Mythbusters punk'd whole internet

[jmmtn4aj]

Originally posted by: smack Down

Originally posted by: jmmtn4aj

Originally posted by: smack Down

Originally posted by: jmmtn4aj

Originally posted by: smack Down

Originally posted by: her209

Originally posted by: smack Down

Originally posted by: Cerpin Taxt
Question for you two: What if we assume that the wheels are connected to the axles by perfectly frictionless bearings? Can the conveyor retard the airplane's forward movement then?

Yes of course it can. If you wish to see that for yourself go get a wheel and put it on a treadmill. Turn on the treadmill and watch the wheel come back at you. Use a wheel with no axle ans you will have almost frictionless bearings.

Thank you for proving to us you have no idea what you are talking about.

So you think if I put a wheel on a treadmill it will just stay put?

Good god man, an undercarriage with frictionless bearings does NOT equal an unattached wheel! Jesus!

What happens to the forward force exerted on the wheel by the axle? Remove the axle and the force is gone, obviously.

Isn't this high school level physics?

My high school physics included a chapter on the fact that forces added. If the wheels would move backwards with no undercarriage attached then they would move backwards with an undercarriage attached with frictionless bearings.

When you remove the axle, you remove the axis of rotation, meaning whatever happens with the bearings stop mattering. without the axis of rotation, the wheel becomes just another object on a moving surface. Without an axle, frictional contact between the tire surface and the treadmill causes a horizontal force in the direction that the treadmill is moving. Sure, it might rotate if the treadmill accelerates fast enough, but that's because it's a round object and hence is inherent unstable. Place a tall block in it's place and if the acceleration is fast enough, it falls.

And it still doesn't not equate to an undercarriage with frictionless bearings. An undercarriage with frictionless bearings still provides and axis of rotation allowing the frictional force between the tire surface and treadmill to be converted to rotational motion, acting as torque, instead of moving the entire wheel back. Frictionless simply means no force is generate in the housing where the axle joins to the wheel. Friction in the bearing causes resistance to the wheels rotation. Resistance means the wheels RESIST rotation, meaning a horizontal force is generated even before it reaches the axle-wheel assembly, meaning it's like the free wheel (albeit on a negligible scale) where the wheels resistance to spinning creates a resultant force that tries to move the entire wheel back, and anything connected to it. Frictionless bearings won't have resistance to rotation, so no resultant force parallel to the ground is created, but it still has to spin around a point first.

God, that didn't really make sense. Tomorrow guys.

You know why it didn't make sense because it is wrong. Just as mass has a resistance to accelerating it also has a resistance to rotation. Both with and with out the axle the wheel has the same axis of rotation.

The fact the wheel moves backwards means it does NOT have an axis of rotation, how on earth can it be the same?

An axle exerts forward force to counter the backwards force created by frictional force between the tire surface and treadmill surface. Frictionless bearings only means the lack of an additional force OVER that, in the form of moments about the axle, which translates into an additional rearward force. When the wheel rotates forwards, frictional force acts in the opposite direction, backwards. Viewed from the upright right side, the wheel is rotating clockwise producing a counter clockwise frictional force, a CCW moment. If assume smooth bearings, thus zero frictional coefficient, that CCW force is gone, and thus a moment about the axle, but NOT the forwards acting force exerted by the axle to counter frictional force caused by the wheels mass and the treadmill surface, that force obviously still has to be there don't you think? By removing the axle you remove that force as well.

Surely no one is really so simple as to think wheels with frictionless contact with the axle are the same as wheels not attached to the axle at all. Frictionless bearings are assumed by taking frictional coefficients to be zero, NOT by removing mass and definitely NOT by removing a surface altogether. Doing either of those fucks up the entire model altogether. It's like testing a plane in a wind tunnel without wings just to remove friction caused by wing skin surface. Jesus christ.

Are you one of those flat earth society guys?

 

[villageidiot111]

The plane would take off, although its wheels and the treadmill would be moving at infinity.

