Conceptual Puzzle: Runway Belt

[Huckleberry]

For those focusing on the wheel behavior:

During normal takeoff, normal meaning on normal ground, it's pretty simple. If the plane's jet thrust has accelerated it to 400mph ground speed, then the speeds are as follows:

Ground speed of axle, or center of wheel = 400 mph
Ground speed of wheel at point of contact with the ground = 0 mph
Ground speed of wheel at top of wheel, diametrically opposed to point of contact = 800 mph

On this conveyor belt, things change but the underlying principles do not. The jets have accelerated the plane's ground speed to 400 mph. This is the controlling factor. The conveyor belt therefore has a ground speed of -400 mph. Therefore the "belt speed" of the plane, or the plane's speed relative to the belt, is 800 mph.

Belt speed of axle, or center of wheel = 800 mph
Belt speed of wheel at point of contact with the belt = 0 mph
Belt speed of wheel at top of wheel, diametrically opposed to point of contact = 1600 mph

Ground speed of axle, or center of wheel = 400 mph
Ground speed of wheel at point of contact with the belt = -400 mph
Ground speed of wheel at top of wheel, diametrically opposed to point of contact = 1200 mph

There is no skidding required.

[Toddzilla]

Originally Posted by BrianD

Then the wheels do more than just spin and they do impart a force on the plane.

Well, yeah, at rest they do. But we're talking about a negligible amount of force. Thinking about how hard it is to keep a car still on a grocery store conveyor. Very little. In the context of firing up the engines to move an airplane 500+ MPH, the wheels impart 0 force on the plane.

[BrianD]

Originally Posted by Toddzilla

Absent of any other force acting on the plane, the wheels would remain motionless and the plane would move backwards at the same rate the conveyor was moving.

To put it another way, what happens if we now apply enough force from the jets to move the plane forward (which makes the wheels roll) at a speed equal to the conveyor?

[KWhit]

Originally Posted by BrianD

To put it another way, what happens if we now apply enough force from the jets to move the plane forward (which makes the wheels roll) at a speed equal to the conveyor?

The wheels have to turn faster than the conveyor is turning.

[BrianD]

Originally Posted by KWhit

The wheels have to turn faster than the conveyor is turning.

Why?

[BrianD]

Originally Posted by BrianD

To put it another way, what happens if we now apply enough force from the jets to move the plane forward (which makes the wheels roll) at a speed equal to the conveyor?

And when I say "forward" here, I mean forward relative to the conveyor, not relative to the ground.

[Toddzilla]

Originally Posted by JHandley

In order for the plane to move forward one extra foot, the wheels have to move forward one extra foot.

If the wheel only covers 100 feet of the conveyor, then the plane only covers 100 feet of the conveyor.

If the plane covers 101 feet of the conveyor, then the wheels cover 101 feet of the conveyor, if the wheel only makes 100 revolutions, then it skidded the extra foot or didn't travel at the same speed as the conveyor.

You are right, and I have completely taken a shit on my explanation, forgetting about relative distances.

Placing a mark on the ground and on the conveyor belt at the same place, the conveyor belt is 100-feet long. We move the conveyor belt one complete revolution and keep the plane in place relative to the ground. The wheels have a 1 foot circumference:

The conveyor belt moved 100 feet - relative to the ground.
The wheels rotated 100 times.
The plane stands still relative to the ground.
(and the plane moved forward 100 feet relative to the conveyor belt).

Again, moving the conveyor belt 1 complete revolution but moving the plane forward 1 foot relative to the ground:

The conveyor belt moved 100 feet - relative to the ground.
The wheels rotated 101 times.
The plane moved 1 foot relative to the ground.
The plane moved 101 feet relative to the conveyor belt.

Do you agree?

[KWhit]

Originally Posted by BrianD

Why?

To compensate for the additional distance travelled by the wheels.

[KWhit]

Originally Posted by Toddzilla

You are right, and I have completely taken a shit on my explanation, forgetting about relative distances.

Placing a mark on the ground and on the conveyor belt at the same place, the conveyor belt is 100-feet long. We move the conveyor belt one complete revolution and keep the plane in place relative to the ground. The wheels have a 1 foot circumference:

The conveyor belt moved 100 feet - relative to the ground.
The wheels rotated 100 times.
The plane stands still relative to the ground.
(and the plane moved forward 100 feet relative to the conveyor belt).

