Plane

[RichA]

What you are suggesting can't happen because the wheels have little resistance, Regardless of what you think the op says . There won't be any loss of traction, just the wheels speeding up and the plane taking off.

Perfect traction and plane moving forward means conveyor and wheels must have different speeds.
The wheel and conveyor belt can only have the same speed if the plane is stationary or the wheels are slipping over the conveyor belt.

 

[Deleted member 35927]

Perfect traction and plane moving forward means conveyor and wheels must have different speeds.
The wheel and conveyor belt can only have the same speed if the plane is stationary or the wheels are slipping over the conveyor belt.

It's funny as thats not what I read and if it were it can't happen unless the wheels have their own drive , which we know they don't.
The point you always just skip over, is the only way the plane wheels move and gain any speed is if the plane moves.

 

[RichA]

It's funny as thats not what I read and if it were it can't happen unless the wheels have their own drive , which we know they don't.

Makes you realise how clever the question is, whether by design or accident.

Those who focus on the freewheel think that everybody else has made the mistake of assuming driven wheels.

I got the freewheel but was so focused on the speed matched conveyor and wheels that the modelling in my head saw the wheels and conveyor as 1:1 gear matched with cogs, so the plane body had to be stationary until the thrust tipped it forwards.

Whereas, in "reality", they are not cogged and the thrust will force the plane and its wheels forward through the friction.

 

[Bobski]

The (logic) problem matching wheel speed to conveyor if they’re travelling in opposite directions is presumably why the OP framed the question how they did, adding a requirement that the conveyor’s movement counters the wheel rotation. As we’ve discussed before, conveyor moving in the opposite direction to plane doesn’t counter, but increases wheel rotation.

I’ve described previously what I think would happen if we ignore the “countering their rotation” phrase, but breaking it down into split seconds may (or may not!) help. So with engines off, plane is stationary and conveyor is stationary. Jet starts engines and begins to move forwards, say at 1 mph. Conveyor, according to the requirements of the problem, starts moving at 1mph in the opposite direction. Immediately this happens the wheels are now spinning at 2mph. (The relative speed difference between plane and conveyor (1 mph) is surely insufficient to lock the wheels/cause wheel spin). So conveyor is 1 mph, wheels are 2 mph and as per the requirement of the problem, the conveyor immediately speeds up to 2mph to match the wheels, which instantaneously increases the wheel speed to 3 mph. You can see where this is going, each time the conveyor speeds up, the wheels are sped up by the same amount, so that when added to the (trivial) initial movement of the plane, they can never match. If the adjustments are happening instantaneously, then within a split second the conveyor (and the plane’s wheels) will be approaching light speed and the physics will start to get really interesting. The relative difference in speed between conveyor and wheels is always 1 mph in this example and insufficient to lock the wheels. You could imagine that there will be some lag in the system and the changes might happen more slowly – in which case the plane will continue to accelerate along and may take off before the conveyor blows up (the plane doesn’t care how fast its wheels are spinng, the wheels have no ability to retard the plane’s progress, they just spin).

Some may argue that the plane can never budge an inch in this scenario, since to do so would require wheel speed which isn’t matched to conveyor speed even if just for a microsecond. This approach is simply taking the question to be “a plane is locked stationary on a treadmill by some mystery force, will it take off?”, which isn’t much of a conundrum. If you write the question as conveyor and plane travel in opposite directions and the conveyor matches the plane’s speed (rather than the wheels), there is no problem – as we’ve previously discussed the plane and the conveyor speed up, the wheels spin twice as fast as both and the plane takes off. I still think the OP in this thread can only really be interpreted as plane and conveyor moving in the same direction.

 

[Deleted member 35927]

Makes you realise how clever the question is, whether by design or accident.

Those who focus on the freewheel think that everybody else has made the mistake of assuming driven wheels.

I got the freewheel but was so focused on the speed matched conveyor and wheels that the modelling in my head saw the wheels and conveyor as 1:1 gear matched with cogs, so the plane body had to be stationary until the thrust tipped it forwards.

Whereas, in "reality", they are not cogged and the thrust will force the plane and its wheels forward through the friction.

There is no friction, you keep adding it but it just doesn't exist to that extent . It's not a cleverly worded puzzle.

 

[RichA]

There is no friction, you keep adding it but it just doesn't exist to that extent . It's not a cleverly worded puzzle.

I'm not sure what you mean there.

 

[Deleted member 35927]

I'm not sure what you mean there.

It's part of the whole sentence, you randomly snipped.
As for friction.
During take off the amount of friction via the wheels is negligible...

Then look at the definition of negligible.

Like I said , you keep ignoring how plane wheels get their forward rotation.

 

[Whereditgo]

It's badly written, either by accident or design, because "to match the planes wheels in the opposite direction" and "counteracting their rotation" is a conflict.

In reality the conveyor can never perfectly match the wheel speed because it will always be playing catch up, reacting to the accelerating wheel. As written, with the conveyor (impossibly) perfectly matching the wheel speed, the tyres would begin to skid as the thrust overcomes the friction (there is some now) between the tyre and the conveyor. Provided the tyres don't fail the plane takes off.

 

[Voyager EMH]

At the point where the wheel and conveyor are touching.
Draw a dot on the wheel and a dot on the conveyor.
The dots move together at the same speed.
The tangential speed of the wheel matches the speed of the conveyor where those two dots touch each other.
Draw a sequence of dots on the conveyor. Draw a sequence of dots on the wheel with matching spaces.
The dots will always match whether the wheel is stationary on the conveyor or moving along the conveyor.