 

[smack Down]

Originally posted by: jmmtn4aj

Originally posted by: smack Down

Originally posted by: jmmtn4aj

Originally posted by: smack Down

Originally posted by: jmmtn4aj

Originally posted by: smack Down

Originally posted by: her209

Originally posted by: smack Down

Originally posted by: Cerpin Taxt
Question for you two: What if we assume that the wheels are connected to the axles by perfectly frictionless bearings? Can the conveyor retard the airplane's forward movement then?

Yes of course it can. If you wish to see that for yourself go get a wheel and put it on a treadmill. Turn on the treadmill and watch the wheel come back at you. Use a wheel with no axle ans you will have almost frictionless bearings.

Thank you for proving to us you have no idea what you are talking about.

So you think if I put a wheel on a treadmill it will just stay put?

Good god man, an undercarriage with frictionless bearings does NOT equal an unattached wheel! Jesus!

What happens to the forward force exerted on the wheel by the axle? Remove the axle and the force is gone, obviously.

Isn't this high school level physics?

My high school physics included a chapter on the fact that forces added. If the wheels would move backwards with no undercarriage attached then they would move backwards with an undercarriage attached with frictionless bearings.

When you remove the axle, you remove the axis of rotation, meaning whatever happens with the bearings stop mattering. without the axis of rotation, the wheel becomes just another object on a moving surface. Without an axle, frictional contact between the tire surface and the treadmill causes a horizontal force in the direction that the treadmill is moving. Sure, it might rotate if the treadmill accelerates fast enough, but that's because it's a round object and hence is inherent unstable. Place a tall block in it's place and if the acceleration is fast enough, it falls.

And it still doesn't not equate to an undercarriage with frictionless bearings. An undercarriage with frictionless bearings still provides and axis of rotation allowing the frictional force between the tire surface and treadmill to be converted to rotational motion, acting as torque, instead of moving the entire wheel back. Frictionless simply means no force is generate in the housing where the axle joins to the wheel. Friction in the bearing causes resistance to the wheels rotation. Resistance means the wheels RESIST rotation, meaning a horizontal force is generated even before it reaches the axle-wheel assembly, meaning it's like the free wheel (albeit on a negligible scale) where the wheels resistance to spinning creates a resultant force that tries to move the entire wheel back, and anything connected to it. Frictionless bearings won't have resistance to rotation, so no resultant force parallel to the ground is created, but it still has to spin around a point first.

God, that didn't really make sense. Tomorrow guys.

You know why it didn't make sense because it is wrong. Just as mass has a resistance to accelerating it also has a resistance to rotation. Both with and with out the axle the wheel has the same axis of rotation.

The fact the wheel moves backwards means it does NOT have an axis of rotation, how on earth can it be the same?

Do you even know what an axis of rotation is?

An axle exerts forward force to counter the backwards force created by frictional force between the tire surface and treadmill surface.

What the hell kind of an axle provides power? Are you talking about in a car when I step on the gas? You don't think a piece of metal generates a force just by the virtue of sitting in a tire do you?

Frictionless bearings only means the lack of an additional force OVER that, in the form of moments about the axle, which translates into an additional rearward force. When the wheel rotates forwards, frictional force acts in the opposite direction, backwards. Viewed from the upright right side, the wheel is rotating clockwise producing a counter clockwise frictional force, a CCW moment. If assume smooth bearings, thus zero frictional coefficient, that CCW force is gone, and thus a moment about the axle, but NOT the forwards acting force exerted by the axle to counter frictional force caused by the wheels mass and the treadmill surface, that force obviously still has to be there don't you think? By removing the axle you remove that force as well.

Surely no one is really so simple as to think wheels with frictionless contact with the axle are the same as wheels not attached to the axle at all. Frictionless bearings are assumed by taking frictional coefficients to be zero, NOT by removing mass and definitely NOT by removing a surface altogether. Doing either of those fucks up the entire model altogether. It's like testing a plane in a wind tunnel without wings just to remove friction caused by wing skin surface. Jesus christ.

I'm sure no has ever used a simpliefed model in a wind tunnel to measure the effects they are concerned about. That would be crazy ever test should be done on a full sized air frame at full speed winds.

Are you one of those flat earth society guys?

But fine lets put a massless body in the picture to make you happy with frictionless contact. Do you agree that when the engines are off our massless plane will act just like 4 wheels placed at the same points without the massless body. IF not what is causing the difference?