Again, moving the conveyor belt 1 complete revolution but moving the plane forward 1 foot relative to the ground:

The conveyor belt moved 100 feet - relative to the ground.
The wheels rotated 101 times.
The plane moved 1 foot relative to the ground.
The plane moved 101 feet relative to the conveyor belt.

Do you agree?

That sounds right to me.

[Toddzilla]

Originally Posted by BrianD

To put it another way, what happens if we now apply enough force from the jets to move the plane forward (which makes the wheels roll) at a speed equal to the conveyor?

OK, now we're talkin....

We throttle up the engines a little and the plane stops moving backwards. The wheels are now turning underneath the plane. The engines are keeping the plane still, and the conveyor belt is moving the wheels underneath the plane.

This is EXACTLY the same scenario as if some giant hand is holding the plane in place. The force imparted onto the plane by our giant hand is exactly equal to the force imparted on the plane by the thrust of the engines.

Do you agree that it is the conveyor belt that is moving the wheels?

[BrianD]

Originally Posted by KWhit

To compensate for the additional distance travelled by the wheels.

My point was that there wouldn't be any additional distance travelled by the wheels. I'm hoping my later edit made that more clear. Relative to the ground, the plane shouldn't have moved at all. Rather than thinking about this problem using a moving plane and then adding a moving conveyor, I was trying to look at it backwards. Moving conveyor first, then add movement to the plane.

[Huckleberry]

Okay, I'll be the first to say it:

Free Body Diagram

Until one of the people that thinks the plane won't take off can explain to me the mechanism by which the conveyor belt applies a force equal and opposite to the jet engines' thrust to the plane, then there is no argument to be had. There is simply no way for the belt to apply that much force to the plane through a free-rolling, i.e., frictionless wheel. It's impossible for the belt to apply any force to the plane.

[JHandley]

Originally Posted by Toddzilla

You are right, and I have completely taken a shit on my explanation, forgetting about relative distances.

Placing a mark on the ground and on the conveyor belt at the same place, the conveyor belt is 100-feet long. We move the conveyor belt one complete revolution and keep the plane in place relative to the ground. The wheels have a 1 foot circumference:

The conveyor belt moved 100 feet - relative to the ground.
The wheels rotated 100 times.
The plane stands still relative to the ground.
(and the plane moved forward 100 feet relative to the conveyor belt).

Again, moving the conveyor belt 1 complete revolution but moving the plane forward 1 foot relative to the ground:

The conveyor belt moved 100 feet - relative to the ground.
The wheels rotated 101 times.
The plane moved 1 foot relative to the ground.
The plane moved 101 feet relative to the conveyor belt.

Do you agree?

Going to take me a bit to draw this up so i can see it visually.

There are enough people that disagree with me in this discussion that I really want to see what I'm missing here because I just can't get my head around a 1 foot wheel travelling more than 100 feet in 100 revolutions.

[BrianD]

Originally Posted by Toddzilla

OK, now we're talkin....

We throttle up the engines a little and the plane stops moving backwards. The wheels are now turning underneath the plane. The engines are keeping the plane still, and the conveyor belt is moving the wheels underneath the plane.

This is EXACTLY the same scenario as if some giant hand is holding the plane in place. The force imparted onto the plane by our giant hand is exactly equal to the force imparted on the plane by the thrust of the engines.

Do you agree that it is the conveyor belt that is moving the wheels?

No, it is still the conveyor belt in combination with the engines. When we had the conveyor belt moving but no engines, there was no wheel spinning.

At this point, the conveyor should be moving at the same speed as the wheels, right?

[st.cronin]

Originally Posted by Huckleberry

For those focusing on the wheel behavior:

During normal takeoff, normal meaning on normal ground, it's pretty simple. If the plane's jet thrust has accelerated it to 400mph ground speed, then the speeds are as follows:

Ground speed of axle, or center of wheel = 400 mph
Ground speed of wheel at point of contact with the ground = 0 mph
Ground speed of wheel at top of wheel, diametrically opposed to point of contact = 800 mph

On this conveyor belt, things change but the underlying principles do not. The jets have accelerated the plane's ground speed to 400 mph. This is the controlling factor. The conveyor belt therefore has a ground speed of -400 mph. Therefore the "belt speed" of the plane, or the plane's speed relative to the belt, is 800 mph.

Belt speed of axle, or center of wheel = 800 mph
Belt speed of wheel at point of contact with the belt = 0 mph
Belt speed of wheel at top of wheel, diametrically opposed to point of contact = 1600 mph

Ground speed of axle, or center of wheel = 400 mph
Ground speed of wheel at point of contact with the belt = -400 mph
Ground speed of wheel at top of wheel, diametrically opposed to point of contact = 1200 mph

There is no skidding required.