Rotational speed and speed along the conveyor are two different things. Rotational speed of the wheel is a passive response.

 

[Bobski]

It's badly written, either by accident or design, because "to match the planes wheels in the opposite direction" and "counteracting their rotation" is a conflict.

In reality the conveyor can never perfectly match the wheel speed because it will always be playing catch up, reacting to the accelerating wheel. As written, with the conveyor (impossibly) perfectly matching the wheel speed, the tyres would begin to skid as the thrust overcomes the friction (there is some now) between the tyre and the conveyor. Provided the tyres don't fail the plane takes off.

Unless you take opposite direction to relate to the direction of travel for the circumference of the wheel compared with the conveyor eg. plane moving right to left, wheels will rotate anticlockwise, circumference of wheel/wheel tread will be moving left-to-right at the point of contact with the conveyor. If the conveyor moves in the opposite direction to this wheel rotation it will be moving right-to-left (same direction as plane), and also countering the wheel rotation. In this scenario the queston reads fine, with no conflicts. I guess it's just counter-intuitve to think someone would construct a problem in which the conveyor isn't going in the opposite direction.

 

[RichA]

It's part of the whole sentence, you randomly snipped.
As for friction.
During take off the amount of friction via the wheels is negligible...

Then look at the definition of negligible.

Like I said , you keep ignoring how plane wheels get their forward rotation.

Can you clarify what I randomly snipped?

Friction is massive. The only way that the 300 ton plane achieves any forward motion is when it's tyres are skidding on the conveyor.

 

[Deleted member 35927]

Can you clarify what I randomly snipped?

Friction is massive. The only way that the 300 ton plane achieves any forward motion is when it's tyres are skidding on the conveyor.

Smh. How do the wheels on a plane get forward rotation.

 

[Whereditgo]

Unless you take opposite direction to relate to the direction of travel for the circumference of the wheel compared with the conveyor eg. plane moving right to left, wheels will rotate anticlockwise, circumference of wheel/wheel tread will be moving left-to-right at the point of contact with the conveyor. If the conveyor moves in the opposite direction to this wheel rotation it will be moving right-to-left (same direction as plane), and also countering the wheel rotation. In this scenario the queston reads fine, with no conflicts. I guess it's just counter-intuitve to think someone would construct a problem in which the conveyor isn't going in the opposite direction.

Agreed, and clearly in that scenario the conveyor matches the acceleration of the plane, the wheels don't rotate and the plane takes off. But if you interpret the question so that the conveyor is moving in the opposite direction to the plane like a treadmill.......so like I said, badly written either by accident or design, I suspect the latter.

 

[Whereditgo]

Smh. How do the wheels on a plane get forward rotation.

During a normal take off there won't be any friction between the tyres and the surface they are rolling on, a bit of rolling resistance, but not friction.

 

[RichA]

At the point where the wheel and conveyor are touching.
Draw a dot on the wheel and a dot on the conveyor.
The dots move together at the same speed.
The tangential speed of the wheel matches the speed of the conveyor where those two dots touch each other.
Draw a sequence of dots on the conveyor. Draw a sequence of dots on the wheel with matching spaces.
The dots will always match whether the wheel is stationary on the conveyor or moving along the conveyor.

Rotational speed and speed along the conveyor are two different things. Rotational speed of the wheel is a passive response.

If the plane is moving forwards then either it's wheels are moving faster than the conveyor or it is skidding.

 

[RichA]

Smh. How do the wheels on a plane get forward rotation.

It's why it's a paradox.
The wheels only turn if the plane is moved forwards by the thrust.
But as soon as the wheels turn the conveyor belt matches their speed in the opposite direction, "perfectly counteracting their rotation."
So the plane doesn't move.
So the wheels don't rotate.
Eventually the thrust overcomes the friction of tyres on the belt, but that's skidding and the tyres aren't rotating so the conveyor isn't rolling.

 

[Whereditgo]

It's why it's a paradox.
The wheels only turn if the plane is moved forwards by the thrust.
But as soon as the wheels turn the conveyor belt matches their speed in the opposite direction, "perfectly counteracting their rotation."
So the plane doesn't move.
So the wheels don't rotate.
Eventually the thrust overcomes the friction of tyres on the belt, but that's skidding and the tyres aren't rotating so the conveyor isn't rolling.

Not quite. The wheels most certainly would be rotating.

 

[RichA]

Not quite. The wheels most certainly would be rotating.

Starting how though?
Other folks (not you) just repeating that 250k bhp is unstoppable doesn't enable a freewheel to roll if the body above it is stationary.
The plane has to move forward for the wheel to roll. Even when the thrust breaks through the friction holding it stationary that is the wheel skidding, not rolling.
Would that allow the wheel to start rolling or would it just continue skidding as if locked?

 

[Beezerk]

Average White Band anyone?

 

[Deleted member 35927]

Starting how though?
Other folks (not you) just repeating that 250k bhp is unstoppable doesn't enable a freewheel to roll if the body above it is stationary.
The plane has to move forward for the wheel to roll. Even when the thrust breaks through the friction holding it stationary that is the wheel skidding, not rolling.
Would that allow the wheel to start rolling or would it just continue skidding as if locked?

The body above isn't stationary. It's moving forward rolling on it's wheels no matter what your conveyor is doing rolling not skidding or dragging.
The 250k ref comes from newtons 3rd law and your ability to suggest it can just be vanished away.