 

[Tweak155]

Originally posted by: smack Down
But fine lets put a massless body in the picture to make you happy with frictionless contact. Do you agree that when the engines are off our massless plane will act just like 4 wheels placed at the same points without the massless body. IF not what is causing the difference?

The wheels will not act like independent wheels from one another because they are attached to an axle. Motion would be random without the axle.

 

[jjzelinski]

I'm not sure why this is so difficult to comprehend. The wheels of an aircraft do not propel the aircraft, that we can agree upon. So what are the wheels for? To reduce friction. The only thing putting the aircraft on a treadmill would do is marginally increase friction thereby requiring slightly more thrust, but it would nonethless move and takeoff.

 

[Jeff7]

Originally posted by: jjzelinski
I'm not sure why this is so difficult to comprehend. The wheels of an aircraft do not propel the aircraft, that we can agree upon. So what are the wheels for? To reduce friction. The only thing putting the aircraft on a treadmill would do is marginally increase friction thereby requiring slightly more thrust, but it would nonethless move and takeoff.

I think a lot of the issues stem from different interpretations of the original problem.

Based on points I've encountered here, yes, a treadmill could prevent forward motion, as it would in fact impart forward momentum into the airplane itself. Someone used an example of a wheel in space, with a string attached to the rim of it. If you tug on the string, yes, the wheel will begin to rotate, but it will also move toward you.

So, if the treadmill's speed is purely a function of the rotational speed of the wheels, the plane should take off, assuming that the mass of the wheels is negligible compared to the plane's mass.

If the treadmill's speed is dependent on the forward velocity of the plane, then the plane would not take off. The treadmill's speed would likely have to increase exponentially to cause the plane to remain stationary, but it could still be done.

If the treadmill's speed is dependent on the rotational speed of the plane's engines, the plane should take off anyway, as the wheels aren't even in this equation.

It all depends on how much you want to factor in (engine speed, mass of components, momentum, bearing resistance, etc), and upon what the treadmill speed is directly dependent on.

 

[Kelemvor]

How the hell is this thread not locked yet...

 

[jjzelinski]

Originally posted by: Jeff7

Originally posted by: jjzelinski
I'm not sure why this is so difficult to comprehend. The wheels of an aircraft do not propel the aircraft, that we can agree upon. So what are the wheels for? To reduce friction. The only thing putting the aircraft on a treadmill would do is marginally increase friction thereby requiring slightly more thrust, but it would nonethless move and takeoff.

I think a lot of the issues stem from different interpretations of the original problem.

Based on points I've encountered here, yes, a treadmill could prevent forward motion, as it would in fact impart forward momentum into the airplane itself. Someone used an example of a wheel in space, with a string attached to the rim of it. If you tug on the string, yes, the wheel will begin to rotate, but it will also move toward you.

So, if the treadmill's speed is purely a function of the rotational speed of the wheels, the plane should take off, assuming that the mass of the wheels is negligible compared to the plane's mass.

If the treadmill's speed is dependent on the forward velocity of the plane, then the plane would not take off. The treadmill's speed would likely have to increase exponentially to cause the plane to remain stationary, but it could still be done.

If the treadmill's speed is dependent on the rotational speed of the plane's engines, the plane should take off anyway, as the wheels aren't even in this equation.

It all depends on how much you want to factor in (engine speed, mass of components, momentum, bearing resistance, etc), and upon what the treadmill speed is directly dependent on.

Even if the wheels were spinning 300mph in the opposite direciton as thrust is initially generated and the plane moves backwards, it will eventually move forward regardless of what the wheels are doing. Sure, the element of friction comes into play limiting the degree to which you could apply counter-rotational movement to the wheels without hindering the planes ability to move forward. However the problem explicitly states that the rpm of the wheels is directly proportional to the amount of thrust the engines are generating.

