Airplane physics question

Whaaaat? Lol!!!!

 

You are halfway there. The plane moves forward the circumference of the wheel for each rotation, btw, not the diameter. Pretty simple ;-).

Now, if the wheels match the rotation of the conveyor belt in the opposite direction, you are right, that means the plane is standing still. That is what the original problem states, and it implies the plane is standing still and will not take off. Exactly as you say.

However, the problem also states that the plane's engines are producing thrust. Whether it's a jet or a prop, if thrust is being produced, free-rotating wheels on the plane cannot and will not oppose that thrust. Therefore, the unopposed thrust will push the airplane forward (wheel speed will instantly stop matching the belt speed if the plane is moving over the conveyor). If that happens, the plane takes off, obviously.

So, the problem states two contradictory conditions. One implies the plane is not moving, the other will ensure that the plane does move.

In real life, the plane would break the first condition instantly (speeds of wheel and belt matching), and it would move forward and take off as soon as it experiences thrust from the prop or jets.

Stupid effing question.

 

Original question states:
The conveyer belt is designed to exactly match the speed of the wheels at any given time, moving in the opposite direction of rotation.

If the engine produces thrust, the plane will move forward. The moment the plane moves forward, this condition cannot be met.

That is why it is such a stupid effing question.

 

My high school math teacher always got mad at me when I answered questions like this.
She always told me although I was essentially right I was also wrong.
She said I needed to use a mathematical formula to answer the question correctly.
I counteracted that if she wanted an answer with symbols then ask a question with symbols.
If she was going to ask a question with words, then I would have to give an answer with words.
Such as : one apple plus one apple equals two apples / 1a + 1a = 2a
The main problem with questions of this type are : rules, definitions, applications and comprehension.
Mathematical questions using symbols only allow rules that are constant.
Questions using mathematical words are variable and as such words can be interpreted differently.
I thought about this question more and decided maybe there is more than one hypothesis.
1. First no additional words can be added or inferred.
2. Definitions: auto, car, vehicle, assembly.
3. Application: motion,movement, transfer,action.
4. Comprehension: up/increase, down/decrease, side/parallel, front/anterior, rear/posterior.

 

As the thrust of the airplane is working against the stationary air, and not the treatmill surface, the airplane will move forward relative to the air causing lift as the air passes over the wings. Thus, the airplane will fly. Regarding the wheels, as long as they remain in contact with the treatmill surface, the rotation rate of the wheels will continue to increase proportionately to the rate of treadmill surface travel until the treadmill can no longer keep up. That is, unless you can figure out how to propell the treadmill surface faster than the speed of light. But then, of course, the wheels could rotate at that speed as well......and then the wheels fall off my theory.

 

Why is this called a physics question? Its a logic question, and logic says the airplane will remain stationary given the conditions represented. Whether those conditions can be matched in real life, is another matter.

Edit - oh geash, I just voted, and its now a 110 vs 110 votes for nay and yay...

 

edit

 

You've almost got it. As i said way back when in the dark ages of this thread, we have a conundrum because of the way the question is asked. We can only infer from what is a defective or incomplete question.
Given that ta planes wheels are not driven (they are merely pulled along by the plane, in which case they begin rotating), if there is NO forward motion of the plane the wheels will not turn and the conveyor need not move to match their speed. if there IS forward motion of the plane, the original premise has been defeated because they conveyor exactly matches the wheels speed, in other words there can not have been any forward motion of the plane to comply with the original parameters of the question.

edit: just saw Zach's post. Ha ha "Stupid effing question" is right!

 

A way to force the wheel speed and conveyor speed to always match is to make the tires sprockets and the conveyor a drive chain. So the question really is, "Can a plane take off while tracting a reverse chain?"

 

I understand, what you and John and Zach want to tell us. What I do not understand, is why all of you assume the speed matching happens in the static framework of reference?

Sit in the plane, the floating framework of reference, and look out of the window at the wheel. Speed of the wheel and speed of the belt always match regardless at what speed and direction the belt is running, because the wheel can spin freely.

The floating framework of reference (plane) moves away from the static framework of reference (ground, belt) with the speed of the plane. Therefore the speed of the belt matches the speed of the wheel plus the speed of the plane from the static point of view.

Why have I been assuming that the author of the question looked at it from the floating point of view? Because otherwise the question wouldn't fit together as you stated above.

