over and sets the treadmill to 10mph to match the *rotational* speed of the wheels.
He watches macal continue pushing up the runway unabated. "Darnit" he says -- "what did I do wrong? I set it to 10mph and that should have stopped him". He now notices that the even though macal is still puttering up the runway at 5mph, the wheels of the wheelchair are now *rotating* at 15mph (macal speed + treadmill speed). "OK", he thinks ... "I can solve this little problem" as he reaches over and sets the treadmill to 15mph to match the *rotational* speed of the wheels.
He watches macal continue pushing up the runway unabated. "DAMMIT" he says -- "what did I do wrong? I set it to 15mph and that should have stopped him". He now notices that the even though macal is still puttering up the runway at 5mph, the wheels of the wheelchair are now *rotating* at 20mph (macal speed + treadmill speed). "OK", he thinks ... "I can solve this little problem" as he reaches over and sets the treadmill to 20mph to match the *rotational* speed of the wheels.
On and on...
See, using the *rotational* speed of the wheels to set the treadmill is IMPOSSIBLE -- as long as the pilot wants to take off (or as long as macal wants to push the wheelchair) it CAN'T BE DONE. Not sure where you got the idea that the problem is asking you to do the impossible, but to each his own.
>how does the speed of the wheels relate to the
>speed of the plane, please clarify?
Well, unless the wheels are mounted on some sort of fore/aft sliding mechanism (they're not), the speed of the wheels will always match the speed of the plane.
JB
http://www.letsrun.com/forum/flat_read.php?thread=1161075&page=0
38 pages of discussion.........shame on you if you stole it from them.
38 pages of discussion.........shame on you if you stole it from them.
I didn't "steal" it from them and have never seen that discussion, though neither do I take credit for authoring the problem. I noted this fact in the linked post.
http://www.elitetrader.com/vb/showthread.php?s=&postid=1654286#post1654286
JB
Went and read a bunch of the posts from that list (there are many lists on the internet discussing that problem apparently).
The most entertaining thing is reading the posts that INSIST that the plane will take off because a plane must have moving air over the wings to fly. -- They are right of course (about the need for airspeed), but they can't get out of the "it can't move" rut.
This is not the equivalent of running on a treadmill towing a kite(no wind). This is not the equivalent of a car on a treadmill with your hand out the window(no wind).
In rough terms this is an airplane (with a propeller or jet) biting into the air, air the treadmill can't effect, grabbing ahold and pulling itself down the runway, treadmill be damned. The prop/jet doesn't know about the treadmill, the prop/jet doesn't care about the treadmill.
It's two different environments folks and there's a reason why the "airplane" isn't called a "groundplane".
It's as if you were to put a moving floor on the bottom of a pool and then tell folks they are *always* at it's mercy --- hardly. Give'm rollerskates and one of these: http://torpedodpv.com/ They will scoot around the pool, skate wheels spinning, and quickly realize how easy it is for the plane to scoot around as well.
JB
The most entertaining thing is reading the posts that INSIST that the plane will take off because a plane must have moving air over the wings to fly. -- They are right of course (about the need for airspeed), but they can't get out of the "it can't move" rut.
This is not the equivalent of running on a treadmill towing a kite(no wind). This is not the equivalent of a car on a treadmill with your hand out the window(no wind).
In rough terms this is an airplane (with a propeller or jet) biting into the air, air the treadmill can't effect, grabbing ahold and pulling itself down the runway, treadmill be damned. The prop/jet doesn't know about the treadmill, the prop/jet doesn't care about the treadmill.
It's two different environments folks and there's a reason why the "airplane" isn't called a "groundplane".
It's as if you were to put a moving floor on the bottom of a pool and then tell folks they are *always* at it's mercy --- hardly. Give'm rollerskates and one of these: http://torpedodpv.com/ They will scoot around the pool, skate wheels spinning, and quickly realize how easy it is for the plane to scoot around as well.
JB
You are making a clear statement that whatever speed achieved by the wheels is matched by the conveyor belt. So the conveyor belt is configured to negate any speed of the wheels.
That eliminates half the discussion & argument about how the speed of the wheels will actually double to account for the conveyor belt.
Plane cannot take off under that condition.
Let's see if I can remember my algebra-
Solve for X:
X + conveyor speed = wheel speed + engine thrust
Assume, as you say, that conveyor speed = wheel speed. And conveyor/wheel speed can spin to infinity, since that is a logical condition of the question.
X = engine thrust.
It is an illogical assumption that the belt could hold back the plane under any circumstances.
Therefore the plane takes off.
Hydro:
You are making a clear statement that whatever
speed achieved by the wheels is matched by
the conveyor belt.
Yes I am, and yes it does.
>So the conveyor belt is configured to
>negate any speed of the wheels.
Uh -- NO! The conveyor is configured to run the same speed as the wheels, but in the *opposite* direction that the wheels are traveling (the wheels are traveling west at Xmph and the conveyor is traveling east at Xmph).
>That eliminates half the discussion & argument
>about how the speed of the wheels will actually
>double to account for the conveyor belt.
I think you're confusing "speed of the wheels" with the speed the wheels are spinning.
Last I checked, X (speed of wheels west) + X (speed of conveyor west) = 2X, meaning the wheels are spinning twice as fast as they are moving.
>Plane cannot take off under that condition.
Then you misunderstand the condition.
Example:
Plane(and it's wheels) 75mph west
Conveyor 75mph east
Wheels *spinning* 150mph
Plane airspeed 75mph
Plane lifts off pretty as you please.
JB
You are making a clear statement that whatever
speed achieved by the wheels is matched by
the conveyor belt.
Yes I am, and yes it does.
>So the conveyor belt is configured to
>negate any speed of the wheels.
Uh -- NO! The conveyor is configured to run the same speed as the wheels, but in the *opposite* direction that the wheels are traveling (the wheels are traveling west at Xmph and the conveyor is traveling east at Xmph).
>That eliminates half the discussion & argument
>about how the speed of the wheels will actually
>double to account for the conveyor belt.
I think you're confusing "speed of the wheels" with the speed the wheels are spinning.
Last I checked, X (speed of wheels west) + X (speed of conveyor west) = 2X, meaning the wheels are spinning twice as fast as they are moving.
>Plane cannot take off under that condition.
Then you misunderstand the condition.
Example:
Plane(and it's wheels) 75mph west
Conveyor 75mph east
Wheels *spinning* 150mph
Plane airspeed 75mph
Plane lifts off pretty as you please.
JB