All that we have to do is establish that if the plane has any capacity to move forward it will eventually be able to take off. The only thing that complicates this is friction, so why not eliminate this as a factor for the sake of simplifying the argument? If the landing gear of said aircraft is perfectly frictionless, then it wouldn't matter if the treadmill were matching the thrust of the engines or moving at light speed as the wheels would be completely isolating the plane from the movement of the treadmill. If you can believe that, then let's go ahead and drop friction back in. Is it really all that different? Not practically, no. the purpose of the free-spinning landing gear is still to reduce friction between the plane and the surface it is taking off from.

 

[Jeff7]

Originally posted by: jjzelinski
Even if the wheels were spinning 300mph in the opposite direciton as thrust is initially generated and the plane moves backwards, it will eventually move forward regardless of what the wheels are doing. Sure, the element of friction comes into play limiting the degree to which you could apply counter-rotational movement to the wheels without hindering the planes ability to move forward. However the problem explicitly states that the rpm of the wheels is directly proportional to the amount of thrust the engines are generating.

All that we have to do is establish that if the plane has any capacity to move forward it will eventually be able to take off. The only thing that complicates this is friction, so why not eliminate this as a factor for the sake of simplifying the argument? If the landing gear of said aircraft is perfectly frictionless, then it wouldn't matter if the treadmill were matching the thrust of the engines or moving at light speed as the wheels would be completely isolating the plane from the movement of the treadmill. If you can believe that, then let's go ahead and drop friction back in. Is it really all that different? Not practically, no. the purpose of the free-spinning landing gear is still to reduce friction between the plane and the surface it is taking off from.

I do fully understand that the engines are the primary movers of the plane.

But read again - say you have a wheel, floating freely in space, with a string attached to the rim. Pull on the string. It will cause the wheel to rotate. BUT - it will also cause the wheel to move toward you.
To make this analagous to the airplane, the string is the treadmill, and the wheel is one of the plane's wheels. Tug on the treadmill, and the wheel will start to rotate, BUT a small amount of linear momentum will be transferred into the wheel, through the axle, and into the plane's body. So yes, the treadmill does have the ability, in theory, to impart linear momentum into the airplane's body. But, would it be enough to stop the plane? That depends....
IF the treadmill's acceleration was tuned such that it could produce a linear force, such that it equals the thrust produced by the plane's engines, then it could hold the plane stationary.

And you mention a lot of "if" statements in there, too. IF it's perfectly frictionless - but do we also neglect the linear momentum transfer, and assume that the treadmill purely imparts angular momentum into the wheels?
IF the rpm of the wheels (and thus speed of the treadmill) is directly (and only) proportional to the thrust of the engines, then (depending on the proportion, assuming there's no multiplier or exponential/nonlinear relationship) the plane should take off.


(Credit where it's due: It was jagec who presented the example of the wheel and string in space.)

 

[jjzelinski]

Originally posted by: Jeff7

Originally posted by: jjzelinski
Even if the wheels were spinning 300mph in the opposite direciton as thrust is initially generated and the plane moves backwards, it will eventually move forward regardless of what the wheels are doing. Sure, the element of friction comes into play limiting the degree to which you could apply counter-rotational movement to the wheels without hindering the planes ability to move forward. However the problem explicitly states that the rpm of the wheels is directly proportional to the amount of thrust the engines are generating.

All that we have to do is establish that if the plane has any capacity to move forward it will eventually be able to take off. The only thing that complicates this is friction, so why not eliminate this as a factor for the sake of simplifying the argument? If the landing gear of said aircraft is perfectly frictionless, then it wouldn't matter if the treadmill were matching the thrust of the engines or moving at light speed as the wheels would be completely isolating the plane from the movement of the treadmill. If you can believe that, then let's go ahead and drop friction back in. Is it really all that different? Not practically, no. the purpose of the free-spinning landing gear is still to reduce friction between the plane and the surface it is taking off from.

I do fully understand that the engines are the primary movers of the plane.

But read again - say you have a wheel, floating freely in space, with a string attached to the rim. Pull on the string. It will cause the wheel to rotate. BUT - it will also cause the wheel to move toward you.
To make this analagous to the airplane, the string is the treadmill, and the wheel is one of the plane's wheels. Tug on the treadmill, and the wheel will start to rotate, BUT a small amount of linear momentum will be transferred into the wheel, through the axle, and into the plane's body. So yes, the treadmill does have the ability, in theory, to impart linear momentum into the airplane's body. But, would it be enough to stop the plane? That depends....
IF the treadmill's acceleration was tuned such that it could produce a linear force, such that it equals the thrust produced by the plane's engines, then it could hold the plane stationary.

