Conceptual Puzzle: Runway Belt

[Arctus]

Originally Posted by Arctus

The conveyor belt does not exert a force on the plane, nor does it cause the wheels to rotate. The discussions regarding the wheels rotating infinitely fast are not correct. The only way for this to happen is if the plane was "pinned" in a fixed position relative to the conveyor belt. This is not the case. Adam, whose point of reference is relative to the conveyor belt, witnesses a plane taxi-ing normally. Bob witnesses a stationary plane, just as I witness a stationary person on a treadmill at my gym. It is only by definition of the puzzle itself that the plane is "pinned" in place from Bob's perspective.

I just realized I butchered this part of my explanation horribly. Let me try it again. Changes in red.

The conveyor belt does not exert a force on the plane, nor does it cause the wheels to rotate. [/b] The discussions regarding the wheels rotating infinitely fast are not correct. The only way for this to happen is if the plane was "pinned" in a fixed position relative to the earth (imagine it being held in place by a giant finger resting on top of it). This is not the case. Adam, whose point of reference is relative to the conveyor belt, witnesses a plane taxi-ing normally. Bob witnesses a stationary plane, just as I witness a stationary person on a treadmill at my gym. It is only by definition of the puzzle itself that the plane is "pinned" in place from Bob's perspective.

Having zero net velocity due to two independent actions is not the same as being "pinned" into being stationary.

Sorry if my shitty first try caused any confusion.

[st.cronin]

Originally Posted by Toddzilla

The correlation of holding a toy car on the conveyor belt at the store is the perfect analogy.

* The tires of the car always maintain contact with the conveyor
* The tires never skid or slip
* The tires are always moving

You can move car the backwards and forwards on the belt with very little force applied to the car, and the above three conditions will always hold.

The concept that was hard for *me* to get my head around, and I suspect it may be vexing you as well, is the fact that the rotation of the wheels and the movement of the car body is for all practical purposes independent of one another.

How fast the conveyor moves is irrelevant, and what direction the conveyor moves is irrelevant. You will always be able to hold the car still, and you will always be able to move the car forward and backwards with relative ease. And that is because the wheels on the car do nothing to the car other than provide a frictionless connection between the car and the conveyor (it is frictionless at the axle). The wheels don't propel the car forward, and they don't slow the car down. They so nothing. And therefore the conveyor does nothing. And so you can move the car with your finger independent of whatever the conveyor does. The car is the plane and your finger is the jet engine.

But moving the toy car back and forth, the speed of the wheels is DIFFERENT from the speed of the conveyor belt.

[JHandley]

I will maintain that the wheels of the toy car *do* skid. They just do so with such relative ease and in such small increments that you don't feel or see it. Much like the force of thrust applied to the wheels of a plane.

[st.cronin]

Originally Posted by JHandley

I will maintain that the wheels of the toy car *do* skid. They just do so with such relative ease and in such small increments that you don't feel or see it. Much like the force of thrust applied to the wheels of a plane.

If the wheels of the plane are allowed to skid, then it's a really stupid problem.

[Toddzilla]

Dola - I see another place where you may be getting confused, as evidenced by the underlined quote in your last message

If the wheel maintains contact with the treadmill the entire time, and does not ever skid, there is simply no way that a circumference of 1 foot can travel more than 100 feet in 100 revolutions regardless of how fast or slow the revolutions are.

The problem is, you are equating "travel 100 feet" of conveyor belt distance with "travel 100 feet" of actual distance in space.

Hold the car still on the conveyor belt. As the conveyor belt moves 100 feet, the 1-foot circumference wheel will have rotated 100 times, or traveled 100 feet *of conveyor belt*. However, as you are just standing there, and so is the cr you are holding still. The car itself hasn't moved at all. We're talking about moving the car (plane), not the wheels.

Now roll the car forward 1 foot in the time it takes the conveyor to move 100 feet. The conveyor moved 100 feet, but the wheels of the car rotated 101 times - 100 times as it maintained contact with the conveyor, and 1 more foot that you moved the car.

Even though the wheels never left the ground, nor skidded, the conveyor belt only moved 100 feet, the wheels rotated 101 times, and the car moved 1 foot is space.

[st.cronin]

Originally Posted by Toddzilla

Dola - I see another place where you may be getting confused, as evidenced by the underlined quote in your last message



The problem is, you are equating "travel 100 feet" of conveyor belt distance with "travel 100 feet" of actual distance in space.