I haven't worked out all your math, but you are outside the parameter of the puzzle. The treadmill's speed does not match the jet's speed - it matches the speed of the WHEELS. You do not match the treadmill to the jet, you match it to some speed of the wheel. I don't think that's a vectoral speed, either - I think it's supposed to be a rotational speed.

[KWhit]

Originally Posted by BrianD

My point was that there wouldn't be any additional distance travelled by the wheels. I'm hoping my later edit made that more clear. Relative to the ground, the plane shouldn't have moved at all. Rather than thinking about this problem using a moving plane and then adding a moving conveyor, I was trying to look at it backwards. Moving conveyor first, then add movement to the plane.

Oh, I see what you're saying now. We were talking about two different things.

[KWhit]

Originally Posted by st.cronin

I haven't worked out all your math, but you are outside the parameter of the puzzle. The treadmill's speed does not match the jet's speed - it matches the speed of the WHEELS. You do not match the treadmill to the jet, you match it to some speed of the wheel. I don't think that's a vectoral speed, either - I think it's supposed to be a rotational speed.

I agree with the young man from st.croninville.

[st.cronin]

Originally Posted by Toddzilla

You are right, and I have completely taken a shit on my explanation, forgetting about relative distances.

Placing a mark on the ground and on the conveyor belt at the same place, the conveyor belt is 100-feet long. We move the conveyor belt one complete revolution and keep the plane in place relative to the ground. The wheels have a 1 foot circumference:

The conveyor belt moved 100 feet - relative to the ground.
The wheels rotated 100 times.
The plane stands still relative to the ground.
(and the plane moved forward 100 feet relative to the conveyor belt).

Again, moving the conveyor belt 1 complete revolution but moving the plane forward 1 foot relative to the ground:

The conveyor belt moved 100 feet - relative to the ground.
The wheels rotated 101 times.
The plane moved 1 foot relative to the ground.
The plane moved 101 feet relative to the conveyor belt.

Do you agree?

What you still have to explain is how the wheels and the treadmill are moving at the same speed in this example. That's the key to the puzzle.

[BrianD]

Originally Posted by KWhit

Oh, I see what you're saying now. We were talking about two different things.

Yes, sorry about that. With all of the different points of reference, it is hard to discuss this clearly.

[albionmoonlight]

Originally Posted by st.cronin

I don't think that's a vectoral speed, either - I think it's supposed to be a rotational speed.

Why?

[KWhit]

Originally Posted by st.cronin

What you still have to explain is how the wheels and the treadmill are moving at the same speed in this example. That's the key to the puzzle.

Right. They're not moving at the same speed. The conveyor has moved 100 feet and the wheels have moved 101 feet.

[Huckleberry]

Originally Posted by st.cronin

I haven't worked out all your math, but you are outside the parameter of the puzzle. The treadmill's speed does not match the jet's speed - it matches the speed of the WHEELS. You do not match the treadmill to the jet, you match it to some speed of the wheel. I don't think that's a vectoral speed, either - I think it's supposed to be a rotational speed.

I think assuming it's supposed to be rotational speed is pretty bold and makes the problem unnecessairly complex. What rotational speed? Tangential speed at the outside of the tire? On which side?

And even if that is the correct assumption, it's irrelevant to answering the question. How is the belt going to apply a force to the plane? If you can't answer that then the plane will move and will take off.

[JHandley]

Originally Posted by Toddzilla

Again, moving the conveyor belt 1 complete revolution but moving the plane forward 1 foot relative to the ground:

The conveyor belt moved 100 feet - relative to the ground.
The wheels rotated 101 times.
The plane moved 1 foot relative to the ground.
The plane moved 101 feet relative to the conveyor belt.

Do you agree?

You moved the plane and wheels forward 1 foot relative to the ground without moving the conveyor. In order for that to be true, it has to move at a different speed than the wheels.

[st.cronin]

Originally Posted by albionmoonlight

Why?

Because, as Huckleberry as illustrated, there are multiple choices for vectoral speeds, and the answer changes depending on what you pick.

[st.cronin]

Originally Posted by Huckleberry

I think assuming it's supposed to be rotational speed is pretty bold and makes the problem unnecessairly complex. What rotational speed? Tangential speed at the outside of the tire? On which side?

And even if that is the correct assumption, it's irrelevant to answering the question. How is the belt going to apply a force to the plane? If you can't answer that then the plane will move and will take off.

