Leaving on a jet plane (or, how smart are you again?)
- Thread starter Turok
- Start date
Cache landing, you refuse to admit that you are incorrect and are changing the paramaters of the original question in a poor attempt to make your answer correct.
Why oh why do you now choose to speak of the base of the wheel, when the original post does not specify. Clearly, if the wheel is spinning, part of it is moving to the left, part to the right, part up and part down. You shouldn't just pick the part of the wheel that is most convenient for the answer you originally posted, but if you do the problem would become more complex as the the bottom of the wheel becomes the top of the wheel, the conveyor belt would have to change directions twice during every revolution!
As the problem is stated, one must assume that the direction the wheel travels was intended to describe the average direction vector of the wheel, and as such it is defined well enough and specifially enough, to allow one and only one answer.
Why oh why do you now choose to speak of the base of the wheel, when the original post does not specify. Clearly, if the wheel is spinning, part of it is moving to the left, part to the right, part up and part down. You shouldn't just pick the part of the wheel that is most convenient for the answer you originally posted, but if you do the problem would become more complex as the the bottom of the wheel becomes the top of the wheel, the conveyor belt would have to change directions twice during every revolution!
As the problem is stated, one must assume that the direction the wheel travels was intended to describe the average direction vector of the wheel, and as such it is defined well enough and specifially enough, to allow one and only one answer.
I have to admit that Cache's answer is one of the most strangely convoluted I have seen.
I've now read enough versions of this problem on the internet (just google "airplane treadmill") to safely surmise what the author wants to learn...
"Can a plane take off from a treamill runway with the runway surface moving against it."
JB
I've now read enough versions of this problem on the internet (just google "airplane treadmill") to safely surmise what the author wants to learn...
"Can a plane take off from a treamill runway with the runway surface moving against it."
JB
I'm not refusing to admit anything. Everyone I asked the question to assumed the reference to the wheels was refering to the wheel rotation and not the hub direction. This might be an incorrect assumption, but it isn't any less correct than assuming that we are talking about hub direction.
Actually, after reading sparahok's answer, it was pretty much what I was getting at, although he phrased it better.
As to your rephrased question. Yes the plane can still takeoff. The treadmill will be moving against the plane at the same speed the plane is travelling. The wheels however will be spinning 2X that fast. The plane still leaves the ground normally assuming the bearings in the wheel provide insignificant friction.
Quote from Haroki:
Worse than one of mine?
I don't see what's so convoluted about it.
If the plane is facing north and you're facing east while watching it takeoff then:
1- the plane is travelling north, propelled by its prop/engine
2- the free-spinning wheels are rotating counter-clockwise
If the original statement is assumed to mean that the treadmill counters the wheel's rotation, then the treadmill must move north at the same speed as the plane.
This is all invalid once you've rephrased the question to specify a south moving treadmill. Then the answer is quite obvious. But the first version of the question is a better brain teaser.
HAHA, but as I read it again...
It is kind of odd that I assumed that the belt was countering the wheels rotation rather than attempting to counter the forward movement of the vehicle.
Thinking outside the box baby!! Or something like that.
It is kind of odd that I assumed that the belt was countering the wheels rotation rather than attempting to counter the forward movement of the vehicle.
Thinking outside the box baby!! Or something like that.
CL:
>I don't see what's so convoluted about it.
...
>If the original statement is assumed to mean that
>the treadmill counters the wheel's rotation, then the
>treadmill must move north at the same speed as
>the plane.
Yes, and your "assumption" is one of the more convoluted that I have read.
The more common assumption people make is that the implied purpose of the treadmill is to keep the plane still while the wheels spin -- you've decided that the plane will move and the wheels will NOT spin.
I personally don't think you've met the "opposite direction" criteria of the problem at all. Depending on your frame of reference, the treadmill is either moving the same speed as the wheel, or not moving at all in relation to the wheel. I don't see how you can argue that it is moving in the opposite direction.
-- Interesting, but convoluted IMO.
JB
>I don't see what's so convoluted about it.
...
>If the original statement is assumed to mean that
>the treadmill counters the wheel's rotation, then the
>treadmill must move north at the same speed as
>the plane.
Yes, and your "assumption" is one of the more convoluted that I have read.
The more common assumption people make is that the implied purpose of the treadmill is to keep the plane still while the wheels spin -- you've decided that the plane will move and the wheels will NOT spin.
I personally don't think you've met the "opposite direction" criteria of the problem at all. Depending on your frame of reference, the treadmill is either moving the same speed as the wheel, or not moving at all in relation to the wheel. I don't see how you can argue that it is moving in the opposite direction.
-- Interesting, but convoluted IMO.
JB