Hold the car still on the conveyor belt. As the conveyor belt moves 100 feet, the 1-foot circumference wheel will have rotated 100 times, or traveled 100 feet *of conveyor belt*. However, as you are just standing there, and so is the cr you are holding still. The car itself hasn't moved at all. We're talking about moving the car (plane), not the wheels.

Now roll the car forward 1 foot in the time it takes the conveyor to move 100 feet. The conveyor moved 100 feet, but the wheels of the car rotated 101 times - 100 times as it maintained contact with the conveyor, and 1 more foot that you moved the car.

Even though the wheels never left the ground, nor skidded, the conveyor belt only moved 100 feet, the wheels rotated 101 times, and the car moved 1 foot is space.

What you have just shown is that the wheels and the conveyor belt are moving at different speeds - thus, you are outside the parameters of the problem.

[JHandley]

Originally Posted by st.cronin

But moving the toy car back and forth, the speed of the wheels is DIFFERENT from the speed of the conveyor belt.

They absolutely must because the speed of the revolutions is irrelevant to the distance travelled.

[MJ4H]

nm

[gstelmack]

Originally Posted by st.cronin

But moving the toy car back and forth, the speed of the wheels is DIFFERENT from the speed of the conveyor belt.

I keep coming back to this, and am again switching back to my original "no take off". Arctus is doing a good job of explaining this.

As the plane tries to move forward, it tries to drag the landing gear forward. As the landing gear tries to move forward, it tries to drag the wheels forward. As the wheels move forward, they either rotate or skid along the ground (there is no third option here). If they only rotate, then they speed up the conveyor belt. As the conveyor belt goes faster, it cancels out forward movement of the airplane by helping to carry the wheels backward.

As long as you make the statement that the mythical conveyor belt speeds up to match the wheels, the plane is going nowhere.

I know everyone talks about the thrust of a jet engine, but keep in mind that an airplane is very large as well. For example, one key feature of the F-15 was that it actually generated more thrust than it weighed, allowing it to accelerate while moving straight up. Most jets don't have that luxury. Look how long a runway they need to get up to speed. You don't have enough thrust here to overcome all that friction. And if you did, you'd make the wheels skid.

I think its pretty clear that gravity and friction mean the jet is moving the conveyor faster and faster without ever taking off. Free-wheeling or no, pushing the axel forward will cause a rotation in the tires. You can spin the tires without moving the plane or car, but you cannot move the tires without spinning them if they are in contact with something.

[Pumpy Tudors]

Originally Posted by Toddzilla

How fast the conveyor moves is irrelevant, and what direction the conveyor moves is irrelevant. You will always be able to hold the car still, and you will always be able to move the car forward and backwards with relative ease. And that is because the wheels on the car do nothing to the car other than provide a frictionless connection between the car and the conveyor (it is frictionless at the axle). The wheels don't propel the car forward, and they don't slow the car down. They so nothing. And therefore the conveyor does nothing. And so you can move the car with your finger independent of whatever the conveyor does. The car is the plane and your finger is the jet engine.

Using the toy car example, this leads me to a question. Of course you can move the car forward and backward with relative ease. I get that part. Suppose you're moving the car forward at, say, 2 MPH. Given the original problem, the conveyor is moving the car backwards at 2 MPH, right?

If this is right, then if you move the car forward at 4 MPH, the belt speeds up and moves it backwards at 4 MPH. Isn't the problem set up to have the belt match the speed of the car, regardless of what it is? Putting additional force on the car just means that the belt moves faster. How does your additional force overcome the explicit piece of the problem that says that the belt moves at the exact same speed?

Now, if all of that is wrong, that puts one question in my mind. Assume that the car is in the absolute center of the belt. The belt moves backwards and the car doesn't. Since the wheels are free-rolling, does the car move (relative to someone who's not on the belt)? If the car stays in the center of the belt but the wheels turn, I get the whole thing. If the car rolls backwards from the center when the belt is in motion, I don't get it at all.

[Toddzilla]

Originally Posted by st.cronin

But moving the toy car back and forth, the speed of the wheels is DIFFERENT from the speed of the conveyor belt.

Form the point of view of the conveyor belt, it is not, since the wheels and conveyor belt are always spinning at the same speed.