My assertion is that the belt doesn't apply a force to the plane - it ABSORBS the force of the plane (or plane's jets, actually), by accelarating its own rotational speed as force is added.

[Huckleberry]

Originally Posted by st.cronin

Because, as Huckleberry as illustrated, there are multiple choices for vectoral speeds, and the answer changes depending on what you pick.

Another thing. What are the options for what the belt is supposed to match? I illustrated the translational speed of the wheels. If you pick rotational speed, what option is there other than the point of contact between wheel and belt? The translational speed solution satisfies that requirement as well. If there is no skidding then it is clearly shown that the belt is matching the rotational speed of the wheel as well.

Please explain the situation where skidding is required. What speed of the wheel is the belt being required to match in that situation?

[Huckleberry]

Originally Posted by st.cronin

My assertion is that the belt doesn't apply a force to the plane - it ABSORBS the force of the plane (or plane's jets, actually), by accelarating its own rotational speed as force is added.

So you're violating both Newton's Second and Third Laws?

You have stated that the belt doesn't apply a force to the plane. We know the engines are applying a force to the plane. Therefore you are claiming a violation of the Second Law if the plane does not accelerate. Then you claim that the belt "absorbs" the force of the plane, which clearly requires it to feel that force via some mechanism, but does not apply an equal and opposite force to the plane. A violation of the Third Law.

[st.cronin]

Originally Posted by Huckleberry

Another thing. What are the options for what the belt is supposed to match? I illustrated the translational speed of the wheels. If you pick rotational speed, what option is there other than the point of contact between wheel and belt? The translational speed solution satisfies that requirement as well. If there is no skidding then it is clearly shown that the belt is matching the rotational speed of the wheel as well.

Please explain the situation where skidding is required. What speed of the wheel is the belt being required to match in that situation?

I think there are two options for what the treadmill is supposed to match, and only one that makes sense. The one that makes sense is the speed of a point on the surface. If the wheel's circumference is 1 foot, and the wheel rotates once per second, then the wheel is "moving" 1 foot per second. The treadmill will then move 1 foot per second.

The choice that doesn't make sense is angular speed - if the wheel rotates once per second, then the treadmill must complete its own cycle once per second. This would make the plane move backwards really fast.

[BrianD]

Originally Posted by Huckleberry

So you're violating both Newton's Second and Third Laws?

You have stated that the belt doesn't apply a force to the plane. We know the engines are applying a force to the plane. Therefore you are claiming a violation of the Second Law if the plane does not accelerate. Then you claim that the belt "absorbs" the force of the plane, which clearly requires it to feel that force via some mechanism, but does not apply an equal and opposite force to the plane. A violation of the Third Law.

The belt has to be applying a force to the plane. Go back to the sitation of of the engines being off. The plane will move backwards (relative to the ground). If you want the plane to not move backwards, you will have to apply some thrust to the engines.

[Toddzilla]

Originally Posted by st.cronin

What you still have to explain is how the wheels and the treadmill are moving at the same speed in this example. That's the key to the puzzle.

Originally Posted by albionmoonlight

Why?

Originally Posted by KWhit

Right. They're not moving at the same speed. The conveyor has moved 100 feet and the wheels have moved 101 feet.

You are getting the points of reference mixed up. In the example where we moved the plane 1 foot:

The conveyor belt moved 100 feet relative to the ground.
The plane moved forward one foot relative to the ground.

so

The plane is now sitting on the conveyor belt one foot past the start line
The wheels rotated 101 times and moves 101 feet relative to the conveyor belt
The conveyor belt moved 101 feet relative to the wheels, too:

At the start, the wheels are on the line. The conveyor starts, the wheels roll, ant the start line moves. The line goes "underneath" the top of the belt and comes back around. It passes under the wheels a second time and comes to rest where it started - at the mark we made in the ground.

The wheels rotated 101 times
The conveyor belt moved 101 feet under the wheels

The "speed" of the conveyor = the "speed" of the wheels

"speed" meaning how far it moved in a given amount of time.

The "speed" of the two can only be compared meaningfully when the points of reference are exactly the same, i.e. the point where the wheels meet the conveyor.

[Huckleberry]

Originally Posted by st.cronin

I think there are two options for what the treadmill is supposed to match, and only one that makes sense. The one that makes sense is the speed of a point on the surface. If the wheel's circumference is 1 foot, and the wheel rotates once per second, then the wheel is "moving" 1 foot per second. The treadmill will then move 1 foot per second.