And you mention a lot of "if" statements in there, too. IF it's perfectly frictionless - but do we also neglect the linear momentum transfer, and assume that the treadmill purely imparts angular momentum into the wheels?
IF the rpm of the wheels (and thus speed of the treadmill) is directly (and only) proportional to the thrust of the engines, then (depending on the proportion, assuming there's no multiplier or exponential/nonlinear relationship) the plane should take off.


(Credit where it's due: It was jagec who presented the example of the wheel and string in space.)

Well I went ahead and re-read your prior post and I see what you're getting at.

"If the treadmill's speed is dependent on the forward velocity of the plane, then the plane would not take off. The treadmill's speed would likely have to increase exponentially to cause the plane to remain stationary, but it could still be done. "

That said, it's definitely a matter of how you phrase the question; just as you suggested.

 

[Jeff7]

Originally posted by: jjzelinski
Well I went ahead and re-read your prior post and I see what you're getting at.

"If the treadmill's speed is dependent on the forward velocity of the plane, then the plane would not take off. The treadmill's speed would likely have to increase exponentially to cause the plane to remain stationary, but it could still be done. "

That said, it's definitely a matter of how you phrase the question; just as you suggested.

Horray, understanding. Tis good.
I guess then we need a clear problem definition. What is the treadmill's speed linked to? What is and is not being factored into the equation? Because that's really what this is.
Just as for y = f(x), y is a function of x. Whenever x changes, y will change as well. If z changes, y will not change, as z is not even in the equation to begin with.
Similarly, if the treadmill's speed is solely dependent on the rpms of the wheels, and the wheel speed is only dependent on the treadmill's speed, then whatever the rest of the plane is doing doesn't even factor into the speed of the treadmill, as it's not in the equation.

But, if we start including other things in the equation, such as linear velocities, or if we make the treadmill's velocity dependent upon additional factors, they too need to be defined in the original problem. The problem must be clear, otherwise there can be amusing twists, such as my little example of the treadmill approaching the speed of light, turning to energy, and promptly vaporizing the airplane. Or this:

The airplane never takes off. The problem didn't specifiy the fuel level, thus I shall assume Fuel Content = 0. Plane has no fuel, engines don't spin. Thus, the plane does not take off.
Or, a plane cannot take off. A plane is simply a theoretical construct, a two-dimensional object that is infinite in length and width.

 

[normalicy]

Well, since the plane isn't using the wheels as a form of movement, no matter how fast the belt is going, then I think that the plane will actually end up pulling itself off of the belt unless they teather it somehow. I don't believe, however, that the engine(s) would have enough power to provide the lift to make the plane take off unless it's allowed to move (this however is completely dependant on the type of plane used).

 

[MasonLuke]

Originally posted by: Throckmorton

Originally posted by: JohnOfSheffield

If the conveyor belt is moving fast enough it will keep the plane in one place, no air passing the wings means no lifting power.

If you are not insane in the membrane you get this without a test.

Friction of wheels moving backwards at the same speed that the plane is propelled forwards means that the plane cannot move, it's as simple as shit and if you don't get it, you're retarded and i don't mean that in like "less knowledgeable" i really mean that you are fucked up in the skull in a way too serious to repair.

Quoted

Amen!

 

[Throckmorton]

Originally posted by: MasonLuke

Originally posted by: Throckmorton

Originally posted by: JohnOfSheffield

If the conveyor belt is moving fast enough it will keep the plane in one place, no air passing the wings means no lifting power.

If you are not insane in the membrane you get this without a test.

Friction of wheels moving backwards at the same speed that the plane is propelled forwards means that the plane cannot move, it's as simple as shit and if you don't get it, you're retarded and i don't mean that in like "less knowledgeable" i really mean that you are fucked up in the skull in a way too serious to repair.

Quoted

Amen!