You cannot measure the speed of the conveyor belt in MPH or feet/second. The conveyor belt - like a treadmill - is stationary. It just sits there. It is basically a big, flat wheel that turns it's belt. It's speed is always 0. It never moves. You need to think of the "speed" of the conveyor as the rotational speed. Because that distinction is what enables the plane to move forward.

The speed of the wheels is ambiguous. We can either talk about the rotational speed, the RPM of the wheel - which is what the conveyor belt will always match, or we can talk about the movement of the wheel through space, the MPH of the wheel. I'm sure you will agree that on a stationary surface - like a road - these two measures are completely dependent on each other (in the absence of a skid). On a surface that moves, the relationship is more complicated, and in our puzzle, the relationship is completely and utterly independent and irrelevant.

When we say the conveyor belt is always moving at the same speed as the wheels, it means the conveyor rotates it's belt at the same speed that the wheel rotates. The wheel can still move forward through space

[Toddzilla]

Originally Posted by st.cronin

What you have just shown is that the wheels and the conveyor belt are moving at different speeds - thus, you are outside the parameters of the problem.

NO! I have demonstrated that while the conveyor belt and wheels are rotating at the same speed - which is the parameter of the problem - the wheels can still move through space - not a parameter.

[Toddzilla]

Originally Posted by JHandley

They absolutely must because the speed of the revolutions is irrelevant to the distance travelled.

Bingo.

[albionmoonlight]

Plane has thrust to move forward at 100 mph.

The conveyor belt, by the definition of the problem, moves in the opposite direction at 100 mph.

The result is that the plane moves forward at 100 mph (less very slight friction), while the wheels spin at 200 mph.

This assumes, of course, that "match[ing] the speed of the wheels at any given time" means matching their lateral and not rotational speed. As someone noted above, however, that assumption is the only one that makes any sense. To assume otherwise is to end up with an infinitely fast conveyer belt after some instantanious (sp?) amount of time.

[st.cronin]

Originally Posted by Toddzilla

NO! I have demonstrated that while the conveyor belt and wheels are rotating at the same speed - which is the parameter of the problem - the wheels can still move through space - not a parameter.

What you said, I THINK, is that it is possible for the wheels to rotate 101 feet in the same amount of time that the treadmill rotates 100 feet. So

Speed of wheels = 101 ft/x
speed of treadmill = 100 ft/x

How are those not different?

[Toddzilla]

[quote=Pumpy Tudors;1339660]Using the toy car example, this leads me to a question. Of course you can move the car forward and backward with relative ease. I get that part. Suppose you're moving the car forward at, say, 2 MPH. Given the original problem, the conveyor is moving the car backwards at 2 MPH, right?[quote]No - this is the major misconception of the problem that has everyone tied in knots. The conveyor belt is NOT moving the car. The conveyor belt has no affect on the car. The conveyor moves the wheels of the car. As I move the car forward 2MPH, the wheels will spin at some RPM, say 100 RPM. If they conveyor moves the wheels the opposite way at -100RPM, then I'll just be holding the car still.

If this is right, then if you move the car forward at 4 MPH, the belt speeds up and moves it backwards at 4 MPH. Isn't the problem set up to have the belt match the speed of the car, regardless of what it is? Putting additional force on the car just means that the belt moves faster. How does your additional force overcome the explicit piece of the problem that says that the belt moves at the exact same speed?

Keep in mind it is not the car moving that is making the wheels turn, it is the conveyor belt that makes the wheels turn.

[JHandley]

Originally Posted by st.cronin

What you said, I THINK, is that it is possible for the wheels to rotate 101 feet in the same amount of time that the treadmill rotates 100 feet. So

Speed of wheels = 101 ft/x
speed of treadmill = 100 ft/x

How are those not different?

Bingo. That's what I'm saying. Speed is irrelevant. It doesn't matter how fast the treadmill is moving, it only matters that the wheel can only cover the amount of tread being laid down that is equal to the number of rotations of the wheel. UNLESS, the wheel moves without rotating.

[Pumpy Tudors]

Hmmm... since the treadmill is much bigger than the wheels on the plane, how about this for fun:

Assume both are moving at 1 RPM. Since the treadmill is so much bigger, after one minute passes, the plane rolls off the back of the treadmill and goes through a wall of the airport. You could make a disaster movie from this. I like it.

[albionmoonlight]

Originally Posted by st.cronin

What you said, I THINK, is that it is possible for the wheels to rotate 101 feet in the same amount of time that the treadmill rotates 100 feet. So

Speed of wheels = 101 ft/x
speed of treadmill = 100 ft/x

How are those not different?