But that is exactly what you do by matching the translational speed. In your example the axle or center of the wheel will necessarily be moving 1 foot per second.

[st.cronin]

Originally Posted by Toddzilla

You are getting the points of reference mixed up. In the example where we moved the plane 1 foot:

The conveyor belt moved 100 feet relative to the ground.
The plane moved forward one foot relative to the ground.

so

The plane is now sitting on the conveyor belt one foot past the start line
The wheels rotated 101 times and moves 101 feet relative to the conveyor belt
The conveyor belt moved 101 feet relative to the wheels, too:

At the start, the wheels are on the line. The conveyor starts, the wheels roll, ant the start line moves. The line goes "underneath" the top of the belt and comes back around. It passes under the wheels a second time and comes to rest where it started - at the mark we made in the ground.

The wheels rotated 101 times
The conveyor belt moved 101 feet under the wheels

The "speed" of the conveyor = the "speed" of the wheels

"speed" meaning how far it moved in a given amount of time.

The "speed" of the two can only be compared meaningfully when the points of reference are exactly the same, i.e. the point where the wheels meet the conveyor.

If this is really your understanding of the puzzle, it is not neccesary for the treadmill to be a treadmill at all. A runway has identical "speed" to the wheels in the same way. A highway has identical speed to the wheels of my car.

I don't think this is the solution.

[Huckleberry]

Originally Posted by BrianD

The belt has to be applying a force to the plane. Go back to the sitation of of the engines being off. The plane will move backwards (relative to the ground). If you want the plane to not move backwards, you will have to apply some thrust to the engines.

No it won't. The plane will not move if the wheels are truly free-rolling, i.e. frictionless.

[KWhit]

Originally Posted by Toddzilla

You are getting the points of reference mixed up. In the example where we moved the plane 1 foot:

The conveyor belt moved 100 feet relative to the ground.
The plane moved forward one foot relative to the ground.

so

The plane is now sitting on the conveyor belt one foot past the start line
The wheels rotated 101 times and moves 101 feet relative to the conveyor belt
The conveyor belt moved 101 feet relative to the wheels, too:

At the start, the wheels are on the line. The conveyor starts, the wheels roll, ant the start line moves. The line goes "underneath" the top of the belt and comes back around. It passes under the wheels a second time and comes to rest where it started - at the mark we made in the ground.

The wheels rotated 101 times
The conveyor belt moved 101 feet under the wheels

The "speed" of the conveyor = the "speed" of the wheels

"speed" meaning how far it moved in a given amount of time.

The "speed" of the two can only be compared meaningfully when the points of reference are exactly the same, i.e. the point where the wheels meet the conveyor.

I don't believe that to be true at all. The conveyor moved 100 feet. The wheels have moved a foot forward, but that doesn't change how far (or fast) the conveyor moved.

[st.cronin]

Originally Posted by Huckleberry

But that is exactly what you do by matching the translational speed. In your example the axle or center of the wheel will necessarily be moving 1 foot per second.

When figuring rotational speed, the CENTER does not move AT ALL!

[st.cronin]

Originally Posted by Huckleberry

No it won't. The plane will not move if the wheels are truly free-rolling, i.e. frictionless.

Then, it is as if the plane was on a sheet of ice, without wheels?

[KWhit]

Originally Posted by Huckleberry

No it won't. The plane will not move if the wheels are truly free-rolling, i.e. frictionless.

Right. However, I think this line of thinking is a slight distraction because I don't think it ultimately affects the answer to the puzzle.

[Huckleberry]

Originally Posted by st.cronin

When figuring rotational speed, the CENTER does not move AT ALL!

Exactly.

So what speed are you matching again? In your previous post you claimed the wheel was moving one foot per second. What part of the wheel is moving one foot per second and relative to what?

[Toddzilla]

Originally Posted by BrianD

The belt has to be applying a force to the plane. Go back to the sitation of of the engines being off. The plane will move backwards (relative to the ground). If you want the plane to not move backwards, you will have to apply some thrust to the engines.

In this puzzle, that force is insignificant. At rest, we can assume that the friction between the wheels and the axle is great enough so that moving the conveyor belt will move the plane. However, once the engines fire up, that force so overwhelms that friction that the force from the friction is meaningless (say .0000000000001% of the force of the engines).

I think the cruz of the puzzle is to understand that a plane on wheels is the same as a plane without wheels sitting on ice. The point is that there is no friction between the plane and the ground where it rests (be that belly of plane against the ice, or the wheels of a plane against the runway (or conveyor belt), so the engines of the plane can provide enough thrust to move the plane.

