Tom said on February 16, 2008:

I'm just giving an example of one of the possible limits of the problem

No, you're not. We've been given a set of rules, either "reality" or the ones given in the stated problem. We're not interested in making up new versions just so that, under an unrealistic set of expectations, the conveyor belt has very much impact at all on the plane's forward progress.

The acceleration or not is a moot point, and if you think an accelerating conveyor belt somehow changes the rolling resistance, you're wrong on that count as well. Friction remains largely the same once the wheels start rolling, and by "same" I also mean "next to nothing" - nil, negligible.

Tom said on February 16, 2008:

If the wheels have zero friction, then the conveyor belt is a red herring because its motion will not be transmitted to the plane, ever. The plane having the advantage of acceleration will always take off.

The wheel friction is so close to zero, that this is indeed how people grounded in reality choose to look at the problem.

Tom said on February 16, 2008:

If the wheels have infinite friction, then the plane won't be able to roll forward and will always have the same velocity as the conveyor belt. The plane will never accelerate and never take off.

Actually, you'd have to lock the plane to the conveyor belt for this to be true. Otherwise I suspect that the plane would simply shred up its tires as it drug them over the pavement. Sea planes can still take off from water, after all - and they don't have wheels. So again, you're wrong.

Tom said on February 16, 2008:

Clearly, the real world is in between.

Yet in either case, the plane takes off. In the second case - the wildly unrealistic one - it's admittedly more difficult (and the wheels may shred and blow up, and sparks may fly as bbum said), but it still takes off if it's not literally locked to the ground.

Tom said on February 16, 2008:

IF the conveyor belt is accelerating, things get tricky and indeed you have to get into issues of static friction etc. etc.

No, they really don't get tricky at all. Acceleration's impact on the rolling resistance of ball bearings is minimal/negligible.

Really, no further comments (from anyone on either side) are necessary.

I actually made no claims about bearing resistance; I'm just giving an example of one of the possible limits of the problem (plane has initial backwards velocity) and how this allows you to start thinking about the problem in simple terms that can then be built upon (first, initial velocity and momentum; only afterwards should you to start build up your model by considering friction).

Solving physics problems is all about stating your initial hypotheses.

1. If the wheels have zero friction, then the conveyor belt is a red herring because its motion will not be transmitted to the plane, ever. The plane having the advantage of acceleration will always take off.

2. If the wheels have infinite friction, then the plane won't be able to roll forward and will always have the same velocity as the conveyor belt. The plane will never accelerate and never take off.

Clearly, the real world is in between. So "solving" the riddle is a question of how your assumptions balance out. Although this was not my initial guess, I do agree that in the real world no conveyor belt would succeed in transferring its full acceleration to the plane, and that the plane will always take off.

Just to beat a dead horse:

IF the conveyor belt has constant velocity -- as was the case in the Mythbusters show -- then the plane will ALWAYS take off under ANY additional assumption (see above)

IF the conveyor belt is accelerating, things get tricky and indeed you have to get into issues of static friction etc. etc.

Your claim is that the rolling resistance of the ball bearings will be great enough to stop the plane from moving forward relative-to-the-air to the point of achieving lift off.

Given that claim, which is actually subtly different than the original claim, then it becomes a question of how much thrust can the plane's engine provide vs. how much rolling resistance can the wheel's bearings provide.

In general and without the bearings failing catastrophically, the answer is "a lot of thrust" vs. "very little resistance".

The quality of the bearings very much do matter simply in that your scenario would require the conveyor belt to be going at 100s or 1000s of miles per hour to provide enough rolling resistance to counteract the thrust of its engine.

Sure -- when you modify the original claim as you have, it could theoretically be possible to pull the conveyor belt "backwards" fast enough to create enough rolling resistance to prevent the plane from taking off.

More likely, at the speeds involved, the bearings would fail catastrophically and this would become a considerably more sparky experiment.

