Leaving on a jet plane (or, how smart are you again?)

[Cache Landing]

Quote from Turok:

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 agree now that my assumption probably wasn't the obvious one.

A little deeper insight into why I made that assumption...

It was the "exact same speed" statement. If I assume that the wheel's circumference and angular velocity represent the speed of the wheels. The wheels would then be skidding down the runway if the treadmill matched that speed. The wheels would only be rotating at half the angular velocity necessary to keep up with the planes forward movement.

To avoid a skidding wheel, my brain assumed that the "teaser" part of the question was referencing a treadmill that would counter the wheels' rotation.

Yep, convoluted.

 

[bellman]

Sorry my tone was a little crappy in the other posts.

So could not another answer be that the treadmill is rotating clockwise to be opposite the counter-clockwise rotation of the wheels?

This would mean that as the treadmill attempts to match the rotational speed of the wheels, the wheels start spinning faster, and the conveyor rotation and wheel rotational speed would approach infiniti, unless slippage occurred between the tires and conveyor belt.

Quote from Cache Landing:

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.

 

[Cutten]

Quote from Turok:

Imagine a plane is sitting on a massive conveyor belt, as wide and as long as a runway. The conveyer belt is designed to exactly match the speed of the wheels, but moving in the opposite direction.

Can the plane take off?

JB

Yes - the wheels would start to skid once the power from the engines overcame the adhesion of the tires to the conveyor belt.

 

[Cutten]

Quote from Turok:



>The wheels and thrust from the jets are disconnected.
>In this hypothetical situation, the plane would move
>forward, no matter how fast you ran the conveyor. For
>instance, if the takeoff speed is say, 150 mph, and you
>ran the conveyor at 150 mph, then the wheels would
>have to spin twice as fast, but it would take off.

You have it *exactly* right.

But you said the conveyor belt moves at the exact opposite speed to the wheels. So this can't hold.

 

[Cutten]

Quote from Turok:

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).

The "speed of the wheels" could be understood to mean the rate they were spinning at, rather than the speed you mention here i.e. the speed of the plane.

For example, if the plane were picked up and lifted down the runway at 5mph, the wheels would not be spinning at all, but you would say they were going 5mph.

IMO you phrased the question unclearly, hence the misunderstanding.

 

[Cutten]

Quote from Turok:

LOL There's a reason that circular actions are measured in *revolutions*, while linear actions are measured in *distance*.

JB

Allow me to quote what you wrote earlier:

"Example:
Plane(and it's wheels) 75mph west
Conveyor 75mph east
Wheels *spinning* 150mph
Plane airspeed 75mph"

Looks like you were measuring circular actions in mph there.

Aren't you contradicting yourself?

 

[Cesko]

Quote from Hydroblunt:

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.

There is a problem of logic with this statement whatever speed achieved by the wheels is matched by the conveyor belt. and I cannot explain what.
But plane would take off for the same reason that plane doesn't need the wheels to fly.
Wheels, conveyor are irrelevant. Airplane engines generate thrust regardless of wheels.
Think, if conveyor was able to prevent plane to take off, planes would never fly.
Wheelchair uses friction against the ground to move. Conveyor would negate the friction. Airplane uses the air resistance (friction??) to move. Therefore irrelevance of conveyor belt.

 

[Cesko]

If logic is hard to use, imagination fills the gap.

 

[Cesko]

Quote from Turok:

Imagine a plane is sitting on a massive conveyor belt, as wide and as long as a runway. The conveyer belt is designed to exactly match the speed of the wheels, but moving in the opposite direction.

Can the plane take off?

JB

Thinking about it. Speed is relative. It must be measured in comparison to something else. Obviously here, against the ground. Based on that, what matches exactly speed of wheel??? Fucking ground. So logically, conveyor is motionless in relation to the ground (if it matches speed of wheels)
So guys, situation described is just the plane taking off nothing more nothing less.LOL.

 

[Cesko]

I feel proud to be the first to see through the bullshit problem.