# Fun conceptual physics problem



## cmhardw (Sep 15, 2012)

Hi everyone!

It's been a while since I've posted around here. I recently got transferred into the calculus class at my school, so now I get to teach calculus - which is amazing and very fun!

My new coworker and fellow lab instructor is something of a physics whiz, and he gave me a very fun conceptual physics problem to stew over. I'm doing my best to relay the problem to you all for your amusement! If I mistype something or if something seems off then just reply in the thread and I'll either correct it right away or ask Chris for the proper way to state it.

Here's the problem:
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This will be a bit wordy, but that is because I am trying to anticipate some of the questions I had by giving the full story in the description.

*Fun conceptual physics problem:*

Imagine a giant treadmill large enough to hold a commercial jet airliner. Picture something like a Boeing 777 or comparably sized plane. The plane is sitting on the treadmill at rest, and the treadmill is not moving.

This treadmill is hooked up wirelessly somehow to the plane, such that the treadmill will move whenever the throttle is opened up on the plane. For example, if the plane accelerates such as it would travel at 100kmh on a standard runway, then the treadmill will be sent this information with negligible time delay and the tread on the giant treadmill will move in the opposite direction to the plane's engine thrust at 100kmh.

The treadmill tread moves in the direction opposite the direction the planes engines will be pushing it forward.

Imagine there is some realistic coefficient of friction between the plane's wheels and the treadmill (this is meant to be a conceptual problem, but pick a coefficient of friction if you want to run some calculations). All of this is happening outside in an area with negligible wind. Assume there is regular air around the plane, and all of this is happening at sea level.

*The Question:* Can the plane still take off on this treadmill runway?


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## ThomasJE (Sep 15, 2012)

Planes get airbourne by getting air under the wings, creating a high pressure zone below the wing and a low pressure zone above. The air doesn't move (negligible wind, so let's say 0 to keep it simple), so the plane needs to move at a fast enough speed to get enough pressure to get airbourne. The plane is travelling at x km/h, so the treadmill would be going at -x km/h (remember, the treadmill is going backwards). So, the speed of the plane is x + -x = 0 km/h. So, we effectively have a stationary plane. Can a stationary plane get airbourne? No. There's your answer.

(I've probably got some minor detail wrong, but oh well.)


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## 5BLD (Sep 15, 2012)

Would you make an awesome hair dryer? Yes. Would it take off? Don't think so. No air would go under the wings.


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## applemobile (Sep 15, 2012)

0/10 old content.


Yes, it would take off. The motors propel the plane, they do not turn the wheels. A car is such situation would not move. If you set the motors to make the plane travel at 100km/h, and the treadmill to travel in the opposite direction, then the plane would travel forwards at 100km/h, but the wheels would be turning at 200kph.

Thank you and good night.


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## shelley (Sep 15, 2012)

I'd argue that this problem is more than just physics, as it requires some basic knowledge about the difference between a car's operation and a plane's operation.


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## mr. giggums (Sep 15, 2012)

applemobile said:


> 0/10 old content.
> 
> 
> Yes, it would take off. The motors propel the plane, they do not turn the wheels. A car is such situation would not move. If you set the motors to make the plane travel at 100km/h, and the treadmill to travel in the opposite direction, then the plane would travel forwards at 100km/h, but the wheels would be turning at 200kph.
> ...



The myth busters did a show and empirically proved this.


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## Stefan (Sep 15, 2012)

shelley said:


> I'd argue that this problem is more than just physics, as it requires some basic knowledge about the difference between a car's operation and a plane's operation.



Is there a relevant difference between them that not everybody knows?


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## shelley (Sep 15, 2012)

Just reread the actual problem given to see that no car was mentioned. Sometimes the problem starts by demonstrating that a car would not move forward and then asking if the airplane would take off.

But it's a little different from most physics problems where a "car" is just a black box and you don't need to know anything about the inner workings; all you know is that it generates acceleration of value a or that it's traveling at velocity v. With this problem, the question of how it attains velocity v is actually relevant.


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## Stefan (Sep 15, 2012)

Yeah, but how many people don't know how planes accelerate? I'd say something that's common knowledge shouldn't make the problem a not-just-physics problem. What about people who don't even know what a plane/treadmill/direction/etc is? Do they count as well? Can their lack of knowledge cause a physics problem to not be considered a just-physics problem?


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## applemobile (Sep 16, 2012)

Would the delorean still go back in time?


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## Cubic (Sep 16, 2012)

Hmm.

A car's wheels turn because the axle is turning.

A plane's wheels turn because the jet engines are sucking in, then expelling, air. This movement of air is surely enough to create the change in air pressure required for the plane to take off.

Those who have flown may well have experienced what happens when a jet aeroplane hits an air pocket.

So yes, the plane will take off.


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## chrissyD (Sep 17, 2012)

ThomasJE said:


> The plane is travelling at x km/h, so the treadmill would be going at -x km/h (remember, the treadmill is going backwards). So, the speed of the plane is x + -x = 0 km/h. So, we effectively have a stationary plane. Can a stationary plane get airbourne? No. There's your answer.
> 
> (I've probably got some minor detail wrong, but oh well.)



You're assuming the engine/s of the plane drive the wheels. The engines drive the entire plane. The wheels just move as a result of being on the ground and the plane moving. they're just there to keep the plane on the ground and to help it move about, not to make the plane move in the air unlike a car where it's movement relies on the movement of the wheels. 
If the treadmill acts with equal force on the driving force of the object on the treadmill (legs, wheels connected to an engine ect) then the object won't move, Hence why when you run on a treadmill you don't move but when you stop moving your legs (driving force) you move backwards, fall over and everyone laughs. Remember on a plane the wheels aren't connected directly to the driving force of the plane however on a car the wheels are connected directly to the crank of the engine.

Yes the plane would take off. If you could make the wheels turn fast enough so the treadmill equals/overcomes the thrust of the engines then the plane wouldn't move/move backwards however you need more thrust to make the wheels turn faster so it's impossible.


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## Stefan (Sep 17, 2012)

chrissyD said:


> If you could make the wheels turn fast enough so the treadmill equals/overcomes the thrust of the engines then the plane wouldn't move/move backwards however you need more thrust to make the wheels turn faster so it's impossible.



What do you mean with "equal the thrust"? And I don't understand the red part.


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