As a result I have been saying that the wheel speed and the question whether the plane takes off or not are independent from each other. And because there is no other force than the force of inertia to balance the thrust, there will be an acceleration and the plane finally takes off.

 

Yes. If it moves along the chain, instead of staying in one spot. If it does that, though, its wheels (gears) are not moving at the same speed as the belt (sprockets).

 

You are arriving at the correct conclusion, but through convoluted and faulty reasoning. The reason you look at it from the external frame of reference (the ground) is because that is the frame of reference it needs to move in relation to, in order to have airflow over the wings, which is what it needs in order for it to take off.

It's a trick question. It poses two conditions. They cannot coexist.
1. If it is sat still on the conveyor belt, wheels spinning so that they match the conveyor belt speed, then obviously the plane is not going to move relative to the ground, and that means there is no air flowing past the wings to generate lift and it cannot take off.

2. If the engine is fired up and drives a propellor or a jet, the plane will experience thrust. If that happens, unless the brakes are applied, or there is some other opposing force, nothing it will move forward. Then, given enough speed, it will take off.

Of course, the moment it starts moving forward, the wheel speeds will not match the belt speed.

Unless you apply brakes, or have reverse thrust applied, you cannot have matching wheel speeds and belt speed if the engine is producing thrust.

Don't overthink it.

 

Funny how only a small minority of the voters have voted for the correct response and most have voted a definite yes or no.

 

If it is sat still on the belt, nothing happens at all, because the belt is not spinning either. Plane does not move, therefore wheels do not move, therefore belt does not move at all in this case. Everything is dead silent!

 

If you are right and the guy who set up this question wants to have his constraints fulfilled in the static frame of reference, then this is not our problem but his problem. Put him on an aircraft carrier and he can see that starting and landing on conveyor belts works. The Navy does this every day. And then he can practice to set up correct kinematic constraints.

Edit:

Voted now: "Question doesn't allow answer."

 

You voted correctly!

 

That's one case where it does not move.

The other case where it does not move is if the wheels are rotating, but the belt is rotating in the opposite direction at the same speed.

That, however, can never happen if the propellor or jet engine is producing thrust, because nothing would counter that force (certainly not the freely rotating wheels) and so the plane would move forward, which would instantly break the condition of the question that the plane is sat still on the conveyor belt, and the wheels are moving at the same speed as the conveyor belt. That can only be true if the plane is not moving forward along the conveyor belt.

 

I think we are all correct. Some brilliant person said in a previous post- it is all relative.

I wonder where this question originated? I would bet it was a middle school question on air flow or something simple. The teacher was probably actually looking to see if students would pick up on the prop makes the plane fly or the wing.

Us type A dominant uber achiever passive aggressive over achieving arm chair geniuses have been busy for 7 years , 113 pages,2242 posts discussing what was originally meant to be a simple question.

Well done!

 

It is a simple question.

Nothing that happens under the free-spinning wheels can affect whether the plane flies.

It doesn't matter what the teacher says. The "question" is irrelevant.

 

It's not that simple. The teacher has also said that it is sitting in place on the conveyor. Sitting in place and moving forward are mutually exclusive. That is what makes the question impossible. You can argue that at any time the plane is moving, one of the stipulations of the question is being broken, and the situation does not apply. You can also make the same argument for the plane sitting still and thrust being applied...again, that simply cannot happen together.

 

I'm interested in the conveyor belts on carriers. Didn't realize that. Do you mean catapults?

 

Yeah, I was wondering about that too.

 

Carrier is moving.

 

It's only sitting in place until it's not. Nothing in the "question" states that the plane can't move, only that the conveyor matches the wheel speed. Once it starts to move (everyone familiar with reality knows it will) the conveyor can try to keep up with the wheels (if you really care) but it really doesn't matter, the plane will fly.

Nothing under the free-spinning wheels can change the laws of physics.

 

I get it- the forward motion of the carrier provides airspeed under the wings to create lift.

I just don't see where the original question has any mention of an aircraft carrier, or ice, or skis, or water,or pontoons ,or a chain, or sprockets, or a rope pulling a glider...

Just to refresh everyone's memory, written at least 7 years ago ( about the time of the 430 hitting US shores)


Imagine a plane is sat on the beginning of a massive conveyor belt/travelator type arrangement, as wide and as long as a runway, and intends to take off. The conveyer belt is designed to exactly match the speed of the wheels at any given time, moving in the opposite direction of rotation.
There is no wind.
Can the plane take off?