I quoted so I can make fun of him later not because he's right

 

[mugs]

Here's a home experiment for you. Stand in rollerblades on a treadmill. Put a rope around your waist and have someone stand in front of the treadmill with that rope attached to a spring scale (fish scale). How much does it say you "weigh"? Now turn the treadmill on and weigh yourself at 1 mph increments. How much does your weight increase for every 1 mph you add to the speed of the treadmill?

 

[randay]

Originally posted by: mugs
Here's a home experiment for you. Stand in rollerblades on a treadmill. Put a rope around your waist and have someone stand in front of the treadmill with that rope attached to a spring scale (fish scale). How much does it say you "weigh"? Now turn the treadmill on and weigh yourself at 1 mph increments. How much does your weight increase for every 1 mph you add to the speed of the treadmill?

Now lets get crazy, lets add an infinite-super-treadmill, and remove friction. So set your treadmill to "infinite" and use the rails of the treadmill to lift yourself off of it to simulate zero friction. Now what does the scale say?

 

[spidey07]

Originally posted by: mugs
Here's a home experiment for you. Stand in rollerblades on a treadmill. Put a rope around your waist and have someone stand in front of the treadmill with that rope attached to a spring scale (fish scale). How much does it say you "weigh"? Now turn the treadmill on and weigh yourself at 1 mph increments. How much does your weight increase for every 1 mph you add to the speed of the treadmill?

That should be a nice demonstration of why the plane can't take off. The "weight" will continually increase as the speed of the treadmill increases.

 

[randay]

Originally posted by: spidey07

Originally posted by: mugs
Here's a home experiment for you. Stand in rollerblades on a treadmill. Put a rope around your waist and have someone stand in front of the treadmill with that rope attached to a spring scale (fish scale). How much does it say you "weigh"? Now turn the treadmill on and weigh yourself at 1 mph increments. How much does your weight increase for every 1 mph you add to the speed of the treadmill?

That should be a nice demonstration of why the plane can't take off. The "weight" will continually increase as the speed of the treadmill increases.

go do it and let us know when the scale reads 10000lbs.

 

[jagec]

Originally posted by: mugs
Here's a home experiment for you. Stand in rollerblades on a treadmill. Put a rope around your waist and have someone stand in front of the treadmill with that rope attached to a spring scale (fish scale). How much does it say you "weigh"? Now turn the treadmill on and weigh yourself at 1 mph increments. How much does your weight increase for every 1 mph you add to the speed of the treadmill?

I swore I'd stop posting in this thread, but...

I agree, neglecting friction, SPEED has nothing to do with any force the treadmill can apply to the plane (or to you, in the rollerblade example).

However, acceleration does. When we're dealing with a steady-state situation (plane on treadmill, treadmills spinning at steady, but ridiculously fast, speed), the wheels simply act to allow free rotation, and the plane is able to move forward or backward with impunity. But if we're dealing with an accelerating system, the wheels have an unintentional side effect of acting like flywheels, soaking up angular momentum derived from the linear force couple of the treadmill and the plane.

Example: An airplane is landing, gear down, wheels stopped (but brakes not applied). At the moment of touchdown, there is a screech of rubber and cloud of smoke as the wheels are VERY quickly accelerated to full speed...and the plane slows down a tiny amount, despite the brakes not having been applied yet. The energy of the plane that was all tied up in linear momentum is now shared between a slightly smaller amount of linear momentum, and some angular momentum in the wheels. Conservation of energy...that angular momentum has to come from somewhere. In this case the runway is immobile, so clearly it isn't providing any energy. So obviously the wheels--those disconnected, independent systems which everyone here assumes can in no way affect the motion of the plane--have somehow converted that linear momentum into angular momentum, and robbed the airplane of speed.

How? Acceleration. The derivative of speed.

Mind you, I agree that it would take a fairly ludicrous amount of acceleration to fully counteract the force of the engines, and that this is somewhat against the "spirit" of the original problem...but when you really, really need to use a treadmill to keep a plane from taking off (escaping villain? runaway bride? Home Alone VXI?), you know who to call.

