A jet plane on a large treadmill

[Bodhi]

Padded room is definitely the spot for this one.

peace,
D.

[dbp]

I'd say completety incorrect because the motorcycle is pushing against the ground and that's what's causing its forward speed. How about replace the cycle with a really big RC airplane and that's more like it. With this scenario can't you imagine the treadmill spinning fast enough such that both the rollerblader and RC plane are stationary WRT the ground?

Really nice diagram, though, other than that!

or better yet, I could replace the motorcycle with a 747 in flight...

edit: It doesn't really matter what is causing the forward speed, as long as it is something unaffected by the treadmill (such as the jet's engine)

[The AD]

or better yet, I could replace the motorcycle with a 747 in flight...

Of course, but I think that's the kind thing that causes it to be hard to think about. If you had a 747 pulling the rollerblader your mind says "oh, that's just going to pull him right off the treadmill!" but it's only because we know the airplane is so powerful. You use an RC plane and the problem is identical, but with forces of a magnitude much more easy for our brains to visualize and then it becomes obvious that the treadmill could hold the rollerblader in place.

Edit: in response to your edit. Of course it matters!

[Parvo Pup]

If a chicken and a half
Lays an egg and a half per day
How many shingles are there on Lassie's doghouse?

Show your work.

[TomK]

Where does the question state this?

No other way to satisfy the statement "This conveyor has a control system that tracks the planes speed and tunes the speed of the conveyor to be exactly the same (but in the opposite direction)."

Since the speed of conveyor is always 100% of speed of plane but in opposite direction, if the plane's speed is zero so is the treadmill's.
At the same moment any plane forward movement starts, the treadmill counters by rolling backwards to keep the plane stationary.
Since the plane can never start moving, it's speed relative to anything else stays zero while the treadmill spins, wheels turn, and the friction counters the forward thrust of the jets.

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On the other hand...
Then there's the effect of the treadmill surface's friction dragging the air past the plane, raising the plane's relative airspeed. By the treadmill moving the AIR while countering the plane's attempted movement, it would be possible for the plane to "take off" like in a wind tunnel. It'd crash after leaving the moving airstream of course, but nothing in the problem asks about what happens after takeoff.

So, I change my answer to yes until someone demolishes that argument.
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[PNWbrit]

I'd say completety incorrect because the motorcycle is pushing against the ground and that's what's causing its forward speed. How about replace the cycle with a really big RC airplane and that's more like it. With this scenario can't you imagine the treadmill spinning fast enough such that both the rollerblader and RC plane are stationary WRT the ground?

Really nice diagram, though, other than that!

Doesn't the bike have to sit on its own treadmill to match the forces of the jet situation?

[dbp]

Doesn't the bike have to sit on its own treadmill to match the forces of the jet situation?

I don't think so. The jet engine isn't effected by the treadmill. It is pushing against air (not the ground) to create movement.

[dbp]

Some people didn't like my motorcycle analogy. Maybe this is better.

[The AD]

Yes. Much better!

Other than the fact the towing 747 would fall out of the sky, why wouldn't the treadmill be able to turn fast enough to prevent the lazy 747 from moving forward?

[dbp]

Yes. Much better!

Other than the fact the towing 747 would fall out of the sky, why wouldn't the treadmill be able to turn fast enough to prevent the lazy 747 from moving forward?

I believe the thinking is that the plane could care less what the free-spinning wheels are doing. It would move with velocity (V), the treadmill -V, and the wheels would be spinning real fast (2V). There really isn't enough friction envolved to counter the power of the jet's engines.

[mcsquared]

Yes. Much better!

Other than the fact the towing 747 would fall out of the sky, why wouldn't the treadmill be able to turn fast enough to prevent the lazy 747 from moving forward?

Because people are making the mistake of assuming that the force (moving the plane on the treadmill to the right) created by the friction between the treadmill and the wheels increases proportionally with the speed of the treadmill. When in reality the force vector pointing to the right is pretty much a constant and is in no way related to the speed of the treadmill. Whereas, the force vector going to the left is not constant and is BIG. This imbalance of forces causes an acceleration in the direction of the resultant force (F=MA)

[The AD]

How about this scenario:

A rollerblader is standing on a powered treadmill and holding a kite (like the ones they use in kite surfing). At time zero the treadmill is moving fast enough to exactly cancel forward movement provided by the kite. Now, the wind picks up, but the treadmill's controls counter this increased force by increasing the speed of the treadmill. If the wind slows down, the treadmill slows down, too. The end result is the rollerblader remains stationary with respect to the ground.

I think you will agree that the forces involved in this example are exactly like those in the original problem. The differences in the scale of the forces is irrelevent. So do you also agree with my conclusion that the rollerblader will not move?