Lets say that you push the car forward 100 ft in that time.

Then you have

Speed of treadmill = 100 ft/x
Speed of Wheels (lateral) = 100 ft/x
Speed of Wheels (rotational) = 200 ft/x

In our problem, the speed of the conveyor matches the lateral (not rotational) speed of the wheels. If it matched the rotational speed of the wheels, you would end up with an infinitely fast conveyer belt (assuming non-relativistic physics, infinite energy, etc.), which seems a bit off to me.

[Toddzilla]

Originally Posted by st.cronin

What you said, I THINK, is that it is possible for the wheels to rotate 101 feet in the same amount of time that the treadmill rotates 100 feet. So

Speed of wheels = 101 ft/x
speed of treadmill = 100 ft/x

How are those not different?

They are different, but one measure - the wheels - is relative to the position of the wheels and the other measure - the treadmill - is relative to the starting point of the wheels. So you cannot compare them.

The wheels rotated 101 times and 101 feet of treadmill passed under them, so the "speed" of the treadmill from this point of view is also 101 ft/x.

If the speed of the treadmill is going to match the speed of the wheels, then it is going to do so at the point the wheels are touching the treadmill, and not from the perspective of some entity not a part of the equation.

[Toddzilla]

Originally Posted by albionmoonlight

Lets say that you push the car forward 100 ft in that time.

Then you have

Speed of treadmill = 100 ft/x
Speed of Wheels (lateral) = 100 ft/x
Speed of Wheels (rotational) = 200 ft/x

In our problem, the speed of the conveyor matches the lateral (not rotational) speed of the wheels. If it matched the rotational speed of the wheels, you would end up with an infinitely fast conveyor belt (assuming non-relativistic physics, infinite energy, etc.), which seems a bit off to me.

And I think THAT is the paradox we are artificially building into the puzzle - we think the wheels start to turn and so the treadmill is somehow conscious of this movement and it starts to move in some meaningful way.

Remember that the wheels move independent of the plane, so it isn't the plane that makes the wheels move, it is the treadmill that makes the wheels move.

[st.cronin]

Originally Posted by Toddzilla

They are different, but one measure - the wheels - is relative to the position of the wheels and the other measure - the treadmill - is relative to the starting point of the wheels. So you cannot compare them.

The wheels rotated 101 times and 101 feet of treadmill passed under them, so the "speed" of the treadmill from this point of view is also 101 ft/x.

If the speed of the treadmill is going to match the speed of the wheels, then it is going to do so at the point the wheels are touching the treadmill, and not from the perspective of some entity not a part of the equation.

If that's your interpretation, then the treadmill doesn't have to move at all. In fact, it doesn't have to be a treadmill. It can be a regular runway, and still meet the parameters of the problem.

I don't think that interpretation makes any sense.

[JHandley]

We're not talking about a relativity issue here, we're talking about movement.

If you cut a tire with a 1 foot circumference and lay it out on it's tread, that's one foot. It will always be one foot. In order for that circle to make a full rotation, it has to travel one foot. If the treadmill underneath that tire is 100 feet long, the tire will travel 100 feet. If the treadmill is 1000 feet, the tire will travel 1000 feet. It cannot travel any more or any less, unless, it has lost contact or skidded.

[Pumpy Tudors]

Originally Posted by Toddzilla

And I think THAT is the paradox we are artificially building into the puzzle - we think the wheels start to turn and so the treadmill is somehow conscious of this movement and it starts to move in some meaningful way.

Remember that the wheels move independent of the plane, so it isn't the plane that makes the wheels move, it is the treadmill that makes the wheels move.

Regardless of what makes the wheels move (and I may be violating the problem by using that phrase), the fact is that the wheels are moving, so the treadmill moves, too. I guess I don't understand why it matters what's causing the wheels to move.

[Arctus]

Originally Posted by albionmoonlight

Plane has thrust to move forward at 100 mph.

The conveyor belt, by the definition of the problem, moves in the opposite direction at 100 mph. (Or more accurately; the surface of the conveyor belt upon which the wheels rest moves in the opposite direction at 100 MPH relative to Bob, who is standing on the earth.)

The result is that the plane moves forward at 100 mph (less very slight friction), while the wheels spin at 200 mph.

