Identical triplets Al, Bob and Chuck buy three identical bush planes. Since they live in Alaska, all three brothers buy and install large balloon “tundra tires” and wheels. The wheels, planes and brothers are identical. All three planes will take off from a normal runway in exactly 100 feet and at exactly 50 mph. The brothers fly their planes to an air show in Wisconsin. At the air show Bob finds and buys a set of fantastic wheels. These wheels are exactly like the wheels he has on his plane in every way except they have half the mass. Their mass is distributed in the same proportion as the wheels that he plans on replacing. Al thinks Bob is silly and is content with his old wheels. Bob thinks that Al will eventually want a set, so he buys a second set to give to Al on their birthday.

Bob finds a buyer for his old heavy wheels and installs a set of his new lightweight ones. He loads the second set into his plane so that it is balanced just as it was before. Bob’s plane now weighs exactly the same as Al’s and Chuck’s, but its wheels have half the mass.

Meanwhile, Chuck runs into a magician who sells him a set of magic wheels. These wheels are exactly like the wheels he has on his plane in every way except they have no mass. Chuck installs his magic wheels. He loads his old set into his plane so that it is balanced just as it was before. Chuck’s plane now weighs exactly the same as Al’s and Bob’s, but its wheels have no mass.

When the brothers leave the air show they request a formation take off. They line up wing tip to wing tip and apply power at exactly the same time. All three planes weigh exactly the same and must hit 50 mph to lift off. When Chuck’s plane lifts off his wheels have no mass, they also have no rotational inertia. When Al’s plane lifts off his heavy wheels are spinning at 50 mph and have considerable rotational inertia. When Bob’s plane lifts off his half-weight wheels are spinning at 50 mph and have exactly half the rotational inertia as Al’s wheels.

Where did the rotational inertia and energy in Bob’s and Al’s wheels come from?
How did the rotational inertia and energy now stored in Bob’s and Al’s wheels affect the take off distance of their planes?
We know that Al’s plane will still take off in exactly 100 feet; where will Bob’s and Chuck’s planes take off?

Extra Credit: what if the truck has an open top?

Ok the speed is as in #2, the 747 tires spin at about twice the speed.
And there is no wind to affect takeoff. Air being blown along the conveyor not counted.

The plane will go forward to takeoff speed, which is 175-185 mph

Being accurate about the takeoff speed won’t matter too much, well because:

THE 747 TIRES HAVE A SPEED RATING OF 235 MPH!

At umm, 160mph the tires are going at about 320 mph.
Lets see if they’ll fail, YES, remember what happened to concord when its tire(s) shredded?

A couple tires will shred, hits from the high speed chunks of tire whacking into other tires, about to pop too, causing a domino effect and a CATASTROPHIC FAILURE.

That’s the right answer. The solution to make it fly is to get landing gear that can take over 360 mph for a normal takeoff, (skis?). The stall speed of a 747 is about 160 mph, but the absolute minimum speed some nut could take off at…

1) The problem never mentions “a plane with wheels of angular mass ‘I’.” Which is what any physics book would do if the author wanted you to take the angular mass into account.
2) The problem is obviously set up to test beginners who are just getting their first experiences with free body diagrams. And at this level “wheel” means frictionless contact unless otherwise stated.

Thus I believe Sriracha is either trying to stir up trouble, or desperately wants attention and thinks he’s super smart by bringing up angular mass.

OR you and Sriracha are one and the same person, in which case Sriracha is indeed a successful troller.

I hate the internet so much sometimes.

This is an interesting physical point, not trolling, Tom, unless you think it’s against the point of the discussion for some people to learn something.

TLDR explanation: This effect doesn’t kick in until the wheels of the plane have mass and the treadmill is constantly accelerating at some very fast rate (not just running at the same constant speed). Therefore, you probably don’t have to worry about it.

And finally before I get into a real explanation, I’ll repeat Randall’s sentiment: *practically* the plane is going to take off (or possibly burn up). We’re operating without the constraints of practicality for the purpose of figuring out some basic principles of mechanics.

A longer explanation:
The plane’s engine provides a force pushing the plane forward. This forward force exists regardless of what the treadmill is doing. Unless the treadmill can exert an equal backwards force on the plane, the plane will move forward and take off.

If the wheels are massless and their axles are frictionless, the treadmill cannot put any force on the plane, and cannot stop the plane from taking off.

However, consider just a (initially stationary) bowling ball on a treadmill (or test it at home if you don’t trust your mental picture). If the treadmill starts running backwards, the ball will also travel backwards, starting to roll as it does so. The direction of the roll will be forwards, but not fast enough to keep the ball stationary.

Now put an frictionless axle through the ball, stand next to the treadmill, and hold the ball stationary, preventing it from rolling backwards. How do you do this? By putting a force on the ball through the axle.

Now let go. The ball remains stationary. Once the ball is spinning forward fast enough to become stationary, it can keep stationary without any additional force. If you increase the speed of the treadmill, though, the ball will start moving backwards again.

Now pretend that axle is connected to an airplane. The plane can keep ball from moving backwards just like the person standing next to the treadmill: by putting a force on it. The plane needs to run its engines to do this–only barely, though, since it doesn’t take nearly a full jet-engine worth of force to keep a bowling ball stationary on a treadmill.

Even if the treadmill is really, really fast–fast enough to really send that bowling ball shooting back–the plane just needs to apply enough force for long enough to accelerate the ball from a backwards velocity to a forwards velocity, and then to a forward velocity large enough to take off.

But if the treadmill keeps speeding up, it will accelerate the bowling ball backwards, more than the plane can keep up with using its engines. Then the plane will never take off.

Anyone who thinks that the rotational mass of the wheels is intended to be a part of this problem is grossly mistaken. Or trolling.

Once the plane left the treadmill it might remain within the quickly flowing boundary layer for a short time, until the plane’s jets moved the plane out of the layer.

We must all remember: this problem has nothing to do with reality. There are no engineering constraints.

http://www.youtube.com/watch?v=-Sn5JL9t_C4

This is absolutely, 100% proof.