airplane vs conveyor belt

Wheels speed = Takeoff speed + takeoff speed

Why would we get to infinity?

Angular, times the radius of the wheel.

How can you state this is 100%. The question does not define it. The first thing we must do is make that determination - how is speed of the wheels to be measured?

See next post.

Gerewhore:
With this sentence in the question:
[HTML_REMOVED]#8220;The conveyer belt is designed to exactly match the speed of the wheels at any given time, moving in the opposite direction of rotation.[HTML_REMOVED]#8221;

And specifically, this part:
[HTML_REMOVED]#8220;match the speed of the wheels at any given time[HTML_REMOVED]#8221;

I see three things:
[HTML_REMOVED]#8220;Match[HTML_REMOVED]#8221; = implying two things must be equal
[HTML_REMOVED]#8220;Speed[HTML_REMOVED]#8221; = method of determining speed is not defined, so we must use other clues in the question to determine this.
[HTML_REMOVED]#8220;at any given time[HTML_REMOVED]#8221;. Can we agree this equates to [HTML_REMOVED]#8220;always[HTML_REMOVED]#8221;?

Here[HTML_REMOVED]#8217;s the argument I use to determine how to measure [HTML_REMOVED]#8216;speed of the wheels[HTML_REMOVED]#8217;:

As the plane starts to move forward, the wheel turns, and so the belt turns in the opposite direction to match the rotation speed. But… the wheel had to move in relation to the belt in order to rotate, so for that moment in time [HTML_REMOVED]#8211; no matter how small [HTML_REMOVED]#8211; the belt and the wheel speeds didn[HTML_REMOVED]#8217;t match. The question states that belt and wheel speed match [HTML_REMOVED]#8220;at any given time[HTML_REMOVED]#8221; , which this interpretation does not allow. This interpretation of speed matching (rotational) must be false.

So, the only thing left is speed of the wheels in a forward direction.
Point out the flaws in my reasoning. Either with the physics, or the interpretation of the question.
(my fuller explanation, of which this is an excerpt, is a couple pages back, so if you think you see a flaw here - go back and read the fuller one - it's probably covered)

How can you state this is 100%. The question does not define it. The first thing we must do is make that determination - how is speed of the wheels to be measured?

See next post.

This has been discussed. We are interpreting it that way so that the question is interesting, otherwise it's obvious the plane takes off.

Imagine:

You are standing on a skateboard, on a treadmill. Your hands are on the handrails surrounding the treadmill.

When the treadmill starts to move, you hold on and the skateboard wheels start to rotate.

NOW, you pull yourself forward with your hands at the same time as hitting the 'faster' button on the treadmill.

What happens?

If the treadmill has the same control system as the conveyor belt in the plane problem then the skateboarder won't move anywhere. The system is designed to prevent any forward movement by creating a resistance in the wheel/belt interface that matches the thrust/pull of the jet/skateboarder.

Unless you interpret the question differently. Like those Mythbuster shitheads!

I can't believe I am diving back into this, but here we go.

The speed of the wheels and the conveyor match at ANY given moment, we know that. So, as has been said before based on this constraint, the wheels cannot move forward without breaking that one key constraint as the speeds will no longer match. So basically, neither the wheels or the conveyor can start spinning. So we can simplify this question to read "Can a plane with it's wheels locked take off on a runway made of conveyor belt?" Since rubber to rubber has a high coefficient of friction, and we have all been in a jet when it runs up it's engines with the brakes on and does not move, the answer is NO, the plane will not take off.

THREAD/

this.

edit: 666th post! I'm heading out to do something evil.

This has been discussed. We are interpreting it that way so that the question is interesting, otherwise it's obvious the plane takes off.

So, it boils down to…

If speed is linear, then plane takes off with wheels rotating at 2X forward speed.
If speed is angular, then plane takes off with wheels at speed infinity. I like your math, but people will take issue with the impossibility of infintie speed. I agree - makes it interesting though.

To the general maases out there…

Where's Occam's razor when you need it…. Can we not use that to clarify? Go look it up.

it isn't. but it is a red herring as it doesn't have any thing to do with the question

if i don't know what i am talking about (i often don't BTW) then you or sammy have a chance to shut me up quick

take 10 seconds and explain what is happening with the wheels of the plane AS PER THE ACTUAL question.

sammy has tried the "they spin twice as fast" fail before, and we can forgive and forget that. let's start from scratch.

if you think the plane takes off, walk us through the whole wheel thing and you'll be a superstar…. imagine finally ending this thread!

take the gerewh0re challenge and answer the question

i dare ya

The question states that the wheel speed is matched by the conveyor, but it doesn't state what frame of reference for the wheel speed.
Since the conveyor is linear motion, then the wheel speed would have to be one of two possibilities, the surface speed of the wheel, or the speed of the centre (hub) of the wheel.
The next assumption is on the direction of the conveyor, matching forward speed or going backward to oppose the speed.

When you think about wheel surface speed vs wheel speed, then imagine the top of a wheel that is rolling on a fixed surface, the surface speed is going to be twice that of the wheel centre, therefore the two are proportional, and any argument that you make, they are analogous (the same). The wheel speed is tied directly to the plane speed (and like it was mentioned, you could argue that it's twice the plane speed depending on reference frame).

Planes driving force isn't a wheel driven force, it's thrust from the engine, be it prop or jet. Increase throttle, and there is a thrust applied that forces the plane forward relative to a fixed ground point.

Assumption A: The conveyor opposes the thrust direction.

When the plane starts moving forward with an instantaneous speed of x relative to the fixed ground point, then the conveyor will have an equal speed of magnitude x, but in the opposite direction, meaning that relative to the fixed ground point, the conveyor will be moving -x, and the plane will be moving x, giving a differential of 2x. The plane needs a certain air speed to take off (the stall speed, SS), this speed is relative to the fixed ground point, not the conveyor (assuming no wind), when x= SS, then the plane takes off and the wheels are moving at 2SS. If the wheels cannot handle 2SS, or there isn't enough power in the plane to overcome the frictional forces of the wheels travelling 2SS, then there may be problems.

Assumption B: The Conveyor travels with the thrust.

When the plane moves forwards with instantaneous velocity x relative to the fixed ground point, then the conveyor will move forward with a speed of x, the differential speed of the wheels to the conveyor will then be x-x=0. The plane accelerates until stall speed and then can take off, assuming that the conveyor can go at SS.

The problem really is a test of understanding ground speed vs air speed and understand relative frames of reference for objects in motion.

Yeah, what he said…..

i love this thread!

some awesome stuff (don't you guys take a lunch or anything) but still no "it will fly" people making this plane take off without having those goshdarn wheels spin faster the the conveyor.

Everyones arguments are futile vs. the fact the plane has no forward motion…Epic fail.

biggles. you are making this harder on yourself thinking about the thrust. stick the the wheels not being able to spin any faster than the conveyor and you'll have your answer way easier than using formulas and brains

biggles. you are making this harder on yourself thinking about the thrust. stick the the wheels not being able to spin any faster than the conveyor and you'll have your answer way easier than using formulas and brains

what makes them spin fast? What's the driving force?

what makes them spin fast? What's the driving force?

He didn't say that they were spinning fast, he said that they couldn't spin at a speed greater than the speed of the treadmill.

And the ratio of Angular Velocity, to Linear Velocity is not proportional when the surface the wheel is travelling on is moving.