Something amazing to tell you concerning physics and motion

[Jenson71]

This blows my mind.

Okay, say you have two ball bearings. You hold one in your hand and drop it. The other you put in a gun, point it straight forward, as level as the one in your hand, and pull the trigger, sending it hundreds of yards.

Which one lands first?

The one dropped in your hand right? RIGHT!?!?

No, actually they both hit the ground at the same time.

This is because the vertical component of motion is the same for both objects. They both fall vertically the same distance at about 10 meters per second squared (gravity, actually more like 9.8).

But Jenson, Jenson! What about the horizontal component of the gun-fired ball bearing? Actually, when air resistance is small enough to ignore as it is in this case (being that the bearings are exactly alike), the horizontal and vertical components of a projectile's velocity are completely independent of one another.

And, in this experiment, the gun-fired bearing is constantly falling from the moment it is fired. Yes, it looks like it is holding up in a straight line, but, it's actually falling and it's just hard to see with our eyes. And again, it is falling at exactly the same speed as the ball bearing you released in your hand -- the speed of gravity.

Post more cool science things in this thread.

I think I will later post Aristotle vs. Galileo and gravity, for a little history spin on science.

[orange]

Originally Posted by KC Fish

How does a plane move forward through the air, once it is off the ground? What gives it forward motion if the wheels are not passing all forward motion on the ground? How do you explain forward motion without the ground contact you are defending?

By your definition, the plane should not be able to progress once the forward motion on the ground is no longer going through the wheels....

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.

[HonestChieffan]

Originally Posted by damaticous

Actually, from what I remember, the ball bearing in your hand would hit the ground first.

when you fire a bullet from a gun the bullet tends to arch upward a bit, so it is actually falling at a different height from the one that is dropped.

I could be wrong, but I remember reading that or seeing it on TV or something.

Otherwise, yes, they'd hit the ground at the same time.

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

[cdcox]

Originally Posted by MagicHef

Yes, the tow rope is externally setting the speed of the person. There is nothing externally setting the speed of the plane.

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.

[Buck]

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?

[Sully]

Originally Posted by DeepSouth

Actually, Jenson is correct.

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

[MagicHef]

Originally Posted by cdcox

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.

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.

[orange]

Originally Posted by cdcox

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.

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

Perfect rolling = no slippage

[MagicHef]

Originally Posted by MediaCenterJunkie

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?

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.

[orange]

Originally Posted by MediaCenterJunkie

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?

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!

[Buck]

Originally Posted by MagicHef

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.

Thats not answering my question.

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

[Baby Lee]

Originally Posted by orange

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.

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.

[MagicHef]

Originally Posted by Baby Lee

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.

When did that ever come in to the question?

[cdcox]

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.

[MagicHef]

Originally Posted by MediaCenterJunkie

Thats not answering my question.

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

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

[orange]

Originally Posted by Baby Lee

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.

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.