Given a powerful enough engine, the presence/absence of rolling wheels is irrelevant. It becomes entirely a question of whether or not you can achieve liftoff prior to the wheels, struts, and belly of the plane being worn through.

b.bum

This is not a frictionless world. If you wear rollerblades and setp onto a conveyor belt you may indeed not *initially* move with the conveyor belt but in a few short moments you will have the same velocity as the conveyor belt. The quality of your ball bearings has nothing much to do with it in the long run.

In other words once equilibrium is reached you will be moving at the same speed as the conveyor belt.

Once that occurs, when you turn on your jetpack the wheels and their bearings are essentially immaterial and the rest of the calculation holds.

Which direction does the plane go? Backward, with velocity V_conveyor.

No. If the brakes aren't on, it's quite possible that the conveyor belt could be moving backwards faster than the plane. Put a roller skate on a tablecloth and yank the tablecloth. Unless you gradually accelerate so as not to overwhelm the resting friction, the skate doesn't immediately move at the same speed as the tablecloth.

And that's without the roller skate supplying its own force opposite the direction of the table cloth (as we have with the plane).

Your math is wrong, your physics are wrong, and your methods are incorrect. V_conveyor accounts for almost no impact on the plane's velocity because the conveyor belt applies almost no force horizontally. The only force it applies is UPWARDS, to counter the weight of the plane. The "backwards" force it applies (opposite the forward direction of the plane) is supplied by the ball bearings and is, again, negligible.

You are wrong… and it's funny you'd come to a post making fun of people who get it wrong and then do as you did.

Which direction does the plane go? Backward, with velocity V_conveyor.

Intuitively it is reasonable to expect that the plane will have to overcome this backward velocity before taking off.

At time T=0, the jet engine is turned on, generating a thrust, F by pressing against (we all agree) the atmosphere. As a result, the plane experiences a forward acceleration A = F/M. Note that the conveyor belt provides no acceleration, just constant velocity. [As an aside, also note that acceleration is independent of any fixed frame of reference].

We are allowed to decompose the velocity of the plane relative to ground (V_total) into the velocity component due to the conveyor belt (V_conveyor) and the velocity resulting from thrust acceleration (V_plane):

V_total = V_plane - V_conveyor

As velocity is the integral of acceleration, at the instant in time T=0 its (forward) velocity component due to the thrust force is still V_plane = 0: the plane is still moving backward relative to earth with velocity V_conveyor - V_plane = V_conveyor.

Time, T, continues to pass. Thrust F guarantees constant acceleration A=F/M, and the equation for the velocity of the plane due to thrust is V_plane=TA.
Thus V_total = TA - V_conveyor. The plane's ground speed V_total will be zero only when

T_null = V_conveyor/A

Until this time the plane will continue to move backward. As more time passes, the plane's forward velocity component due to thrust will continue to increase linearly with time, whereas the backward velocity component due to the conveyor belt motion will remain constant, and so the plane will progressively pick up forward velocity (V_total = TA - V_conveyor > 0 ), develop lift and take off.

Thus if the conveyor belt has constant velocity the plane will, of course, teventually take off. If the conveyor belt's velocity increases linearly with time at a rate A, then the plane will not develop forward velocity and will not take off.

And by calling these people "stupid" and "idiots" you achieve what exactly?

he made me laugh while pointing out some really obvious points that all these people would have understood if they were just more intelligent.

Seaplanes, obviously, can take off just fine facing upstream up a river no matter how fast the water is going. Might help them visualize how the treadmill just doesn't matter.

And by calling these people "stupid" and "idiots" you achieve what exactly?

I succeed in telling the truth? In calling a spade a spade? What would you have me call them? The word "stupid" and "idiots" mean something, and to me, the definitions pretty much line right up with what these people are doing, saying, typing, etc.

No doubt I could have used synonyms, but then you'd just be asking me what I achieve by calling people clueless, dolt-like, unintelligent, braindead, deficient, dim, dopy, dumb, foolish, mindless, moronic, obtuse, thickheaded, unthinking, slow, ignorant buffoons.

bbum said on January 31, 2008:

Any pilot in the "no fly" camp is no pilot that I'd want flying the plane I'm in....

Indeed. I'm amazed at how many of the "no fly" people are outing themselves as pilots. Wow.