The plane is no longer contacting the ground at that point. It's held up by air (much, much less friction*). The wheels don't have to roll.


*In fact, for ideal rolling friction between the ground and the wheel is infinite.

The assumption is the shot one is shot level with a surface with no trajectory via elevation added.

OK, now we are making progress. We've established that there are situations in which wheels and a treadmill cannot match speeds.

Back to the original airplane/treadmill case. There are two areas of slippage relative to the plane. The air slipping over the wings and the wheels and tread mill creating a similar plane of slippage between the plane ground. The jet engines are very powerful and are the driving force of the plane. After you account for the slippage of wind over the wing, they externally set the acceleration of the plane relative to the ground just as surely as the the tow rope sets the speed of the the person. You could speed the tread mill up, slow it down, run it backward, it would not affect the speed of the plane because the prime mover of the plane are the jet engines pushing against the air. The wheels will just free spin (slip) to compensate for the treadmill as needed to give whatever velocity needed to make the plane move at the correct velocity given the acceleration imparted by the force of the jet engines.

Heres the original quote

"Imagine a 747 is sitting on a conveyor belt, as wide and long as a runway. The conveyor belt is designed to exactly match the speed of the wheels, moving in the opposite direction. Can the plane take off?"

All it says is exactly match the speed of the wheels. It doesn't say anything about velocity or what kind of speed?

I know that sounded reeruned, but IMO the wheels have 2 different speeds.

The speed in which they are traveling in a straight line, forward, connected to the plane, and the speed in which they are spinning.

So which speed are we talking about here?

Help me out.
The problem says he takes $2 (from $30) leaving $27. How is that math correct?

If the wheels compensate speed at any point, the treadmill will do the exact same. Due to the structure of the question, the speed of the plane will always be zero relative to the ground. Unless there is wind, there is no lift being created by the wings. 0 + X + (-X) + 0 = 0

If you want to want to discuss the problem in terms of force, the force counteracting the engine thrust comes from the wheel bearings. They would be spinning at an unbelievably unrealistic speed to generate that type of force, but that's why this question is theoretical. Therefore, the engines do not externally set the acceleration of the plane, as you must consider all forces acting on the plane.

So you're building a critical flaw into the test. Way to get the answer you want.

Perfect rolling = no slippage

As I understand it, the speed of an atom of rubber at the very bottom dead center of the wheel at any given instant is equal to the speed of the surface of the top of the treadmill.

The correct problem has the plane sitting on a free-spinning treadmill that will absorb all the energy the wheels impart to it.

That original quote by MagicHef is more or less the way Mythbusters stated the problem.

It's not the correct problem. Read the objection here:

Troy Allen • Jan 30 2008 • 10:53PM
I am completely disappointed at Mythbusters handling of this experiment. The science they used and the “explanations” were both completely flawed. The original myth, and ALL of the discussion, centered around one central conceit: The plane would have NO FORWARD MOTION RELATIVE TO THE GROUND because of the conveyor belt matching the speed of the plane. NOT the “speed of the WHEELS of the plane” or any other contrived version.

Of course the plane is going to take off if it has enough forward motion RELATIVE TO THE GROUND to create the Bernoulli effect required to lift the wing because of the airflow over the wing.

I really expected more “science” from MythBusters. They almost explained it properly with the “model car example”. I guess it was the original Myth that was flawed, or my understanding of the Myth. I guess in their mind the myth is that no plane on a conveyor belt can take off if the “speeds are matching in opposite directions”. That is far too simplistic to make a determination, so it is flawed from the get-go.

Those of us who claimed the plane would not take off without forward motion relative to the ground due to the laws of physics are still correct. The planes both had significant forward motion relative to the ground. I just hope everyone involved in the debate understands these distinctions, otherwise this will just dumb down the TV watching public a bit more. It sure was fun though!

Thats not answering my question.

Are you talking about the atoms Speed going forward or speed rotating?

With frictionless wheel bearings, the only function of the wheels on the conveyor is to provide a normal force separating the plane from the ground by the width of the tires. In all other respects this situation is identical to flying with the landing gear extended.

The only possible other outcome is to say '**** frictionless, these wheels have so much friction, their rolling resistance is more powerful than 4 jumbo jet engines.' But that's kind of a cheat, because unless otherwise indicated, friction is generally assumed to be non-existent or negligible in hypos like this.

When did that ever come in to the question?

Let's try once more from physics.

The plane is initially at zero velocity. To start moving, it needs to accelerate. The acceleration of the plane a = F/m where F is the force and m is the mass of the plane.

The jet engines are one source of force. They push on the air. It is what makes a normal plane move forward.

To keep velocity zero, we need to keep acceleration zero. In order to do that we need a force that opposes the jet engine. The only place it can come from is the tread mill. The tread mill transmits it's force to the wheel and the wheel to the bearing. If the bearing were frictionless, there would be no force on the airplane from this spinning wheel. But in real life, there is friction. The friction would impart a force something like friction force = m*g*k where k is a friction coefficient. Regardless the friction force is small relative to the force of the jet engines. If it were not, the plane couldn't roll in the first place. The velocity of the wheel has very little to do with the amount of friction in the bearing. You can't spin the wheels fast enough to keep the plane stationary by generating more friction at the wheel. It is like the example of a person holding on to the tow rope.

If you take an infinitesimally small amount of time, they will be the same. In other words, speed going forward.

Except for one critical difference - you're NOT airborne. Where did you get the initial lift to get off the ground?

There are two COMPLETELY DISTINCT STATES. Plane sitting on ground - plane moving in air.