The Plane problem:
Here’s where I’m having problems: One of Sharynf’s reply was “You can discount friction”. And I may be taking that out of context. Another of Sharynf’s replies was the example of using the brakes on a plane while firing the engines, and the friction of the tires on the
runway counter the
thrust, so the plane does not move. It seems there are two conflicting assumptions – discount friction or don’t.
And the original problem statement is perhaps ambiguous: Is it a non-powered belt (like a series of rollers) or a powered belt, like a gym treadmill? I think the original problem is that it’s a non-powered belt, but it says “…a rolling belt…” and “…the belt rolls exactly in sync…”. The latter implies (to me) a powered belt, like a treadmill or people mover. This makes it difficult to answer, but I don’t think it’s meant as a “trick”. [A classic “trick” question is two coins add up to 55 cents and one is not a nickel.] [Or maybe “belt rolls in sync” is a red herring and is to be interpreted otherwise.]
In order for this not to be a “trick” question, I’m going to consider friction. [If there is no friction, the tires simply do not grab, and the treadmill premise goes away. One might as well have a frictionless runway.] So, on a standard concrete
runway, brakes on, engine fires: No movement. Next, on a standard
runway, brakes off, engines fire, the plane moves, and wheels rotate in response to the friction between the
runway and the tires.
Now, the rolling belt
runway. First assume a non-powered belt. Now, brakes off and slowly fire up the engine. The plane is not anchored, so the wheel axles are not anchored, so the wheels begin to
roll along the belt. The belt is free to move, but so is the plane. The
thrust pushes the plane and the wheels
roll along the belt, and the belt does not move. Presumably, the plane develops enough speed to
take off. [I can’t convince myself about whether air resistance will cause some loss of thrust and hold the plane to some degree, allowing the belt to slip.] Thinking another way: set the brakes and fire up the engine, and the plane moves by causing the belt to
roll.
Now if the powered belt is assumed (“…the belt rolls exactly in sync…”), how does the plane respond? (Never mind how the sensors work, assume they work.) If the plane starts to
roll forward because of the friction between the tires and the belt, then the belt, by design, compensates and the plane does not move, by design. Or, consider this: put the plane on the powered belt, put on the plane’s brakes, and turn on the belt (on
manual at a constant speed). The plane moves back. Turn on the plane’s engines and plane’s backward progress is slowed, until it finally overcomes the belt speed and moves forward.
Switch the belt speed into “automatic” and the plane eventually becomes motionless.
[Am I missing something else in the premise? The whole concept sounds like some government pork barrel project….]
Joe