This assumes, of course, that "match[ing] the speed of the wheels at any given time" means matching their lateral and not rotational speed. As someone noted above, however, that assumption is the only one that makes any sense. To assume otherwise is to end up with an infinitely fast conveyer belt after some instantanious (sp?) amount of time.

Absolutely not.

Throwing friction of all types aside:

The jet of the plane exerts a force that accelerates the plane. Using your numbers, lets say that this results in the plane having a velocity of 100 MPH relative to Adam, who is standing on the conveyor belt.

The conveyor belt, by the definition of the problem, moves in the opposite direction at 100 mph.

Relative to Adam, the plane is moving at 100 MPH.

Relative to Bob, who is standing on the ground next to the conveyor belt, the plane is moving at 0 MPH and Adam is moving at 100 MPH.

Relative to Bob, the plane's wheels are spinning as if the plane should be moving at 100 MPH.

The wheels are not spinning so that the plane moves at 200 MPH. (At least not from any relevant reference plane)

[JHandley]

I believe that the thrust of the jet will make the wheel skid. But, the wheel must skid in order for a 1 foot circumference to travel 101 feet in 100 rotations.

[albionmoonlight]

Originally Posted by Arctus

Absolutely not.

Throwing friction of all types aside:

The jet of the plane exerts a force that accelerates the plane. Using your numbers, lets say that this results in the plane having a velocity of 100 MPH relative to Adam, who is standing on the conveyor belt.

The conveyor belt, by the definition of the problem, moves in the opposite direction at 100 mph.

Relative to Adam, the plane is moving at 100 MPH.

Relative to Bob, who is standing on the ground next to the conveyor belt, the plane is moving at 0 MPH and Adam is moving at 100 MPH.

Relative to Bob, the plane's wheels are spinning as if the plane should be moving at 100 MPH.

The wheels are not spinning so that the plane moves at 200 MPH. (At least not from any relevant reference plane)

Relative to Adam, the plane is moving forward at 200 MPH and the ground is still.

Relative to Bob, the plane is moving forward at 100 MPH and the ground is moving backwards at 100 MPH.

From Adam's perspective, the wheels are rotating at 200 MPH, which makes sense to him because from his perspective the ground is still and the plane is moving at 200 MPH.

From Bob's perspective, the wheels are rotating at 200 MPH, which makes sense to him because he sees the plane moving forward at 100 MPH and the ground under the plane moving backwards at 100 MPH.

[Arctus]

Originally Posted by albionmoonlight

Relative to Adam, the plane is moving forward at 200 MPH and the ground is still.

Relative to Bob, the plane is moving forward at 100 MPH and the ground is moving backwards at 100 MPH.

From Adam's perspective, the wheels are rotating at 200 MPH, which makes sense to him because from his perspective the ground is still and the plane is moving at 200 MPH.

From Bob's perspective, the wheels are rotating at 200 MPH, which makes sense to him because he sees the plane moving forward at 100 MPH and the ground under the plane moving backwards at 100 MPH.

I contend that if this is true:

From Adam's perspective, the wheels are rotating at 200 MPH, which makes sense to him because from his perspective the ground is still and the plane is moving at 200 MPH.

Then by definition of the puzzle, the surface of the conveyor belt upon which the plane's wheels rest must be moving at 200 MPH relative to Bob.

[st.cronin]

Originally Posted by JHandley

I believe that the thrust of the jet will make the wheel skid. But, the wheel must skid in order for a 1 foot circumference to travel 101 feet in 100 rotations.

I think this is the only way to make the plane take off - the wheels must skid.

[albionmoonlight]

Originally Posted by Arctus

I contend that if this is true:



Then by definition of the puzzle, the surface of the conveyor belt upon which the plane's wheels rest must be moving at 200 MPH relative to Bob.

We just disagree over the "definition of the puzzle."

I think that "match the speed of the wheels at any given time" means match the lateral speed of the wheels (i.e. the center of the axle).

You think that "match the speed of the wheels at any given time" means match the rotational speed of the wheels.

While the phrase can, on its surface, be read both ways, I think that my reading is better because it does not result in an infinitely fast conveyor belt.

[albionmoonlight]

dola--

As QS points out, this ends up being about semantics.

[Arctus]

Originally Posted by Toddzilla

Remember that the wheels move independent of the plane, so it isn't the plane that makes the wheels move, it is the treadmill that makes the wheels move.