 

[randay]

Originally posted by: jagec

Originally posted by: mugs
Here's a home experiment for you. Stand in rollerblades on a treadmill. Put a rope around your waist and have someone stand in front of the treadmill with that rope attached to a spring scale (fish scale). How much does it say you "weigh"? Now turn the treadmill on and weigh yourself at 1 mph increments. How much does your weight increase for every 1 mph you add to the speed of the treadmill?

I swore I'd stop posting in this thread, but...

I agree, neglecting friction, SPEED has nothing to do with any force the treadmill can apply to the plane (or to you, in the rollerblade example).

However, acceleration does. When we're dealing with a steady-state situation (plane on treadmill, treadmills spinning at steady, but ridiculously fast, speed), the wheels simply act to allow free rotation, and the plane is able to move forward or backward with impunity. But if we're dealing with an accelerating system, the wheels have an unintentional side effect of acting like flywheels, soaking up angular momentum derived from the linear force couple of the treadmill and the plane.

Example: An airplane is landing, gear down, wheels stopped (but brakes not applied). At the moment of touchdown, there is a screech of rubber and cloud of smoke as the wheels are VERY quickly accelerated to full speed...and the plane slows down a tiny amount, despite the brakes not having been applied yet. The energy of the plane that was all tied up in linear momentum is now shared between a slightly smaller amount of linear momentum, and some angular momentum in the wheels. Conservation of energy...that angular momentum has to come from somewhere. In this case the runway is immobile, so clearly it isn't providing any energy. So obviously the wheels--those disconnected, independent systems which everyone here assumes can in no way affect the motion of the plane--have somehow converted that linear momentum into angular momentum, and robbed the airplane of speed.

How? Acceleration. The derivative of speed.

Mind you, I agree that it would take a fairly ludicrous amount of acceleration to fully counteract the force of the engines, and that this is somewhat against the "spirit" of the original problem...but when you really, really need to use a treadmill to keep a plane from taking off (escaping villain? runaway bride? Home Alone VXI?), you know who to call.

air traffic control.

 

[Tweak155]

Originally posted by: jjzelinski

Originally posted by: Jeff7

Originally posted by: jjzelinski
Even if the wheels were spinning 300mph in the opposite direciton as thrust is initially generated and the plane moves backwards, it will eventually move forward regardless of what the wheels are doing. Sure, the element of friction comes into play limiting the degree to which you could apply counter-rotational movement to the wheels without hindering the planes ability to move forward. However the problem explicitly states that the rpm of the wheels is directly proportional to the amount of thrust the engines are generating.

All that we have to do is establish that if the plane has any capacity to move forward it will eventually be able to take off. The only thing that complicates this is friction, so why not eliminate this as a factor for the sake of simplifying the argument? If the landing gear of said aircraft is perfectly frictionless, then it wouldn't matter if the treadmill were matching the thrust of the engines or moving at light speed as the wheels would be completely isolating the plane from the movement of the treadmill. If you can believe that, then let's go ahead and drop friction back in. Is it really all that different? Not practically, no. the purpose of the free-spinning landing gear is still to reduce friction between the plane and the surface it is taking off from.

I do fully understand that the engines are the primary movers of the plane.

But read again - say you have a wheel, floating freely in space, with a string attached to the rim. Pull on the string. It will cause the wheel to rotate. BUT - it will also cause the wheel to move toward you.
To make this analagous to the airplane, the string is the treadmill, and the wheel is one of the plane's wheels. Tug on the treadmill, and the wheel will start to rotate, BUT a small amount of linear momentum will be transferred into the wheel, through the axle, and into the plane's body. So yes, the treadmill does have the ability, in theory, to impart linear momentum into the airplane's body. But, would it be enough to stop the plane? That depends....
IF the treadmill's acceleration was tuned such that it could produce a linear force, such that it equals the thrust produced by the plane's engines, then it could hold the plane stationary.

And you mention a lot of "if" statements in there, too. IF it's perfectly frictionless - but do we also neglect the linear momentum transfer, and assume that the treadmill purely imparts angular momentum into the wheels?
IF the rpm of the wheels (and thus speed of the treadmill) is directly (and only) proportional to the thrust of the engines, then (depending on the proportion, assuming there's no multiplier or exponential/nonlinear relationship) the plane should take off.