[Huckleberry]

Originally Posted by KWhit

Right. However, I think this line of thinking is a slight distraction because I don't think it ultimately affects the answer to the puzzle.

The entire portion of the thread after the part where someone said "yes it will take off" is a big distraction.

[KWhit]

Originally Posted by KWhit

Right. However, I think this line of thinking is a slight distraction because I don't think it ultimately affects the answer to the puzzle.

Well.... I take that back... It might affect the answer, I suppose. Carry on.

[BrianD]

Originally Posted by Huckleberry

No it won't. The plane will not move if the wheels are truly free-rolling, i.e. frictionless.

So if we put a plane on a moving conveyor belt, the plane will stay motionless relative to the ground (assuming the plane is off)?

[albionmoonlight]

Let's try one more thing for the "plane ain't gonna move" crowd.

I'll grant you a suped up runway. Your conveyor belt is moving backwards at 1,000,000,000 mph.

Now, I have a plane whose engine thrust is such that, if it were on solid ground, it would go forward at 400 mph.

When I drop my plane (with engines running) on the conveyor, does it go backwards at 1,000,000,000 mph (less 400 mph). If not, then can you see why the speed of the wheels just does not matter?

If so, then you and I just differ on our understanding of free rolling wheels.

[Huckleberry]

Originally Posted by st.cronin

Then, it is as if the plane was on a sheet of ice, without wheels?

Not sure what side of the discussion about that analogy you were on but it is indeed like that as far as the plane is concerned. Obviously it's not like that when analyzing the wheels' behavior because they don't exactly exist in the on ice without wheels world.

[st.cronin]

Originally Posted by Huckleberry

Exactly.

So what speed are you matching again? In your previous post you claimed the wheel was moving one foot per second. What part of the wheel is moving one foot per second and relative to what?

If the wheel was a clock, the time it takes the big hand to move from 12 oclock to 6 oclock, for example. Movement on the circle. In terms of rotation, this is the same for all points on the wheel - it is not different for the top of the wheel and the bottom of the wheel.

[Huckleberry]

Originally Posted by BrianD

So if we put a plane on a moving conveyor belt, the plane will stay motionless relative to the ground (assuming the plane is off)?

Absolutely.

[Huckleberry]

Originally Posted by st.cronin

If the wheel was a clock, the time it takes the big hand to move from 12 oclock to 6 oclock, for example. Movement on the circle. In terms of rotation, this is the same for all points on the wheel - it is not different for the top of the wheel and the bottom of the wheel.

Which is the angular velocity option you already nixed. Now you are trying somehow to tie in the belt's linear velocity with the wheel's angular velocity. I'd like to see how that can be accomplished. In your example you can't say that the wheel is rotating one foot per second, the wheel is rotating one revolution per second. 360 degrees per second.

[Toddzilla]

Originally Posted by KWhit

I don't believe that to be true at all. The conveyor moved 100 feet. The wheels have moved a foot forward, but that doesn't change how far (or fast) the conveyor moved.

This is the key to understanding the problem, however. The conveyor moved 100 feet relative to the ground, one complete revolution, but it moved 101 feet relative to the wheels (and the plane).

[BrianD]

Originally Posted by Toddzilla

In this puzzle, that force is insignificant. At rest, we can assume that the friction between the wheels and the axle is great enough so that moving the conveyor belt will move the plane. However, once the engines fire up, that force so overwhelms that friction that the force from the friction is meaningless (say .0000000000001% of the force of the engines).

I think the cruz of the puzzle is to understand that a plane on wheels is the same as a plane without wheels sitting on ice. The point is that there is no friction between the plane and the ground where it rests (be that belly of plane against the ice, or the wheels of a plane against the runway (or conveyor belt), so the engines of the plane can provide enough thrust to move the plane.

There has to be friction, or the wheels wouldn't move. If the plane can still move forward on the moving runway, then the runway is not moving as fast as the wheels. It means that the moving runway will be spinning the wheels in addition to the plane's thrust is moving the wheels. This means we will have to have a runway moving at infinite speeds which seems to make the puzzle's premise impossible.

[Toddzilla]

Originally Posted by BrianD

So if we put a plane on a moving conveyor belt, the plane will stay motionless relative to the ground (assuming the plane is off)?

Originally Posted by Huckleberry

Absolutely.

If the wheels are, indeed, frictionless at the axle.