While this site has much to offer readers with an interest in music, psychodrama and abandoned mental hospitals, it’s possible I’ve neglected any engineers and physicists among us. To remedy this mortifying oversight, here’s a little thought experiment, courtesy of Sam Hughes:
A plane is standing on a runway that can move (like a giant conveyor belt). This conveyor has a control system that tracks the plane’s speed and tunes the speed of the conveyor, relative to the Earth, to be exactly the same (but in the opposite direction).
Now comes the question.
Will the plane be able to take off?
The answer isn’t quite as obvious as one might assume. Needless to say, a detailed pondering ensues.
Update: Because you know you secretly want to, How to Destroy the Earth.
Sam Hughes is always good. My favorite is How to Destroy the Earth-
“Destroying the Earth is harder than you may have been led to believe. You’ve seen the action movies where the bad guy threatens to destroy the Earth. You’ve heard people on the news claiming that the next nuclear war or cutting down rainforests or persisting in releasing hideous quantities of pollution into the atmosphere threatens to end the world. Fools. The Earth is built to last. It is a 4,550,000,000-year-old, 5,973,600,000,000,000,000,000-tonne ball of iron. It has taken more devastating asteroid hits in its lifetime than you’ve had hot dinners, and lo, it still orbits merrily. So my first piece of advice to you, dear would-be Earth-destroyer, is: do NOT think this will be easy.”
http://qntm.org/?destroy
The Earth destroying problem is a work of terrible genius. I like the fact we’re encouraged to fret about the inconvenient amount of time it would take to find an Earth-sized chunk of antimatter, or alternatively, rotate the entire planet through a fourth spatial dimension. After all, if you wanted to annihilate the planet in a fit of pique, you’d probably want to do it pretty sharpish. Setting aside the building of enormous and improbable devices, the main drawback seems to be patience.
Re: plane on a treadmill, isn’t the simple answer ‘yes’?
Mythbusters have the answer:
http://www.youtube.com/watch?v=YORCk1BN7QY
(Surprisingly few planes take off by sending power to their wheels.)
See also this:
http://blag.xkcd.com/2008/09/09/the-goddamn-airplane-on-the-goddamn-treadmill/
Plane gets airborne, as long as the wheel bearings are up to the task.
And the tyres.
So what about a helicopter on a counter-rotating turntable? 🙂
GREAT link, David! Best you’ve had in a long time. I like the list of things which will *not* destroy the earth. Last on the list: Gay Marriage.
Speaking of destroying the Earth:
How to build a space ship: http://www.projectrho.com/rocket/
And the obligatory death ray: http://panoptesv.com/SciFi/DeathRay.html
From an engineer: The problem is “ill posed”. It is not clear exactly what is meant by the phrase “has a control system that tracks the plane’s speed and tunes the speed of the conveyor, relative to the Earth, to be exactly the same (but in the opposite direction).”
I think it means that at time=0, both the plane and the conveyor belt are stationary, relative to the earth, but then the plane starts to move forward and the belt moves backward so that the plane stays in the same position, relative to the earth.
If this is the case, then the plane only “takes off” when the wheels/wheel bearings fail in an exciting fashion, with the debris propelling the plane above them to a higher altitude.
Otherwise, there is no relative speed of the airplan thru the air, so the wings never see any lift, and the plane stays right where is is on the treadmill, stationary in relation to the earth below it.
If the quoted phrase means something else, then that needs to be described better, so that an analysis can be done.
I have not gone to the link, so I don’t know whether this is the correct interpretation.