I do not believe this to be true.

The unbalanced force created by the jet (or prop) of the plane cause the plane to move forward. The wheels offer no lateral resistance to prevent this.

The treadmill does not make the wheels move at all. No more than the runway at an airport makes the wheels of any plane move.

If the plane was "off" and the conveyor belt was "on", the plane would remain in place relative to Adam who is on the conveyor belt, and would move at the the same speed as the conveyor belt relative to Bob, who is standing on the earth.

Both Adam and Bob would witness no wheel rotation.

[MJ4H]

Not really.

edit: jeeze you guys post fast. Im just going to stay out of this, by the time I post there are 3 more replies. This puzzle is not about semantics.

[Arctus]

Originally Posted by albionmoonlight

We just disagree over the "definition of the puzzle."

I think that "match the speed of the wheels at any given time" means match the lateral speed of the wheels (i.e. the center of the axle).

You think that "match the speed of the wheels at any given time" means match the rotational speed of the wheels.

While the phrase can, on its surface, be read both ways, I think that my reading is better because it does not result in an infinitely fast conveyor belt.

Actually, it does. That was the point of my first post today.

[st.cronin]

Originally Posted by albionmoonlight

We just disagree over the "definition of the puzzle."

I think that "match the speed of the wheels at any given time" means match the lateral speed of the wheels (i.e. the center of the axle).

You think that "match the speed of the wheels at any given time" means match the rotational speed of the wheels.

While the phrase can, on its surface, be read both ways, I think that my reading is better because it does not result in an infinitely fast conveyor belt.

I'm not sure I understand the difference. I can think of two ways of measuring the speed of either the wheel or the treadmill.

1. The speed of a given point on the surface. This is the meaning I believe the puzzle intends.

2. Angular speed - the amount of time it takes to complete a cycle. Since the treadmill must be larger than the wheel, if the angular speed is equal, then the plane will be able to achieve lift (assuming that the treadmill is actually long enough.) whoops, edit - if the angular speeds are equal, the plane will be carried backwards (I think)

I am, quite frankly, not sure what you are talking about.

[Pumpy Tudors]

Originally Posted by MattJones4Heisman

Not really.

edit: jeeze you guys post fast. Im just going to stay out of this, by the time I post there are 3 more replies. This puzzle is not about semantics.

Wait, you're the one who brought all this up to begin with.

I understand that this is obviously a very difficult thing to explain, but could you attempt to explain why the plane can take off, please? Even without regard to what others have posted, I'm just curious about what your explanation is.

[albionmoonlight]

Originally Posted by st.cronin

I am, quite frankly, not sure what you are talking about.

That's OK. I'm never sure about what I'm talking about.

I'm not a physics guy, and I have explained it as best I can. I might, however, just be wrong and/or bad at explaining things.

I'll leave it for someone more skilled than I to provide the post that places into stark relief the unmistakable truth--whatever it may be.

[MJ4H]

Originally Posted by Pumpy Tudors

Wait, you're the one who brought all this up to begin with.

I understand that this is obviously a very difficult thing to explain, but could you attempt to explain why the plane can take off, please? Even without regard to what others have posted, I'm just curious about what your explanation is.

Post #96 is the clearest explanation I can give. If that doesn't help, read the posts of ANut, who is the rocket scientist I mentioned earlier in this thread (seriously). Believe me when I tell you, he gets it.

[Toddzilla]

Originally Posted by st.cronin

If that's your interpretation, then the treadmill doesn't have to move at all. In fact, it doesn't have to be a treadmill. It can be a regular runway, and still meet the parameters of the problem.

I don't think that interpretation makes any sense.

Well, that is the point of the exercise. It doesn't matter what the runway or treadmill does. The plane is always going to take off regardless of what the wheels are making contact with. The wheels are only a means by which the plane has no friction with the surface underneath so that it's engines can move the plane fast enough to achieve flight.

The plane would take off without wheels if it were on it's fuselage on a giant sheet of ice. The wheels are just there to spin - NOT to impart force to the plane (like the wheels on an automobile).

[Toddzilla]

Originally Posted by JHandley

I believe that the thrust of the jet will make the wheel skid. But, the wheel must skid in order for a 1 foot circumference to travel 101 feet in 100 rotations.