[squirrelmurphy]

imagine this. using the motorcycle/rollerblader or plane/plane diagrams above, imagine instead that the treadmill is moving 4000 m/s in the opposite direction. or 8000. or a fucking million.
Now:
1) if there is no friction in the rollerblade/airplane wheel bearings, there is only air resistance keeping the person/plane from moving.
2) if there is friction in the bearings, the plane/person will move unless the friction is greater than the force provided by the motorcycle engine/other plane.

the plane will move, and eventually take off

[bagtagley]

I think you will agree that the forces involved in this example are exactly like those in the original problem. The differences in the scale of the forces is irrelevent. So do you also agree with my conclusion that the rollerblader will not move?

No. If the kite pulls the skateboarder forward at 5mph, the treadmill will spin in the opposite direction at 5mph. Thus, the skateboard wheels will spin twice as fast, but the skateboarder will still move forward.

As his speed increases, the speed of the treadmill increases proportionately, and the speed of the wheels rotation will increase. However, the skateboarder will still move forward.

Edited for tonghands.

[DJSapp]

No other way to satisfy the statement "This conveyor has a control system that tracks the planes speed and tunes the speed of the conveyor to be exactly the same (but in the opposite direction)."

Since the speed of conveyor is always 100% of speed of plane but in opposite direction, if the plane's speed is zero so is the treadmill's.

ok

At the same moment any plane forward movement starts, the treadmill counters by rolling backwards to keep the plane stationary.

Incorrect, the treadmill counters by moving backward at an equal rate. The airplane's wheels do not transfer the treadmills speed to the aircraft. The aircraft continues moving forward relative to the air.

Since the plane can never start moving, it's speed relative to anything else stays zero while the treadmill spins, wheels turn, and the friction counters the forward thrust of the jets.

But then the wheels would never begin moving, and the treadmill would never start.

Airspeed = 1 to begin moving
conveyor = 1 to match
Wheelspeed = airspeed + conveyorspeed

wheelspeed = 1 + 1 = 2

according to your argument:

wheelspeed = conveyorspeed

2 does not equal 1

Your argument is incorrect.

[mcsquared]

I think you will agree that the forces involved in this example are exactly like those in the original problem. The differences in the scale of the forces is irrelevent. So do you also agree with my conclusion that the rollerblader will not move?

No I don't. Frictional force is not a function of velocity. Friction is a function of Mass, gravity and a coefficient. When you sand furniture is the difficulty of moving the sanding block a function of how fast you move it or how hard you press down?

[The AD]

No. If the kite pulls the rollerblader forward at 5mph, the treadmill will spin in the opposite direction at 5mph. Thus, the rollerblade wheels will spin twice as fast, but the rollerblader will still move forward.

See, that's the flaw--at least in my thinking. It isn't pulling him ahead at 5 mph. It's causing the wheels to spin at 5mph. That's what the control system of the treadmill is countering.

[The AD]

No I don't. Frictional force is not a function of velocity. Friction is a function of Mass, gravity and a coefficient. When you sand furniture is the difficulty of moving the sanding block a function of how fast you move it or how hard you press down?

Consider this, though. If you are standing on a moving treadmill while wearing rollerblades and holding on to the handrails (thereby imparting a resistive force much like the 747's engines) won't you have to hold on "tighter" (i.e., resist the force of the treadmill more) if the treadmill speeds up?

[DJSapp]

See, that's the flaw--at least in my thinking. It isn't pulling him ahead at 5 mph. It's causing the wheels to spin at 5mph. That's what the control system of the treadmill is countering.

Wheelspeed cannot equal treadmill speed. The plane could never begin moving.

[The AD]

The plane could never begin moving.

See, finally we agree

[mcsquared]

When your car is stuck in the snow does flooring it and making your tires go 10 times as fast make your tires grip any better?

[DJSapp]

I give up. Your argument is fundamentally incorrect. You are switching the treadmills speed from airspeed to wheelspeed.

Fuck this. I'm going skiing. (well, after 4 more hours of work and continuing to fight over this)

[The AD]

You are switching the treadmills speed from airspeed to wheelspeed.

It was never stated in the problem which speed the treadmill is reacting to.

[dbp]

It was never stated in the problem which speed the treadmill is reacting to.

It doesn't really matter how fast the treadmill is going. As stated by mcsquared above, friction doesn't depend on velocity. The treadmill can be going a gazillion miles an hour. Unless the plane gets a lot heavier, the resistive force provided by friction is going to be dwarfed by the engines once they get up to speed.

[The AD]

friction doesn't depend on velocity.

which is utterly and completey wrong. Ever heard of wind resistance or drag? Do you believe that is dependent on velocity? Guess what, that's friction.