(Credit where it's due: It was jagec who presented the example of the wheel and string in space.)

Well I went ahead and re-read your prior post and I see what you're getting at.

"If the treadmill's speed is dependent on the forward velocity of the plane, then the plane would not take off. The treadmill's speed would likely have to increase exponentially to cause the plane to remain stationary, but it could still be done. "

That said, it's definitely a matter of how you phrase the question; just as you suggested.

Provided a realistic airplane that isn't underpowered and a treadmill / conveyor belt that man can make, anyone with common sense should agree the airplane will take off.

I won't ever disagree that you COULD CREATED a scenario where it wouldn't, but any logical person would agree it isn't realistic.

 

[spidey07]

Originally posted by: Tweak155
Provided a realistic airplane that isn't underpowered and a treadmill / conveyor belt that man can make, anyone with common sense should agree the airplane will take off.

I won't ever disagree that you COULD CREATED a scenario where it wouldn't, but any logical person would agree it isn't realistic.

Again,

Stay in bounds of the original question.

I honestly think this type of question is what separates smart people from others. All kinds of assumptions are made by plane take off folks. The truly smart people, that have a really good grasp of the physics involved can see and mentally and mathematically deduce the problem.

Then again me and my buddies used to ride on a skateboard on a treadmill at max speed and first hand experienced just how much the treadmill can push you back. Real world + experience + advanced physics = plane doesn't take off.

 

[ultimatebob]

Originally posted by: spidey07

Originally posted by: Tweak155
Provided a realistic airplane that isn't underpowered and a treadmill / conveyor belt that man can make, anyone with common sense should agree the airplane will take off.

I won't ever disagree that you COULD CREATED a scenario where it wouldn't, but any logical person would agree it isn't realistic.

Again,

Stay in bounds of the original question.

I honestly think this type of question is what separates smart people from others. All kinds of assumptions are made by plane take off folks. The truly smart people, that have a really good grasp of the physics involved can see and mentally and mathematically deduce the problem.

Then again me and my buddies used to ride on a skateboard on a treadmill at max speed and first hand experienced just how much the treadmill can push you back. Real world + experience + advanced physics = plane doesn't take off.

Exactly. I still say that the Mythbusters are going to end up crashing the plane!

 

[ConstipatedVigilante]

A plane's ability to take off is based on the lift it can get under its wings. If it's not moving forward (thus the air moving around the wings) then it can't take off. Right?...

Edit: Some people seem to think that the plane's speed relative to the ground is what's important, but that's not true. Its speed relative to the air around it is what matters. That's how lift works. Now, if you had the plane on said conveyor belt/treadmill with a headwind, then it would take off, but fly backwards. So it would have to be going a bit faster than the treadmill to take off in place in a wind tunnel. I think.

 

[spidey07]

Originally posted by: ultimatebob

Originally posted by: spidey07

Originally posted by: Tweak155
Provided a realistic airplane that isn't underpowered and a treadmill / conveyor belt that man can make, anyone with common sense should agree the airplane will take off.

I won't ever disagree that you COULD CREATED a scenario where it wouldn't, but any logical person would agree it isn't realistic.

Again,

Stay in bounds of the original question.

I honestly think this type of question is what separates smart people from others. All kinds of assumptions are made by plane take off folks. The truly smart people, that have a really good grasp of the physics involved can see and mentally and mathematically deduce the problem.

Then again me and my buddies used to ride on a skateboard on a treadmill at max speed and first hand experienced just how much the treadmill can push you back. Real world + experience + advanced physics = plane doesn't take off.

Exactly. I still say that the Mythbusters are going to end up crashing the plane!

Do you know just how hard it is to pull off a kickflip on a treadmill?

Such a simple trick that you can do without thought while rolling. Try it on a treadmill. It's hard. really hard.

To deny the treadmill doesn't push the plane back - I just can't see how people can even believe this. Come up with all kinds of analogies you wish. You can't deny physics.

I know it seems like trolling but we really did spend countless hundreds of hours on a skateboard on a treadmill. What the heck were we gonna do? It was raining.

As the treadmill sped up you had to pull yourself harder and harder just to maintain position.