Again, you are thinking about this all wrong. The wheel only covers 100 feet of conveyor. Only 100 feet of conveyor belt will pass under the wheels. The plane will have moved only one foot. You cannot add the one foot of plane movement to the 100 feet of conveyor movement. They are not part of the same equation and not related. My apologies if I confused this issue in a previous post.

[Toddzilla]

Originally Posted by albionmoonlight

We just disagree over the "definition of the puzzle."

I think that "match the speed of the wheels at any given time" means match the lateral speed of the wheels (i.e. the center of the axle).

You think that "match the speed of the wheels at any given time" means match the rotational speed of the wheels.

While the phrase can, on its surface, be read both ways, I think that my reading is better because it does not result in an infinitely fast conveyor belt.

Yes, semantics, indeed! But the mistake here is that the conveyor can not match the speed of the center of the axle, since the center of the axle and the conveyor are (1) not connected and therefore (2) not related to one another.

The conveyor is in contact with the surface of the wheels, and that is the dependency as laid out in the original puzzle.

[BrianD]

Originally Posted by Toddzilla

The plane would take off without wheels if it were on it's fuselage on a giant sheet of ice. The wheels are just there to spin - NOT to impart force to the plane (like the wheels on an automobile).

So what would the motion of the plane be if the plane was off and the conveyor was moving (pick any speed you want)?

[BrianD]

Originally Posted by Toddzilla

Again, you are thinking about this all wrong. The wheel only covers 100 feet of conveyor. Only 100 feet of conveyor belt will pass under the wheels. The plane will have moved only one foot. You cannot add the one foot of plane movement to the 100 feet of conveyor movement. They are not part of the same equation and not related. My apologies if I confused this issue in a previous post.

If 100 feel of conveyor has moved relative to a point on the ground (off of the conveyor), and the plan has moved 1 foot from the same point on the ground, the plane must have traveled over 101 feet of the conveyor. You have to add the two together.

[Toddzilla]

Originally Posted by Arctus

I do not believe this to be true.

The unbalanced force created by the jet (or prop) of the plane cause the plane to move forward. The wheels offer no lateral resistance to prevent this.

The treadmill does not make the wheels move at all. No more than the runway at an airport makes the wheels of any plane move.

If the plane was "off" and the conveyor belt was "on", the plane would remain in place relative to Adam who is on the conveyor belt, and would move at the the same speed as the conveyor belt relative to Bob, who is standing on the earth.

Both Adam and Bob would witness no wheel rotation.

That is where you are wrong. It IS the runway that makes the wheels move. The wheels of an airplane do not move otherwise. Flip the plane on it's back and gun the engines - the wheels will NOT move. The wheels only move when they are in contact with the runway. The plane is moving, the runway is not, and so when the wheels come in contact with the runway they begin to turn to match the speed of the plane. Make no mistake, it is the runway that moves the wheels of a plane, not the engines or anything else.

[JHandley]

Originally Posted by Toddzilla

Again, you are thinking about this all wrong. The wheel only covers 100 feet of conveyor. Only 100 feet of conveyor belt will pass under the wheels. The plane will have moved only one foot. You cannot add the one foot of plane movement to the 100 feet of conveyor movement. They are not part of the same equation and not related. My apologies if I confused this issue in a previous post.

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.

[BrianD]

Originally Posted by Toddzilla

That is where you are wrong. It IS the runway that makes the wheels move. The wheels of an airplane do not move otherwise. Flip the plane on it's back and gun the engines - the wheels will NOT move. The wheels only move when they are in contact with the runway. The plane is moving, the runway is not, and so when the wheels come in contact with the runway they begin to turn to match the speed of the plane. Make no mistake, it is the runway that moves the wheels of a plane, not the engines or anything else.

Actually it is a combination of the engines and the runway. Engines create force in one direction, the runway creates force in the other direction. Rotation of the wheels is the result.

[KWhit]

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.

Yeah. That sounds right to me.

[Toddzilla]

Originally Posted by BrianD

So what would the motion of the plane be if the plane was off and the conveyor was moving (pick any speed you want)?

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.

[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.

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

[Toddzilla]

Originally Posted by BrianD

Actually it is a combination of the engines and the runway. Engines create force in one direction, the runway creates force in the other direction. Rotation of the wheels is the result.

Wrong. The engines have no direct affect on the wheels. Deploy the landing gear in mid-flight. Do the wheels move? No, because there is nothing to make them move. The runway makes the wheels move, the speed of the plane - as dictated by the force of the engines - determines how fast the wheels move.